Manufacturing Is Knowledge Work Too

Executive Summary

Manufacturing ramp-up is one of the clearest periods in which a production system is still discovering how to perform reliably. Operators are learning, engineering is refining the method, quality losses are being understood, and the system is gradually absorbing disturbances that initially require active problem solving.

Factories already have strong instruments for performance. Learning curves show how cycle time or cost changes with accumulated experience. OEE, yield, throughput, scrap, and standard-hours measures show how effectively the process is operating. What they do not directly provide is a normalized way to interpret the remaining shortfall as a possible knowledge-discovery burden.

KEDE approaches that problem from the opposite direction. It begins with a latent information-theoretic quantity, Knowledge To Be Discovered:

KTD = H (X | Y),

where $X$ represents the success-relevant response class and $Y$ represents the disturbance information already available to the regulator. The quantity is latent because a factory manager normally cannot observe the production system's internal probability distribution over possible responses.

The operational KEDE model therefore uses an observable execution ledger. For a measurement window $I$ , let $S_{net} (I)$ be the number of units that survive the declared acceptance and invalidation rules, and let $N (I)$ be the capacity admitted by the declared unit convention. The operational KEDE ratio is

{KEDE}_{op} (I) = \frac{S_{net} (I)}{N (I)} .

Under the manufacturing convention developed in this article, that is algebraically a familiar production-efficiency ratio. This should be stated plainly. The arithmetic is not new.

The contribution is elsewhere. It consists of four parts: an independently specified denominator, a derivation connecting the operational ratio to a latent conditional-entropy estimand, an explicit accounting model specifying what enters the numerator and denominator, and a validity envelope stating when the knowledge interpretation should be weakened or rejected.

The denominator is the critical manufacturing advantage. A capacity-conversion ratio is only as defensible as its reference capacity. Negotiated targets can be gamed. Historical averages encode previous limitations. Best-observed periods move whenever a new best is achieved. None provides an independent calibration for interpreting the learning process.

Manufacturing may be unusually well suited to solving that problem because industrial engineering already provides method-specific time standards through predetermined motion-time and related engineering systems. For a declared method with synthetic standard time $t_{std}$ and admissible operating time $T_{adm} (I)$ , capacity can be fixed as

N (I) = \frac{T_{adm} (I)}{t_{std}} .

The central thesis of this article is therefore simple:

manufacturing can fix the denominator before observing the learning curve.

That is not the same as claiming that a predetermined motion-time system automatically measures Shannon information. The information-theoretic interpretation still depends on a calibration bridge. The derivation separates the remaining difference between the operational estimate and latent KTD into a calibration error and the sub-one-bit source-coding gap. The operational ratio is exact as an accounting quantity; its interpretation as latent entropy is conditional on that bridge.

This error structure also narrows the useful operating region. The source-coding gap is additive, so its relative importance grows as residual KTD approaches zero. Near a mature production ceiling, small differences in latent discovery burden become difficult to resolve. During ramp-up, where the residual burden should be materially larger, the same coding resolution can be more informative.

The proposal is therefore deliberately scoped to high-KTD conditions: new-product launch, production transfer, retooling, major engineering change, line qualification, and other transitions in which the production system is still absorbing substantial new knowledge. It is not proposed as another permanent steady-state dashboard metric.

That scope comes with strict validity conditions. The task class, method, response-equivalence convention, acceptance rules, unit convention, and system boundary must be declared and controlled. Changes in product difficulty or disturbance mix must not be mistaken for learning. Capacity outside the declared regulatory problem must not be silently charged as discovery. And the observation window must contain enough comparable units to produce a stable signal.

Finally, this article does not claim that the manufacturing interpretation has already been empirically demonstrated. Section 7 specifies a falsifiable ramp-up protocol instead. The denominator, boundary, acceptance rules, windowing, and failure criteria are fixed before the KEDE trajectory is examined. The test is then whether the resulting series behaves in a way consistent with a declining knowledge-discovery burden and whether it contributes anything beyond conventional ramp-up measurements.

If it does not, the interpretation should fail the test. If it does, manufacturing would provide something uncommon in attempts to measure knowledge: a knowledge-oriented metric whose reference point was fixed before the learning it is intended to measure was observed.

1. The Ramp-Up Problem

A mature production line is difficult to run well. A ramp-up is harder for a different reason: the production system is still discovering how to run.

During a new product introduction, production transfer, major engineering change, retooling, or crew transition, many of the relationships that will later appear routine are not yet settled. Operators are still learning the work. Engineering is still refining the method. Quality criteria may be stable on paper while the practical means of meeting them are still being discovered. Cycle times move. Yields move. Rework changes. Bottlenecks migrate. Problems appear that were not visible during process design.

This is not merely a period of poor performance before the factory reaches its target. It is a period in which the production system is repeatedly encountering disturbances and discovering which responses allow it to produce acceptable output reliably.

The difficulty for management is that most familiar production measures describe the result of this process without directly separating the learning component from the rest of the performance change.

A conventional learning curve can show that unit time or unit cost is falling as cumulative production increases. That is useful. It tells us that experience and performance are related. But it is normally retrospective: after enough units have been produced, a curve can be fitted to the observed history. The curve shows that the system became faster or cheaper; by itself it does not tell us how much of the remaining performance gap corresponds to unresolved discovery.

Operational measures such as Overall Equipment Effectiveness are useful for a different purpose. They help managers understand how effectively available production time is being converted into good output through losses associated with availability, performance, and quality. That makes them indispensable for running a production system. But they were not designed to answer a different question: how much of the remaining shortfall during ramp-up should be interpreted as a still-unresolved knowledge burden?

In practice, managers therefore combine several signals. They look at cycle time, yield, scrap, rework, downtime, output, and cumulative experience. They talk to launch engineers and supervisors. They walk the line. They use judgment to decide whether the process is genuinely converging or merely having a good week.

That judgment matters because important decisions depend on it. A launch support team cannot remain on one program forever. Temporary containment cannot remain in place indefinitely. Additional engineering attention has an opportunity cost. At some point management has to decide that the production system has learned enough to be treated as a stable operating process rather than as a continuing launch problem.

The measurement gap is therefore more specific than saying that factories need another performance metric. The question is whether the remaining gap can be expressed in a way that distinguishes between what the production system already knows how to do and what it is still having to discover during execution.

In information-theoretic language, the quantity of interest is not simply the observed cycle time or the number of defective units. It is the residual uncertainty over the response required to regulate the disturbances presented by the production task. In the KEDE framework this latent quantity is called Knowledge To Be Discovered.

The practical problem is that this internal uncertainty is not directly observable on a factory floor. We can observe attempts, accepted output, elapsed time, rework, interruptions, and other external consequences. We do not directly observe the production system's internal knowledge state.

That leaves a concrete question for a ramp-up:

Can the launch curve be given a unit that lets us estimate how much discovery burden remains, using quantities that can be declared and observed before the learning curve itself is known?

The denominator is the key. If the reference capacity is selected from the same performance history that we are trying to interpret, the reasoning becomes circular. A best observed week, a negotiated target, or a historical average can normalize performance, but none of them gives us an independent basis from which to interpret the learning process.

Manufacturing has an unusual advantage here. Industrial engineering already contains methods for specifying the time required by a declared production method independently of the subsequent ramp-up performance. That creates the possibility of fixing the denominator before observing the learning curve.

That is the possibility developed in the next section.

2. Manufacturing Already Has the Missing Denominator

Any ratio that compares actual output with possible output is only as meaningful as its denominator. This is the central calibration problem.

Suppose a production line delivers 700 accepted units during a week. To say that the line operated at 70% requires another number: 1,000 units must somehow have been declared possible during that same period. But where did that number come from?

If the denominator is negotiated between production and management, the resulting efficiency depends partly on the negotiation. If it is based on historical average performance, it embeds the limitations of the system that produced that history. If it is defined as the best period previously observed, then the reference moves whenever the system exceeds its previous best. All three approaches can be useful for operational management, but none gives the measurement required here: an independently specified reference against which the subsequent learning process can be observed.

For a knowledge-discovery interpretation, the denominator must be declared before the performance being evaluated is observed. Otherwise the same observations are being used both to define the reference and to measure departure from it.

A declared unit convention

The KEDE framework approaches this problem by first declaring the elementary unit used by the operational ledger. Let $Δ$ denote the duration assigned to one such generic action unit under the adopted convention. For an observation window of usable duration $| I |$ , the corresponding number of available action units is

N (I) = \frac{| I |}{Δ} .

