Business Science EnterpriseHOME

Business Science Enterprise Platform

Success through Action

From Inspiration to Outcomes

← All webtoons

MANUFACTURING & OPERATIONS

The Silent Factory: Bayesian Diagnosis of a Short Shot

Two possible causes of a short shot. Morning certainty falters in the face of afternoon evidence.

Read webtoon ↓Read original story ↗

An injection molding factory in operation

THUD—

HISS

A short-shot case held in a gloved hand

The foreman shows a defective part

The end is still short.

Two people discuss temperature and pressure

Temperature or pressure?

Check the heater first?

The engineer asks to review the records

Before taking it apart, let's check the records.

Records of causes from the previous quarter

Last quarter: short-shot causes

Temperature 60%

Pressure 40%

A notebook compares two hypotheses

Comparison model

H_T Temperature: assumed defect rate 8%

H_P Pressure: assumed defect rate 4%

Let's compare the samples under these assumptions.

1.5 to 1

O_{0} = \frac{0.60}{0.40} = 1.5

We begin with odds of 1.5 to 1 for temperature versus pressure.

Two-hypothesis comparison · Fixed defect rates across both samples · Random, conditionally independent samples assumed

A random sample is requested

Please take 50 at random from the current run.

An inspection tray at ten in the morning

TAP

Morning sample inspection results

Morning D₁ 5 defective · 45 good

The engineer considers the evidence

Which hypothesis makes this result more likely?

Likelihood ratio of the morning evidence

{BF}_{1} = \frac{P (D_{1} | H_{T})}{P (D_{1} | H_{P})}

= {(\frac{0.08}{0.04})}^{5} \times {(\frac{0.92}{0.96})}^{45}

\approx 4.7141

5 defective45 good

This evidence is about 4.7 times as likely under the temperature hypothesis.

Morning probabilities

O_{1} = 1.5 \times 4.7141 \approx 7.0711

P (H_{T} | D_{1}) = \frac{7.0711}{1 + 7.0711}

\approx 87.6 %

Temperature at 87.6%…

Morning probabilities and instructions to stand by for maintenance

After the morning sample

Temperature 87.6%

Pressure 12.4%

Have maintenance stand by. We'll check the barrel temperature first.

A worker prepares for maintenance

Understood. We'll be ready.

The engineer feels certain of the diagnosis

So… it was temperature.

Temperature at 87.6%…

Time passes into the afternoon

Afternoon

The foreman brings another sample

We checked another 50.

Afternoon sample inspection results

Afternoon D₂ 1 defective · 49 good

The engineer is surprised by a single defective part

Just one?

Good parts are evidence too

The 49 good parts are evidence too.

Which defect rate fits this result better: 8% or 4%?

Likelihood ratio of the afternoon evidence

{BF}_{2} = \frac{P (D_{2} | H_{T})}{P (D_{2} | H_{P})}

= {(\frac{0.08}{0.04})}^{1} \times {(\frac{0.92}{0.96})}^{49}

\approx 0.24851

1 defective49 good

This evidence is about 4 times as likely under the pressure hypothesis.

After the morning and afternoon samples

We continue the calculation from the morning result.

O_{2} = 7.0711 \times 0.24851 \approx 1.75724

P (H_{T} | D_{1}, D_{2}) = \frac{1.75724}{1 + 1.75724}

\approx 63.7 %

Temperature 63.7% · Pressure 36.3%

Probabilities after the morning and afternoon samples

After both samples

Temperature 63.7%

Pressure 36.3%

The engineer reconsiders that certainty

The 49 good parts were evidence too…

Temperature is still higher, though.

Dismantling is postponed and another inspection requested

Wait. Hold off on dismantling.

Please take another 50 at random from the next lot.

The foreman agrees

Understood. I'll bring them.

A hand holds a toolbox

A notebook retains earlier results and leaves space for the next sample

Start: temperature 60% After morning: 87.6% After both samples: 63.7% Next sample:

The engineer revises the decision

I was too hasty.

Let's narrow it down with another inspection before dismantling.

The short-shot case is examined again

The factory keeps running

The engineer looks across the factory

THUD—

HISS

EXA Business Science Lab

Let the story linger through the original prose

The tension and emotion conveyed through expressions and scenes gain another depth in prose. Following the original text offers a deeper sense of the characters’ inner lives, the weight of their choices, and the emotions and narrative that connect events.

If the story stays with you, we recommend reading the original fiction as well.

The Silent Factory: Bayesian Diagnosis of a Short Shot · Read original story →

Explore the science behind the story

Read the mathematical explanation →Bayesian lab →More stories →

The Silent Factory: Bayesian Diagnosis of a Short Shot | EXA Enterprise