The important point is not that $Δ$ is a universal physical constant. It is not. It is a declared measurement convention tied to the process being modeled. What matters is that the convention has an independent basis and is held fixed while the corresponding observations are compared.

In simple examples, such a basis can sometimes be obtained directly from physical or empirical constraints. Typing can be expressed against an empirically established inter-key interval. A repetitive manual assembly operation can be expressed against an independently specified duration for the required action. These examples illustrate the kind of calibration object the framework needs: a duration associated with a declared action convention that does not have to be inferred from the learning curve being measured.

Industrial engineering already does this

Manufacturing is unusually well equipped for this requirement because industrial engineering has spent decades developing predetermined motion-time systems such as MTM, MOST, and Work-Factor.

These systems decompose a declared work method into standardized motion or activity elements and assign engineered times to those elements. The resulting synthetic standard time is not simply the average time previously achieved by the current operator or line. It is constructed from the specified method.

That distinction is crucial.

A predetermined motion-time system should not be interpreted as discovering a fundamental physical quantum of human action. The decomposition remains an engineering model, and the selected method remains part of the measurement frame. For KEDE, however, that is enough. The requirement is not a metaphysically smallest motion. It is a stable, declared, independently specified unit convention from which the available execution capacity can be calculated.

Let $t_{std}$ be the synthetic standard time required to produce one unit using the declared method, and let $T_{sched} (I)$ be the scheduled operating time admitted by the system boundary for observation window $I$ . Then the method-defined production capacity of that window is

N (I) = \frac{T_{sched} (I)}{t_{std}} .

Here, $N (I)$ is not the number of units that management hopes to produce, nor the number produced during the plant's best historical week. It is the number implied by the declared method and the scheduled operating time admitted into the measurement frame.

For example, if a method has a synthetic standard time of 36 seconds per unit and the declared observation window contains 25,200 seconds of scheduled operating time, then

N = \frac{25200}{36} = 700 .

The denominator is therefore fixed without asking how many units the line actually manages to produce during the observation window.

The denominator follows the method, not the observed curve

This also provides a disciplined answer to what happens when the production system itself changes.

If operators simply become better at executing the same declared method, the standard-time basis does not move with them. Their changing performance is observed against the same denominator.

If engineering changes the method itself — for example by eliminating an operation, introducing a fixture, changing the sequence, or automating part of the work — then the measurement frame has changed. Industrial engineering would normally establish a new standard for the new method. KEDE should do the same. The old and new series should not be silently joined as though the denominator had remained invariant.

This is a feature rather than a defect. A historical-best denominator tends to drift precisely when performance improves. A method-based denominator changes for a different reason: because the thing being measured has changed.

The distinction can be written schematically as

same method \to hold t_{std} fixed,

changed method \to recompute t_{std} and start a new measurement frame .

This is substantially stronger for the present purpose than choosing a denominator after the fact. A negotiated target can be renegotiated. A historical average contains the performance deficits of the past. A best-observed period changes whenever a new best is achieved. A method-specific synthetic standard, by contrast, can be declared before the ramp-up observations that will later be compared against it.

That does not prove that a predetermined motion-time standard is automatically an information- theoretic calibration of Knowledge To Be Discovered. The relationship between the engineering unit convention and the latent entropy quantity still has to be established, and its calibration error still matters. That problem is addressed later in the derivation and validity envelope.

What manufacturing provides at this stage is narrower but extremely important: an independently engineered denominator.

That may make manufacturing one of the strongest practical domains in which to test KEDE. Many forms of knowledge work have to infer their reference capacity from observed performance. A manufacturing process with a properly specified method can do something much more useful: fix the denominator before observing the learning curve.

3. Then Be Honest: The Ratio Is Familiar

Once the denominator has been fixed, the operational KEDE calculation is almost embarrassingly simple.

For an observation window $I$ , let $S_{net} (I)$ be the number of completed units that survive the declared acceptance criterion, and let $N (I)$ be the method-defined capacity of the same window. Then the operational Knowledge-Discovery Efficiency is

{KEDE}_{op} (I) = \frac{S_{net} (I)}{N (I)} .

There is nothing novel about the arithmetic.

Manufacturing has been dividing realized production by some form of expected, standard, earned, or available production for decades. Depending on the plant and the accounting convention, closely related ratios appear in measures described as production efficiency, line efficiency, standard-hours efficiency, earned-hours performance, or as components of Overall Equipment Effectiveness.

That resemblance should not be hidden. It should be made explicit.

The same arithmetic can represent different measurements

Two ratios can have the same mathematical form and still measure different things because their numerators and denominators were defined differently.

Consider the generic efficiency form

η = \frac{credited output}{reference output} .

The equation itself tells us very little until both terms have been specified. A plant may use a historical standard in the denominator. Another may use an engineered standard. Another may calculate earned hours against booked labor hours. Another may construct a performance component from ideal cycle time and actual production. All are legitimate operational conventions for their intended purposes, but they are not automatically the same measurement.

Under the manufacturing convention proposed here, the denominator has a specific meaning:

N (I) = \frac{T_{sched} (I)}{t_{std}},

where $t_{std}$ is the independently specified standard time of the declared method and $T_{sched} (I)$ is the operating time admitted by the declared system boundary.

The numerator is equally specific. It is not simply everything that came off the line. It is accepted output:

S_{net} (I) = units that survive the declared acceptance criterion .

A completed unit that is subsequently invalidated by the accounting rules cannot quietly retain the same credit as an accepted unit. The operational ledger therefore distinguishes between attempting or completing work and producing a unit that remains valid under the declared criterion.

Relationship to OEE

The closest familiar comparison is often Overall Equipment Effectiveness. In its conventional decomposition, OEE combines availability, performance, and quality:

OEE = A \times P \times Q .

If performance is calculated against a declared standard cycle time and quality gives credit only to good output, then part of the resulting arithmetic can resemble $S_{net} / N$ very closely.

But the measurements should not therefore be treated as interchangeable. OEE deliberately includes availability as one of its major loss categories. The KEDE manufacturing convention developed here handles time exclusions through the declared system boundary. Capacity lost to an event outside the regulatory problem being measured is removed from the admissible window rather than automatically interpreted through the KEDE ratio. The boundary rules are developed explicitly in Section 6.

The difference is therefore not that one formula contains multiplication and another contains division. After algebraic simplification, familiar manufacturing measures can collapse to very similar ratios. The difference lies in what was allowed into the numerator, what was allowed into the denominator, and why.

Relationship to standard-hours and earned-hours efficiency

The same point applies to standard-hours accounting. If a plant credits an accepted unit with a fixed quantity of standard work, then multiplying accepted production by standard time gives earned standard time:

T_{earned} (I) = S_{net} (I) t_{std} .

Dividing that earned time by the scheduled time admitted to the KEDE frame gives

\frac{T_{earned} (I)}{T_{sched} (I)} = \frac{S_{net} (I) t_{std}}{T_{sched} (I)} = \frac{S_{net} (I)}{N (I)} .

Under these matching conventions, the familiar manufacturing efficiency ratio and operational KEDE are algebraically identical.

That is not an embarrassment for the argument. It is an important constraint on what can legitimately be claimed.

The arithmetic is not the contribution

KEDE does not become a new measurement merely because a familiar ratio is given a new name. If the argument ended at $S_{net} / N$ , a manufacturing manager would be right to ask why another metric was needed.

The proposed contribution begins somewhere else.

First, the denominator is constrained to an independently declared, method-specific engineering basis rather than being inferred from the performance history being interpreted.

Second, the accounting model specifies what counts as an accepted unit, what counts as execution capacity, and what must remain outside the measurement boundary.

Third, and most importantly, the KEDE framework proposes a theoretical bridge from this operational ratio to a different object: a latent conditional entropy representing the Knowledge To Be Discovered by the regulator.

The claim is therefore not

manufacturing has been unknowingly calculating a new efficiency metric all along.

It is instead:

under a specific numerator, denominator, boundary, and calibration convention, a familiar production-efficiency ratio may also serve as an operational estimator for a latent knowledge-discovery quantity.

Whether that additional interpretation is justified cannot be established by the ratio itself. It requires the information-theoretic derivation.

That is the next step.

4. Why the Ratio Can Carry a Knowledge Interpretation

The previous section deliberately removed any novelty from the arithmetic. Under the manufacturing convention used here, ${KEDE}_{op} = \frac{S_{net}}{N}$ is a familiar capacity-conversion ratio. The remaining question is the important one: why should that ratio carry any interpretation about knowledge?

The answer does not begin with production efficiency. It begins with the regulatory problem.

From regulation to Knowledge To Be Discovered

In Ashby's formulation, a regulator must respond to disturbances in a way that keeps goal-relevant outcomes inside an acceptable region. A production system can be read in the same way. Each production episode presents a particular configuration of conditions and disturbances, and the regulator — an operator, team, machine, control system, or some combination of them — must produce a response that results in an acceptable unit.

The relevant uncertainty is not uncertainty over every physically possible action. Different concrete actions may be equivalent if they lead to the same acceptable regulatory result. The KEDE derivation therefore defines a response-equivalence variable $X$ , whose values distinguish only response classes that matter to the adopted success criterion. Let $Y$ denote the disturbance information already available to the regulator when the episode begins.

The latent Knowledge To Be Discovered is then the residual conditional entropy

KTD := H (X | Y) .

This quantity is measured in bits. It represents how much uncertainty remains about the success-relevant response after the regulator has already used the information available at the start of the episode. If $H (X | Y) = 0$ , the required response class is already determined by the available knowledge. If it is positive, some uncertainty remains to be resolved before unit.

That is the information-theoretic object KEDE is trying to estimate. It is defined independently of production efficiency. The ratio introduced later is therefore not being declared to be knowledge by definition; it is being proposed as an observable operational estimator for this latent quantity under stated assumptions. :contentReference[oaicite:0]{index=0}

From entropy to a discovery depth

Conditional entropy is theoretically well defined but normally invisible on a factory floor. A manager does not observe the regulator's full internal probability distribution over response classes. What can be observed is the execution trace.

The bridge is supplied by source coding. For a discrete response-class variable, an optimal binary decision procedure can be represented as a prefix-free binary code: each binary question narrows the remaining candidate set, and the number of questions needed to identify the required response corresponds to the codeword length.

For an optimal binary code, the expected decision depth $\bar{q}^{*}$ obeys the familiar source-coding bracket

H (X | Y) \leq \bar{q^{*}} < H (X | Y) + 1 .

The significance of this result is practical. It lets us replace the unobservable question “what is the regulator's latent conditional entropy?” with a second question: “how much binary-equivalent narrowing was required to identify the successful response?” The two quantities are not identical, but the optimal binary-question depth lies within one bit of the corresponding entropy under the source-coding assumptions.

The KEDE derivation then introduces an operational one-bit convention: counted non-unit action units are read as one-bit-equivalent narrowing steps. This does not mean that every physical movement literally contains one bit of Shannon information. It is a calibration convention connecting the observed execution ledger to the ideal binary-question depth. The quality of that bridge matters and will be treated explicitly in the next section. :contentReference[oaicite:1]{index=1}

From discovery depth to the observable ledger

Now consider a window $I$ containing many comparable production episodes. The operational ledger partitions the available execution capacity into unit units and non-unit action units.

Let $N (I)$ be the total capacity admitted by the declared unit convention, and let $S_{net} (I)$ be the number of units that survive the acceptance and invalidation rules.

Each surviving episode contributes one unit unit. The remaining capacity is therefore the effective non-unit depth:

Q_{eff} (I) = N (I) - S_{net} (I) .

Dividing that effective non-unit count by the number of surviving units gives the observed average one-bit-equivalent depth per accepted unit:

{\hat{KTD}}_{eff}^{1bit,net} (I) = \frac{N (I) - S_{net} (I)}{S_{net} (I)} .

Hence

{\hat{KTD}}_{eff}^{1bit,net} (I) = \frac{N (I)}{S_{net} (I)} - 1 .

This equation is exact as an operational accounting ratio. It can be computed without observing the regulator's internal probability model. But that exact accounting statement must be kept separate from the stronger information-theoretic claim. The operational quantity becomes interpretable as an estimator of latent Knowledge To Be Discovered only through the calibration bridge between counted non-unit units and ideal binary discriminations. :contentReference[oaicite:2]{index=2}

From an unbounded burden to a bounded efficiency

Knowledge To Be Discovered is naturally unbounded above. For management comparison, KEDE applies a monotone bounded transform:

{KEDE}_{op} (I) = \frac{1}{1 + {\hat{KTD}}_{eff}^{1bit,net} (I)} .

Substituting the operational estimator gives

{KEDE}_{op} (I) = \frac{1}{1 + (\frac{N (I)}{S_{net} (I)} - 1)} = \frac{S_{net} (I)}{N (I)} .

We have therefore arrived back at the familiar ratio from Section 3, but by a very different route.

The arithmetic alone says:

What fraction of the declared execution capacity became accepted units?

The KEDE derivation adds a conditional interpretation:

Under the declared one-bit calibration and source-coding assumptions, how much one-bit-equivalent discovery depth was required, on average, per accepted unit?

In plant language, the reading is approximately: for each good part, how much of the declared method capacity was consumed resolving what the production system did not already know well enough to close directly?

The word approximately matters. The operational ratio is observed. The conditional entropy is latent. The derivation supplies a bridge between them, not an unconditional identity. The remaining gap has two components: calibration error in treating counted action units as binary-equivalent discriminations, and the source-coding gap between optimal binary-question depth and entropy.

Those errors are not a footnote. They determine where the knowledge interpretation has useful resolution.

That is the subject of the next section.

5. Why the Measurement Resolution Favors Ramp-Up

The operational KEDE ratio can be calculated at any stage of production. That does not mean its knowledge interpretation has equal resolving power everywhere. The distinction matters most near the mature end of a learning curve.

The reason follows from the error structure connecting the observable operational estimator to the latent Knowledge To Be Discovered. The derivation separates two different gaps: a calibration error associated with the measurement convention, and a source-coding gap associated with representing entropy by an optimal binary-question depth.

Let ${\hat{KTD}}_{eff}^{1bit,net} (I)$ denote the operational effective-depth estimator introduced in the previous section, and let ${KTD}_{avg}^{start-real,net} (I)$ denote the corresponding latent realized average starting Knowledge To Be Discovered. The operational-to-latent relation is

{\hat{KTD}}_{eff}^{1bit,net} (I) - {KTD}_{avg}^{start-real,net} (I) = ε_{cal} (I) + δ (I),

with

0 \leq δ (I) < 1 .

The two terms should not be conflated. $ε_{cal}$ is an operational calibration error: it captures mismatch between the counted execution units and the ideal binary-discrimination depth that the information-theoretic model requires. $δ$ is different. It is the ordinary source-coding gap between entropy and optimal binary-question depth. The theorem bounds the second term; it does not, by itself, supply a useful empirical bound on the first.

The coding gap matters more as the residual becomes small

First consider the source-coding term by itself and suppose, temporarily, that the calibration error has been made negligible:

ε_{cal} (I) \approx 0 .

Then

{KTD}_{avg}^{start-real,net} (I) = {\hat{KTD}}_{eff}^{1bit,net} (I) - δ (I) .

Because the coding gap is additive rather than proportional, its relative importance increases as the quantity being estimated approaches zero.

Consider a mature line with an operational KEDE of $0.95$ . The corresponding operational KTD estimate is

\hat{KTD} = \frac{1}{0.95} - 1 \approx 0.053 bits per accepted unit .

With negligible calibration error, non-negativity of latent KTD together with the coding bracket means that the latent quantity can lie anywhere between zero and approximately $0.053$ bits per accepted unit. The estimator therefore tells us that the remaining discovery burden is small, but it has little power to resolve how small. In relative terms, the unresolved interval is as large as the quantity being estimated.

Now consider an early ramp-up with an operational KEDE of $0.35$ . The operational KTD estimate becomes

\hat{KTD} = \frac{1}{0.35} - 1 \approx 1.86 bits per accepted unit .

Again assuming negligible calibration error, the source-coding bracket places the corresponding latent quantity in the interval

0.86 < {KTD}_{avg}^{start-real,net} \leq 1.86 .

That is still an interval, not a precise recovery of the latent entropy. But it is qualitatively more informative. Unlike the mature-line example, the coding gap alone cannot make the latent burden indistinguishable from zero. A substantial residual discovery burden remains compatible with the observation across the entire coding interval.

This is the sense in which measurement resolution favors ramp-up. The theorem does not say that a mature-line KEDE value is invalid. The operational ratio remains perfectly computable. It says that the entropy interpretation loses relative discriminating power as the residual Knowledge To Be Discovered becomes small.

Calibration error is a separate problem

The previous comparison deliberately held $ε_{cal}$ near zero. That assumption cannot simply be granted.

The source-coding theorem supplies the bound $0 \leq δ < 1$ . It does not supply an equivalent universal bound on $ε_{cal}$ . If the operational units are poorly related to the binary-equivalent selection depth assumed by the derivation, then even a large operational KTD value can be a poor quantitative estimator of the latent entropy.

This is why the denominator problem in Section 2 is not an administrative detail. The manufacturing opportunity is that predetermined motion-time systems provide a disciplined, method-specific, independently declared basis for the execution ledger. They give us a candidate mechanism for controlling and, ultimately, empirically testing $ε_{cal}$ .

That claim must be kept correctly sized. A PMTS standard does not, merely by existing, prove that its motion-time decomposition is equivalent to an ideal sequence of one-bit discriminations. What it does provide is something the framework otherwise lacks: an independently engineered and reproducible unit basis that can be fixed before the learning observations are seen.

The relationship can therefore be summarized as follows:

Predetermined motion-time calibration disciplines the operational side of the bridge; the source-coding theorem bounds the coding side of the bridge.

The first addresses the calibration error $ε_{cal}$ as an empirical and engineering problem. The second gives the irreducible sub-one-bit coding gap $δ$ under the model assumptions.

A launch instrument, not a permanent dashboard

This gives KEDE a natural operating region. It should be most informative where the residual discovery burden is expected to be material: new-product launch, line qualification, production transfer, major engineering change, retooling, a materially new crew or shift, and other conditions in which a production system must absorb significant new knowledge before stable regulation is achieved.

As the process converges and operational KEDE approaches one, the ratio does not suddenly become wrong. Rather, increasingly small differences in latent KTD sit inside an additive measurement envelope whose relative size is becoming larger.

At that point, the appropriate management response is not to squeeze ever finer conclusions from the same instrument. It is to recognize that the launch question has largely been answered and return to the steady-state measures designed for mature production.

In that sense, saturation is useful information. KEDE is not proposed here as another permanent number on the factory dashboard. It is proposed as a high-KTD instrument whose strongest use is during periods when a production system is still visibly discovering how to regulate its work.

That interpretation is only defensible if the measurement frame itself is controlled. The next section translates those conditions into plant language.

6. The Validity Envelope, in Plant Language

The equations in the previous sections are easy to calculate. The harder question is whether the resulting number still carries the interpretation we have assigned to it.

That depends on the measurement frame. A KEDE value should not be interpreted in isolation from the task being repeated, the method used to define capacity, the criterion for accepting a unit, the disturbances presented to the production system, and the boundary deciding which losses belong to the regulatory problem.

In plant language, the rule is simple: do not interpret a KEDE series unless the following conditions have been declared and controlled.

1. Keep the learning problem comparable

KEDE is intended to observe learning across repeated regulatory episodes. The knowledge state is therefore supposed to change. If operators, automation, work instructions, or organizational routines retain what was discovered in earlier episodes, the starting Knowledge To Be Discovered in later episodes should fall.

What must remain sufficiently stable is not the knowledge state but the comparability frame.

In the formal KEDE model, a comparable task class fixes, or provides explicit correspondences for, the disturbance information $Y$ , the required response-equivalence variable $X$ , the response-equivalence abstraction, and the modeling resolution at which Knowledge To Be Discovered is evaluated.

Translated to a manufacturing ramp-up, comparison windows should therefore refer to sufficiently similar production problems: the same part or declared part family, the same production method, the same acceptance criterion, the same relevant response distinctions, and a sufficiently similar operating context.

This does not require every episode to be identical. If it did, there would be little regulatory problem to learn. It requires the episodes to remain instances of the same declared learning problem.

A major engineering change, process redesign, tooling change, acceptance-rule change, or substitution of a materially different production system should therefore not be treated as another ordinary point on the same KEDE curve. It is a candidate frame break.

The practical test is:

Are we still asking the production system to solve the same kind of regulatory problem, or have we changed the problem itself?

If the latter is true, start a new frame.

2. Keep the response-equivalence convention stable

Comparability also applies to what counts as the required response. KEDE does not measure uncertainty over every microscopic difference in physical execution. Its latent quantity is defined over response-equivalence classes: distinctions between responses that matter to the adopted regulatory criterion.

In manufacturing terms, two methods of completing an action may be treated as equivalent if the model deliberately regards them as interchangeable for the success criterion being studied. If engineering later decides that a distinction previously ignored now matters, the response variable has changed.

For example, suppose two fastening sequences were initially accepted as equivalent because both produced conforming assemblies. If a later reliability finding makes only one sequence acceptable, the response classification has changed. The resulting KEDE values should not be compared as though $X$ had remained fixed.

This is another frame break, not evidence that the previous line suddenly forgot something.

3. Compare windows exposed to a sufficiently comparable disturbance regime

A launch does not present exactly the same difficulties in every shift or every week. One window may contain easy variants, another difficult variants. One may experience a cluster of tolerance problems, another none. A high-mix operation may schedule very different product combinations in adjacent periods.

That matters because $H (X | Y)$ depends not only on what the regulator knows but also on the regulatory problems it encounters. A harder disturbance mix can raise the observed burden even if no knowledge has been lost.

For comparison across windows, the analyst should therefore ask whether the disturbance regime is sufficiently representative of the same declared task class. Product mix, option mix, defect opportunities, supplier characteristics, environmental conditions, and other difficulty drivers should either remain reasonably comparable or be explicitly stratified.

This is a practical comparability requirement, not a claim that finite-window KEDE mathematically requires a stationary and ergodic stochastic process. The operational estimator

{KEDE}_{op} (I) = \frac{S_{net} (I)}{N (I)}

is a finite-window count ratio and can be computed without stationarity or ergodicity. Those stronger assumptions become relevant only if the analyst wants to interpret a long trajectory as estimating an underlying stochastic entropy rate.

For the ramp-up use proposed here, the simpler discipline is enough: do not attribute a change to learning when the difficulty distribution changed at the same time.

4. Freeze the unit convention before looking at the result

The denominator must remain independent of the curve it is being used to interpret.

Before the measurement period begins, declare the method, its standard-time basis $t_{std}$ , the admissible operating-time rule, and therefore

N (I) = \frac{T_{adm} (I)}{t_{std}},

where $T_{adm}$ is the portion of the observation window admitted by the declared system boundary.

Do not change the standard because the first KEDE values look implausibly low. Do not replace it with the best observed week after the launch begins. Do not modify the exclusion rules to make the curve smoother.

If the production method genuinely changes, establish a new method basis and start a new measurement frame. The point of the convention is not that $N$ can never change. It is that it must not change merely because the observed performance changed.

5. Declare the system boundary before deciding which losses to exclude

This is probably the most important practical safeguard.

Not every minute in which a line fails to produce a good part should automatically be interpreted as unresolved knowledge. Whether a loss belongs inside the KEDE measurement depends on the regulatory problem that has been declared.

Suppose a workstation is the regulator under study. If material never reaches it because an upstream conveyor has failed, the resulting starvation may lie outside that workstation's regulatory problem.

Now enlarge the black box to the entire production line. The same conveyor failure may be a disturbance that the line-level production system is expected to regulate.

Enlarge the boundary again to the factory, and supplier availability, maintenance coordination, or internal logistics may move inside the problem as well.

Therefore the correct rule is not:

Exclude every loss that does not look like learning.

That would allow the analyst to explain away the result after observing it. The rule is:

Declare the regulatory boundary first. Exclude capacity associated with events outside that declared problem.

For a narrowly defined line-level ramp-up, typical exclusions might include demand shortfall, planned shutdown outside launch operation, material unavailability declared external to the line, upstream starvation, or downstream blocking. Those are examples, not universal rules. If the line is explicitly responsible for regulating one of those conditions, it belongs inside the frame instead.

The denominator is therefore better written as admissible rather than simply calendar or scheduled time:

T_{adm} (I) = T_{sched} (I) - T_{outside} (I) .

The exclusions represented by $T_{outside}$ must be declared from the system boundary, not reverse-engineered from undesirable KEDE values.

6. Keep discovery work, unit, and feedback time conceptually separate

The full KEDE execution-channel model distinguishes three kinds of capacity.

A non-unit action unit $Q$ represents execution associated with narrowing or discriminating among possible responses. A unit unit $S$ represents the final commitment that closes an episode. A fedback unit $F$ represents capacity that goes into neither discrimination nor commitment: physical unfolding, feedback latency, waiting, automatic cycle, or idle observation.

Conceptually,

execution trace \to {Q, S, F} .

This separation matters on a production line. Automatic machine cycle after a response has already been committed is not necessarily additional discovery. Waiting for a process result is not automatically another discrimination. Neither should silently acquire a one-bit knowledge charge simply because time passed.

There is, however, an important black-box qualification. Under the strict observational form of KEDE, the analyst does not directly observe the hidden internal sequence of $Q$ actions. The primitive observations can be restricted to unit events, their timestamps, and later invalidations. The unit convention and execution-channel model are what provide the bridge from that external trace to an effective non-unit depth.

For manufacturing, this means that $Q$ , $S$ , and $F$ should be kept conceptually separate even when the available plant data do not permit all three to be observed directly. The analyst should not pretend that every unexplained second has been observed as a knowledge- seeking action.

7. Count surviving units, not merely completions

A unit can be recorded when produced and later invalidated. The operational ledger therefore distinguishes gross units from units that survive the relevant evaluation criterion.

Let $S_{gross} (I)$ be the gross units recorded in the window and $W_{obs} (I)$ be the observed invalidation load. Then

S_{net} (I) = S_{gross} (I) - W_{obs} (I) .

In plant terms, the acceptance rule must specify what happens to scrap, rework, provisional acceptance, later inspection failures, and any other event capable of invalidating an earlier unit.

The rule must also specify the attribution convention when invalidation occurs after the window in which the original unit was recorded. Whatever rule is chosen, it should be declared before comparison begins and applied consistently.

An important conceptual distinction follows. An operational invalidation is an accounting event. It is not automatically a bit-valued knowledge loss. A failed unit can still teach the production system something that is retained in later episodes; an accepted unit can produce no retained learning at all. The operational ledger records what survived. The latent knowledge model concerns what the regulator carries forward.

8. Use windows large enough to estimate a pattern, not a story about one episode

The operational estimator is defined only when there are surviving units to divide by. In particular,

S_{net} (I) > 0

is a basic mathematical requirement. The operational ledger also requires the declared capacity to be capable of containing the recorded gross units:

N (I) \geq S_{gross} (I) .

Those conditions make the estimator mathematically defined. They do not make a tiny sample managerially trustworthy.

A window containing five accepted units can produce a KEDE number, but one additional scrap event can move that number dramatically. A window containing hundreds of comparable units will usually provide a more stable estimate of the underlying pattern.

There is no universal minimum number of units supplied by the KEDE derivation. The appropriate window depends on event frequency, product mix, serial dependence, and the natural variance of the production process. Therefore a fixed rule such as “always use 30 units” would create false precision.

A practical starting rule is instead: choose the shortest window that contains enough comparable accepted units for the KEDE series to be stable against one or two individual outcomes, while remaining short enough to reveal changes during the ramp.

The falsifiable protocol in the next section should test that choice explicitly by recalculating the series at more than one reasonable window size. If the apparent learning pattern disappears whenever the window boundary moves slightly, the signal is not yet strong enough to support the proposed interpretation.

The validity checklist

Before interpreting a manufacturing KEDE series, the analyst should therefore be able to answer yes to the following questions:

Are the compared episodes members of the same declared learning problem?
Has the success-relevant response-equivalence convention remained stable?
Are the compared windows exposed to a sufficiently comparable disturbance regime, or has the mix been stratified?
Was the method basis and unit convention fixed before the resulting KEDE curve was observed?
Was the regulatory system boundary declared before exclusions were applied?
Have discovery work, unit, feedback or waiting, and external exclusions been kept conceptually separate rather than collapsed indiscriminately into elapsed time?
Is accepted output based on a declared surviving-unit and invalidation rule?
Does the observation window contain enough comparable units to support a stable signal?

If one of these conditions fails, the correct response is not to repair the curve after the fact. It is to mark the affected window as a frame break, revise the measurement design, or weaken the knowledge interpretation.

This validity envelope is deliberately restrictive. KEDE is not intended to turn every production loss into a statement about ignorance. It is intended to make a narrower proposition testable: when the regulatory problem, unit convention, boundary, and unit rules are fixed in advance, does the resulting operational series behave as an observable proxy for a declining knowledge-discovery burden during ramp-up?

That question can now be tested rather than asserted.

7. A Falsifiable Ramp-Up Protocol

The argument so far is theoretical and operational. It has defined a latent quantity, an observable estimator, an independently specified denominator, and a set of validity conditions under which the resulting series may carry a knowledge interpretation. That is not yet evidence that the interpretation is useful on a real ramp-up.

The next step is therefore not to present an illustrative success story. It is to specify a measurement protocol that could support the claim, weaken it, or falsify it.

The protocol should be designed so that the measurement rules are fixed before the KEDE curve is observed. Otherwise the central claim of this article — that manufacturing can fix the denominator before observing the learning curve — has not actually been tested.

7.1 Select a genuine ramp-up

The candidate process should be one in which substantial learning is expected rather than inferred after the fact. Suitable cases include new-product introduction, production transfer, line qualification, major retooling, a substantial engineering change, or another controlled transition in which the production system must learn a materially new task.

The process should also produce enough repeated units to support windowed comparison. A one-off engineering build may involve substantial discovery, but it does not provide the repeated episodes needed to observe a ramp-up trajectory.

Before data collection begins, declare the task class being measured. At minimum, record:

the product or declared product family,
the production method,
the acceptance criterion,
the crew or crew-definition rule,
the system boundary,
the relevant disturbance regime, and
the response distinctions that are treated as success-relevant.

These declarations form the comparison frame. If one of them changes materially during the study, the change should be recorded as a potential frame break rather than silently absorbed into the same learning curve.

7.2 Freeze the denominator before observing the ramp

The most important pre-registration step is the denominator. For the declared method, obtain an independently engineered standard time

t_{std}

from an accepted predetermined motion-time or equivalent industrial-engineering method. The basis of that standard should be documented before the resulting KEDE series is calculated.

For each observation window $I_{t}$ , calculate admissible operating time according to the boundary rules declared in Section 6:

T_{adm} (I_{t}) = T_{sched} (I_{t}) - T_{outside} (I_{t}) .

The corresponding capacity is

N (I_{t}) = \frac{T_{adm} (I_{t})}{t_{std}} .

The rule is strict: do not revise $t_{std}$ because the first weeks perform badly, and do not replace it later with the best observed cycle time. If the method itself changes, establish a new standard and begin a new measurement frame.

This is the first test of the article's thesis. If the denominator cannot be declared independently of the observed ramp-up, the proposed manufacturing advantage has failed operationally.

7.3 Declare the observation windows and acceptance rules

Choose the window rule before inspecting the resulting KEDE trajectory. Weekly windows may be appropriate for many launches, but the correct duration depends on throughput, product mix, and the frequency of accepted units.

For each window, record at least:

scheduled time $T_{sched}$ ,
excluded time $T_{outside}$ ,
admissible time $T_{adm}$ ,
gross units $S_{gross}$ ,
observed invalidations $W_{obs}$ ,
and net surviving units $S_{net}$ .

The net unit count is

S_{net} (I_{t}) = S_{gross} (I_{t}) - W_{obs} (I_{t}) .

The invalidation rule must be fixed in advance. If a part produced in one window can fail inspection in a later window, the attribution rule for that invalidation must also be declared before analysis.

7.4 Calculate the operational series

For every valid observation window, calculate the operational Knowledge To Be Discovered estimate:

{\hat{KTD}}_{eff}^{1bit,net} (I_{t}) = \frac{N (I_{t})}{S_{net} (I_{t})} - 1,

and the corresponding operational KEDE:

{KEDE}_{op} (I_{t}) = \frac{S_{net} (I_{t})}{N (I_{t})} .

The basic analysis table should therefore have the following form:

Window	Scheduled time	Excluded time	Admissible time	Standard time / unit	N	S_gross	W_obs	S_net	Operational KTD	Operational KEDE
I₁	…	…	…	…	…	…	…	…	…	…
I₂	…	…	…	…	…	…	…	…	…	…
…	…	…	…	…	…	…	…	…	…	…

No smoothing rule should be chosen after seeing which version produces the most attractive curve. If smoothing is used, its rule should be declared in advance and the unsmoothed series should remain available.

7.5 Plot KEDE beside the conventional learning curve

The KEDE series should not be inspected alone. The point of the experiment is to compare it with the conventional measures already used to judge the ramp.

At minimum, plot operational KEDE against time and plot the conventional learning variable — for example cycle time or labor time per unit — over the same observation period.

If a Wright-style learning curve is also fitted, preserve the distinction between its independent variable and the KEDE windows. A conventional learning curve is commonly expressed against cumulative production:

T (x) = a x^{b},

where $x$ is cumulative output, while KEDE is computed over finite calendar or production windows $I_{t}$ . The two should therefore be aligned on a common time axis for comparison rather than treated as if they were mathematically the same type of series.

The first empirical question is deliberately modest:

As the ramp proceeds through comparable episodes, does ${KEDE}_{op}$ show systematic convergence toward the declared method-capacity ceiling?

Equivalently, does

{\hat{KTD}}_{eff}^{1bit,net} (I_{t})

tend to decline as retained learning accumulates?

The hypothesis does not require monotonic improvement in every window. Real ramp-ups contain noise, temporary regressions, new disturbances, and local forgetting. The claim is about a detectable convergence pattern within a stable frame, not a perfectly smooth line.

7.6 Predeclare what would count against the hypothesis

A protocol is not falsifiable merely because data are collected. It becomes falsifiable when observations that would count against the proposed interpretation are specified before the results are known.

At least three failure tests should therefore be applied.

Test A: Denominator independence

The standard time, boundary rule, exclusion rule, acceptance rule, and window rule must all be declared before the KEDE trajectory is inspected.

If the analysis requires repeatedly changing the denominator or exclusions after seeing the curve in order to produce a plausible learning pattern, the core manufacturing-calibration claim has failed for that case.

Test B: Convergence under comparable learning

Where independent evidence indicates that the production system is retaining substantial learning across comparable episodes, operational KTD should show a corresponding tendency to fall, or KEDE a tendency to rise.

If no such pattern appears across adequately sized and valid windows, that is evidence against the claim that the operational series is tracking the declining discovery burden in that ramp.

The result should not be rescued automatically by labeling every contradiction a frame break. Frame breaks must be identified using the rules declared before the KEDE result is interpreted.

Test C: Incremental management value

The operational KEDE arithmetic is familiar. Therefore reproducing a conventional efficiency curve is not, by itself, evidence that the knowledge interpretation adds practical value.

The protocol should ask whether KEDE changes the interpretation of the ramp in a way that is useful for a real management decision.

Examples include:

a divergence between improving cycle time and stagnant KEDE that triggers investigation,
a frame break that becomes visible only after denominator and unit rules are made explicit,
or a saturation pattern that gives a principled reason to stop treating small late-stage differences as meaningful changes in latent KTD.

If KEDE persistently reproduces a conventional production-efficiency measure without yielding a different interpretation, a new discrepancy signal, or a different management decision, then the practical manufacturing contribution has not been demonstrated even if the underlying derivation remains mathematically coherent.

7.7 Treat frame breaks as observations, not inconvenient data

A useful ramp-up dataset should contain at least one event capable of testing the validity rules: a crew substitution, engineering change, tooling modification, supplier-material change, altered acceptance rule, or another material shift in the measurement frame.

The protocol should ask whether the checklist from Section 6 identifies that event independently of the resulting KEDE movement.

If a method change occurs at time $t_{f}$ , the correct representation is not necessarily a continuous series:

{KEDE}_{frame A} : I_{1}, \dots, I_{f}

{KEDE}_{frame B} : I_{f + 1}, \dots

with a new method basis where required. The discontinuity is information about the experiment, not a defect to be smoothed away.

7.8 Test sensitivity to the chosen window

The conclusion should not depend entirely on one convenient aggregation choice. Recalculate the series using at least one reasonable alternative window width while preserving the same underlying measurement rules.

For example, if weekly windows are primary, compare them with two-week windows or another operationally meaningful aggregation.

The requirement is not that every numerical point remain unchanged. It is that the central interpretation — convergence, divergence, or absence of a detectable signal — should not disappear merely because the boundary of the observation window moves slightly.

If it does, the correct conclusion is that the available data do not yet support a stable knowledge-discovery reading.

7.9 Report the result even if it is disappointing

There are several legitimate outcomes.

KEDE may converge in step with conventional cycle-time improvement. In that case the knowledge interpretation may still be theoretically useful, but the empirical series has not shown additional timing information.

It may diverge from the conventional curve in specific periods and produce a useful discrepancy signal. That would be stronger evidence of incremental management value, provided the divergence survives the validity checks.

It may fail to exhibit a stable ramp pattern at all. That result should also be reported. It may indicate that the disturbance mix is too heterogeneous, that the denominator does not control the calibration error sufficiently well, that the chosen system boundary is inappropriate, or that the operational estimator simply does not track latent Knowledge To Be Discovered closely enough in the tested setting.

The protocol is successful if it lets those possibilities be distinguished without rewriting the measurement rules after seeing the answer.

What this protocol can establish

A single ramp-up study cannot prove that KEDE is a universal manufacturing knowledge metric. It can test a narrower proposition:

When a manufacturing ramp is measured against an independently specified method capacity, within a predeclared regulatory frame, does the resulting operational KEDE series behave in a way consistent with a declining knowledge-discovery burden and provide information that is useful beyond the conventional learning curve?

If the answer is no, the knowledge interpretation has failed an important manufacturing test. If the answer is yes, the result would support something more interesting than another efficiency ratio: a knowledge-oriented measurement whose denominator was fixed before the learning curve was observed.

8. The Decision It Changes

A measurement earns its place in management only if it changes a decision. For ramp-up, one of the most consequential decisions is also one of the most common: when can the launch support team be released?

Consider a line in week nine of a new-product launch. Cycle time has improved steadily for several weeks and is now close to plan. Yield has also improved. On the conventional launch dashboard, the story looks positive.

Management now has to decide whether the engineers, manufacturing specialists, and quality support assigned to the launch can move to the next program.

If the decision is made too early, the line may regress as soon as the temporary support structure disappears. If it is made too late, expensive launch resources remain tied to a process that no longer needs them.

The conventional learning curve helps, but it answers only part of the question. It tells management that the line is becoming faster. It does not, by itself, tell management whether the production system is also converging toward the independently declared method capacity under the same measurement frame.

Case A: the curves converge together

Suppose cycle time is falling while operational KEDE is rising across the same valid windows. For example:

{KEDE}_{op} : 0.42 \to 0.55 \to 0.67 \to 0.76 \to 0.82 .

The corresponding operational Knowledge To Be Discovered estimate is falling:

\hat{KTD} = \frac{1}{{KEDE}_{op}} - 1 .

In this case the two measurements tell a consistent story. The line is becoming faster, and accepted output is also converging toward the independently declared method-capacity reference.

That does not prove that all remaining problems have been solved or that KEDE has directly observed the line's internal knowledge state. It does provide a second, independently framed signal that is consistent with the hypothesis that the ramp-up burden is being absorbed.

If the validity conditions from Section 6 continue to hold, management has a stronger basis for concluding that the line is closing out as a launch problem.

The decision may therefore be: release the launch support team according to the normal exit criteria.

Case B: cycle time improves, but KEDE does not

Now consider the more interesting case. Cycle time continues to improve, but operational KEDE remains approximately flat:

{KEDE}_{op} : 0.58 \to 0.60 \to 0.59 \to 0.61 .

A cycle-time curve alone still appears encouraging. The line is faster than it was four weeks ago.

But KEDE says something different: accepted output is not moving materially closer to the declared method-capacity ceiling within the same frame.

That discrepancy is the useful signal.

KEDE does not tell management why the curves diverged. A black-box estimator cannot legitimately make that causal jump. Several explanations remain possible.

The product or option mix may have become easier.
The denominator or system boundary may have been violated.
Equipment performance may have improved while quality losses remained.
Overtime or additional staffing may be masking unresolved execution difficulty.
The disturbance regime may have changed.
The acceptance criterion may have shifted.
Or the production system may genuinely be becoming faster without reducing the operational discovery burden represented by the KEDE frame.

The metric therefore does not provide a diagnosis. It provides a reason not to accept the simple explanation offered by the cycle-time curve.

The decision rule

The management rule can now be stated explicitly:

If cycle time indicates that the ramp is closing but KEDE does not converge under the same valid measurement frame, do not release launch support until the discrepancy is understood.

The next action is investigation, not automatic escalation. The team should first test the validity conditions: Was the product mix comparable? Did the method change? Were exclusions applied consistently? Did the acceptance criterion move? Was there a crew or supplier change? Did the denominator remain fixed?

If the divergence disappears after identifying a frame break, the measurement has done something useful: it exposed that the apparent trend was being interpreted across unlike conditions.

If the frame remains valid and the divergence persists, management has stronger reason to believe that the conventional learning curve is not telling the whole story.

That is the practical contribution. The instrument does not replace engineering judgment. It tells management when judgment is still required.

Why this is different from simply watching another efficiency number

A skeptic could reasonably ask why a production manager could not reach the same conclusion by looking at standard-hours efficiency, yield, or OEE.

Sometimes they could. The falsifiable protocol in Section 7 explicitly allows that outcome. If operational KEDE always reproduces the same signal and never changes interpretation or decision, its incremental management value has not been demonstrated.

The proposed value appears when the KEDE measurement frame makes a discrepancy explicit: the denominator was independently declared, accepted units were defined in advance, the regulatory boundary was frozen, and the resulting series is being interpreted against a stated knowledge-discovery hypothesis.

The question is therefore not merely:

Is the line getting faster?

It is:

Is accepted production converging toward the independently declared method capacity in a way consistent with the ramp-up burden being absorbed?

Those two questions can produce different management responses from the same apparent cycle-time improvement.

A second decision: removing temporary containment

The same logic applies to temporary containment. During launch, a plant may add an additional inspection, verification step, or quality gate that is intentionally more conservative than the intended steady-state process.

As performance improves, pressure grows to remove it. The extra control consumes time and labor, and its continued presence may itself limit throughput.

If conventional performance improves and KEDE also shows sustained convergence under a valid frame, removing the containment becomes easier to justify alongside the normal quality evidence.

If cycle time improves but KEDE remains flat or unstable, the correct conclusion is not that the containment must remain. It is that the apparent maturity of the process is not yet unambiguous. The discrepancy should be explained before removing a protection whose purpose is to compensate for an incompletely stabilized process.

Again, KEDE does not make the decision. It changes the burden of proof.

The value is the disagreement

The most useful KEDE reading may therefore not be a high number. It may be a disagreement.

When the conventional learning curve and KEDE move together, they reinforce the same operational story. When they move differently under a valid frame, the disagreement tells management that the ramp cannot yet be summarized by speed alone.

That is enough to change a real decision.

9. Where the Instrument Fails

KEDE is useful only if its limits are stated as clearly as its promise. The operational ratio is easy to compute. The knowledge interpretation is conditional. Several failure modes can make the number misleading, weak, or simply irrelevant.

It is not a diagnostic

KEDE can indicate that a production system is converting less of its declared method capacity into accepted units than expected under the measurement frame. It cannot, by itself, tell management why.

A falling KEDE value may be associated with poor training, method instability, quality problems, tooling, coordination, changed product mix, altered disturbances, an invalid denominator, or a boundary violation. The metric does not identify the causal mechanism.

In that limited sense, KEDE behaves like a thermometer: it can indicate that something has changed without identifying the cause. The analogy should not be pushed too far, however. A thermometer has a physically established scale. KEDE depends on a declared unit convention, system boundary, acceptance rule, and method basis. Its reference frame is engineered, not given by nature.

It fails when the denominator is allowed to move with the result

The strongest claim in this article is that manufacturing can fix the denominator before observing the learning curve. If that discipline is lost, much of the argument collapses.

Revising the standard time after seeing poor KEDE values, substituting the best observed cycle time, or renegotiating the reference capacity until the curve looks reasonable destroys the independence of $N$ .

The resulting ratio may still be operationally useful, but it no longer provides the calibration claimed here.

It fails when the measurement frame changes unnoticed

A KEDE series assumes that compared windows belong to the same declared learning problem. If the method, acceptance criterion, product family, response-equivalence convention, crew definition, or disturbance regime changes materially, then the meaning of the series can change even if the formula does not.

The danger is particularly high during launch because engineering changes are common precisely when learning is being measured.

A major method change should therefore create a new frame rather than another point on the old curve. If frame breaks are hidden inside a continuous series, apparent learning or forgetting may be nothing more than comparison across different problems.

It fails when exclusions are chosen after the fact

The system boundary determines which capacity belongs inside the regulatory problem. That boundary must be declared before the result is interpreted.

If analysts remove every inconvenient downtime category by labeling it "non-knowledge loss," the metric becomes unfalsifiable. A material shortage, for example, may be outside the boundary of a workstation but inside the boundary of a factory.

The correct sequence is:

declare boundary \to derive exclusions \to calculate KEDE,

not the reverse.

It can be gamed

Like most operational measures, KEDE has obvious gaming surfaces. Three are especially important:

The acceptance criterion. Loosen what counts as an accepted unit and $S_{net}$ rises.
The method basis. Inflate the standard time and $N$ falls, mechanically improving KEDE.
The observation window. Choose only favorable periods and the apparent trajectory improves without any change in the production system.

The controls should therefore be organizational, not merely mathematical. The acceptance criterion should be owned by the appropriate quality authority. The method-time basis should be owned and versioned through industrial engineering. The window and exclusion rules should be predeclared in the measurement protocol. Changes should be auditable.

A metric whose inputs can be silently changed by the same manager being evaluated against it will eventually measure negotiation rather than learning.

It loses resolution near the mature ceiling

As shown in Section 5, the source-coding gap is additive. Its relative significance therefore increases as latent Knowledge To Be Discovered approaches zero.

When operational KEDE is already close to one, the corresponding operational KTD estimate

\hat{KTD} = \frac{1}{{KEDE}_{op}} - 1

becomes small. The remaining coding and calibration uncertainty can then become large relative to the residual quantity being interpreted.

This does not make the operational ratio invalid. It means that fine distinctions near the ceiling should not be over-interpreted as equally fine differences in latent knowledge.

For this reason, the manufacturing use proposed here is a ramp-up instrument rather than a permanent steady-state dashboard. Once the series has saturated and the launch question has been answered, conventional production metrics are better suited to managing small steady-state losses.

There is no universal retirement threshold

It may be tempting to declare that KEDE should always be retired above a fixed value such as $0.85$ or $0.90$ . The derivation does not justify such a universal threshold.

The useful stopping point depends on the calibration error, the variability of the process, window size, and the management decision being supported.

A more defensible rule is empirical: retire the instrument when additional movement in KEDE is smaller than the resolution needed for the decision at hand, or when the series no longer provides information beyond the mature-line metrics already in use.

It fails when the operational units are poor proxies for discovery depth

The operational estimator rests on a calibration bridge between counted execution units and the ideal binary-equivalent discrimination depth.

A predetermined motion-time standard gives manufacturing a disciplined and independently specified denominator. It does not automatically prove that the resulting motion-time decomposition has a small calibration error $ε_{cal}$ .

If that mapping is weak, the ratio remains a valid operational efficiency calculation but the interpretation as latent Knowledge To Be Discovered should be weakened accordingly.

This is one of the main reasons the protocol in Section 7 is necessary. The manufacturing claim is not that PMTS has already solved the entropy-calibration problem. It is that PMTS gives us an unusually strong, independently engineered basis on which that claim can be tested.

It fails when accepted output is badly defined

The numerator is not innocent either. If "good part" changes meaning across windows, then $S_{net}$ does not represent a stable unit criterion.

The same problem appears when rework and later invalidations are handled inconsistently. A unit that passes an initial station but fails final inspection cannot be treated one way in one window and another way in the next.

The unit and invalidation rules therefore need version control just as much as the method standard does.

It can confuse changed difficulty with changed learning

A production system can appear to improve because the work became easier. It can also appear to regress because the disturbance mix became harder.

If a high-mix line runs a simpler option mix this week than last week, a higher KEDE value does not automatically imply that more knowledge has been retained.

This is why disturbance comparability matters. Where mix cannot be stabilized, the analysis may need to be stratified by product family, complexity class, or another declared difficulty dimension.

Without that control, the metric risks attributing environmental change to the regulator's knowledge state.

It can become noise when the window is too small

The finite-window ratio is mathematically defined whenever $S_{net} > 0$ . That does not make every finite window statistically useful.

With very few units, one scrap event, one invalidation, or one unusually difficult episode can move the ratio sharply. A noisy sequence can then be mistaken for learning, forgetting, or a frame break.

The window should therefore be large enough for individual outcomes not to dominate the signal, and the conclusion should survive at least one reasonable alternative aggregation. If it does not, the correct conclusion is that the available data do not support a stable interpretation yet.

It does not share the learning curve's natural axis

A traditional Wright-style learning curve is usually expressed against cumulative production:

T (x) = a x^{b},

where $x$ is cumulative output.

Operational KEDE, by contrast, is computed over finite windows:

{KEDE}_{op} (I_{t}) = \frac{S_{net} (I_{t})}{N (I_{t})} .

The two series can be compared on a common time axis, but they should not be presented as though they are measurements indexed in the same way. The cumulative learning curve smooths history by construction. The KEDE window can reveal local movement, but it is also more exposed to mix, noise, and frame changes.

It does not replace the metrics already needed to run a factory

Even under ideal calibration, KEDE would not replace throughput, cost, yield, scrap, OEE, delivery performance, lead time, safety, or other operational measures.

Those metrics answer different management questions.

KEDE's proposed role is narrower: to provide a bounded operational reading that can, under a declared calibration and validity frame, be interpreted against the hypothesis of a declining knowledge-discovery burden during ramp-up.

If a conventional metric already answers the decision completely, adding KEDE creates no value. If the KEDE interpretation conflicts with the conventional story, the disagreement must survive the validity checks before it deserves management attention.

The failure conditions are part of the instrument

A useful measurement is not one that produces an answer under every condition. It is one whose user knows when the answer should not be trusted.

For KEDE, that means being willing to say: the frame changed; the denominator was not independent; the disturbance mix is not comparable; the calibration error is uncontrolled; the window is too small; the acceptance rule moved; or the metric has reached a region in which its knowledge interpretation no longer has enough resolution for the decision.

Those are not exceptions to the theory. They define the boundary of the claim.

10. Conclusion

The interesting claim is not that manufacturing is knowledge work. Factories have always learned. Operators learn methods, engineers learn process limits, maintenance teams learn failure modes, and production systems gradually absorb disturbances that once required active problem solving.

The harder problem has been measurement.

If Knowledge To Be Discovered is treated as a latent conditional entropy,

KTD = H (X | Y),

then the quantity of interest is not directly visible on the factory floor. What can be observed is execution: available capacity, units, invalidations, and the external behavior of the production system. KEDE supplies an operational bridge from that observable ledger to the latent quantity.

Under the manufacturing convention developed here,

{KEDE}_{op} (I) = \frac{S_{net} (I)}{N (I)},

and the corresponding operational Knowledge To Be Discovered estimate is

\hat{KTD} (I) = \frac{N (I)}{S_{net} (I)} - 1 .

The arithmetic is familiar. That is not the contribution.

The contribution is the attempt to place that familiar ratio inside a much stricter measurement frame: define the latent estimand first, fix the operational denominator independently of the subsequent performance curve, state the accounting rules, expose the calibration gap, and specify the conditions under which the knowledge interpretation should be weakened or rejected.

Manufacturing is particularly interesting because industrial engineering may already provide the missing piece that is difficult to obtain in other domains. Predetermined motion-time and related engineering methods can provide a method-specific time basis that is declared independently of the observed ramp-up.

In other words:

manufacturing can fix the denominator before observing the learning curve.

That does not prove that a motion-time standard is automatically a one-bit information-theoretic calibration. The calibration error remains an empirical question. Nor does the source-coding bridge give arbitrarily fine resolution near zero residual entropy. Its additive coding gap becomes proportionally more important as the discovery burden becomes small.

Those limitations determine the scope of the proposal.

KEDE is not proposed here as another permanent factory dashboard metric. Its strongest candidate use is where Knowledge To Be Discovered should be comparatively large: new-product launch, production transfer, retooling, major engineering change, line qualification, and other transitions in which a production system is visibly learning how to regulate a new task.

As the process matures, the operational ratio can still be calculated, but increasingly small differences should not be over-interpreted as equally precise differences in latent knowledge. At that point, conventional steady-state measures should again do most of the management work.

This deliberately narrow scope is a strength. A measurement framework becomes more credible when it specifies not only what its numbers mean, but also when those numbers stop being informative.

The next step is therefore empirical rather than rhetorical. The protocol in Section 7 fixes the denominator, boundary, acceptance rules, windowing, and failure conditions before the KEDE trajectory is seen. It then asks whether the resulting series behaves in a way consistent with a declining knowledge-discovery burden during a genuine manufacturing ramp-up, and whether it adds anything to the decisions already supported by conventional production measures.

The claim should be allowed to fail.

If a PMTS-based denominator cannot be fixed without reference to observed ramp performance, the calibration argument weakens. If the resulting KEDE trajectory does not converge during otherwise credible retained learning, the proposed knowledge interpretation weakens. If the series does nothing more than reproduce an existing efficiency measure and never changes an interpretation or decision, its practical manufacturing value has not been demonstrated.

Those are meaningful failure conditions. They are what make the proposal testable.

If the protocol survives those tests, however, the result would be more significant than the introduction of another efficiency ratio. It would show that an ordinary-looking production measure can be anchored to a declared information-theoretic estimand without choosing its reference point after seeing the outcome.

That is the proposition this article puts forward:

A manufacturing launch may be one of the rare places where a knowledge-discovery metric can be calibrated before the learning it is intended to measure has occurred.

Whether that proposition survives contact with a real ramp-up is the next experiment.

Manufacturing Is Knowledge Work Too

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Executive Summary

1. The Ramp-Up Problem

2. Manufacturing Already Has the Missing Denominator

A declared unit convention

Industrial engineering already does this

The denominator follows the method, not the observed curve

3. Then Be Honest: The Ratio Is Familiar

The same arithmetic can represent different measurements

Relationship to OEE

Relationship to standard-hours and earned-hours efficiency

The arithmetic is not the contribution

4. Why the Ratio Can Carry a Knowledge Interpretation

From regulation to Knowledge To Be Discovered

From entropy to a discovery depth

From discovery depth to the observable ledger

From an unbounded burden to a bounded efficiency

5. Why the Measurement Resolution Favors Ramp-Up

The coding gap matters more as the residual becomes small

Calibration error is a separate problem

A launch instrument, not a permanent dashboard

6. The Validity Envelope, in Plant Language

1. Keep the learning problem comparable

2. Keep the response-equivalence convention stable

3. Compare windows exposed to a sufficiently comparable disturbance regime

4. Freeze the unit convention before looking at the result

5. Declare the system boundary before deciding which losses to exclude

6. Keep discovery work, unit, and feedback time conceptually separate

7. Count surviving units, not merely completions

8. Use windows large enough to estimate a pattern, not a story about one episode

The validity checklist

7. A Falsifiable Ramp-Up Protocol

7.1 Select a genuine ramp-up

7.2 Freeze the denominator before observing the ramp

7.3 Declare the observation windows and acceptance rules

7.4 Calculate the operational series

7.5 Plot KEDE beside the conventional learning curve

7.6 Predeclare what would count against the hypothesis

Test A: Denominator independence

Test B: Convergence under comparable learning

Test C: Incremental management value

7.7 Treat frame breaks as observations, not inconvenient data

7.8 Test sensitivity to the chosen window

7.9 Report the result even if it is disappointing

What this protocol can establish

8. The Decision It Changes

Case A: the curves converge together

Case B: cycle time improves, but KEDE does not

The decision rule

Why this is different from simply watching another efficiency number

A second decision: removing temporary containment

The value is the disagreement

9. Where the Instrument Fails

It is not a diagnostic

It fails when the denominator is allowed to move with the result

It fails when the measurement frame changes unnoticed

It fails when exclusions are chosen after the fact

It can be gamed

It loses resolution near the mature ceiling

There is no universal retirement threshold

It fails when the operational units are poor proxies for discovery depth

It fails when accepted output is badly defined

It can confuse changed difficulty with changed learning

It can become noise when the window is too small

It does not share the learning curve's natural axis

It does not replace the metrics already needed to run a factory

The failure conditions are part of the instrument

10. Conclusion

Dimitar Bakardzhiev