Verification of Discipline: Stratification and the Trap of the Charts
不安定さは、誰のせいか
工程が乱れたとき、人はまず「誰が悪いのか」と問います。
しかし統計は、その問いにすぐには答えません。
それが示すのは、責任ではなく挙動です。
今回の章では、Machineという仮説が検証されます。
経験や声量ではなく、管理図と層別という手法によって。
安定しているのか。
それとも構造が揺らいでいるのか。
その違いは、感覚ではなく、規律ある観察によってのみ明らかになります。
桜子は疑いを拡張しているのではありません。
仮説を順番に潰しているのです。
4Mは犯人探しの道具ではありません。
因果を整理するための枠組みです。
そして次に残るのは、Materialsです。
Returning from the “Ohno Circle,” Sakurako headed straight for the Maintenance Department. To verify the Machine branch of her diagram, she had to confront its gatekeeper: Manager Tamura.
Tamura looked up from a desk cluttered with grease-stained manuals and metal dust. His voice rumbled like a heavy engine.
“Maintenance? We follow procedure to the last bolt. Check the logs yourself.”
He dropped a thick binder onto the desk.
“The powder metallurgy data is within specification. Preventive inspections are all green. You’re chasing the wrong variable. The customer tolerances are tight—that’s the reality. The floor is barely keeping the line running under those conditions. We endure and push through.”
Tamura’s defense was not structured around analysis, but around authority—years of experience arranged like a wall.
As Sakurako turned to leave, Nishino, a young technician, approached quietly.
“Sakurako-san… I ran a comparison test,” he whispered, glancing around.
“I moved the dies to our newest high-precision press and ran a controlled batch. Same result. Dimensions scattered widely, and the tool edges chipped almost immediately. Even when we improved the Machine factor, the output behavior didn’t stabilize. That suggests the source lies elsewhere… but we’re not encouraged to pursue that line.”
Back in her apartment, Sakurako opened her laptop and reconstructed the recent production data.
First, she calculated the subgroup means and ranges, then plotted an X̄–R Control Chart.
Several points breached the Upper Control Limit. More concerning, seven consecutive points trended upward before the breach. The pattern could not be explained as random fluctuation.
(How would Dr. Deming interpret this?) she wondered.
Deming warned against confusing Common Cause Variation—the inherent noise of a stable system—with statistical signals that indicate instability. What she was observing were signs that the process was not in statistical control.
Before discussing capability, stability had to be addressed.
She performed Stratification, breaking the production data down by manufacturing date, shift, and Material Lot.
Within certain lots, subgroup variation remained relatively consistent. When the lot changed, new control violations appeared. The variation pattern shifted.
This was not yet a statement about performance.
It was a statement about instability.
Next, she constructed a Scatter Diagram.
Vertical axis: Dimensional Variance.
Horizontal axis: Time Elapsed Since Container Opening.
The slope was unmistakable.
Even within the same lot, dimensional dispersion increased as exposure time increased.
According to the mill certificates, every shipment had passed inspection. Grain size distribution and density were documented as compliant and within tolerance.
The certificates described conformity at the point of shipment.
They did not describe behavior after exposure.
Somewhere between certification and production, the material was changing.
Sakurako leaned back in her chair and opened her original Fishbone Diagram.
Man had been examined.
Machine had been statistically separated.
Neither branch fully explained the instability.
Her pen moved to the next spine of the diagram.
Materials.
If variation intensified with lot transitions, and if dispersion increased after container opening, then the hypothesis was no longer centered on human error or mechanical drift.
It was material response under environmental conditions.
She reviewed the incoming inspection protocol.
Chemical composition: within specification.
Grain size distribution: verified.
Density: confirmed.
Certificates: approved.
Yet none of these documents defined storage conditions after release.
Specification ensured conformity.
It did not guarantee stability.
Beneath “Materials,” Sakurako wrote a single line:
Post-release transformation?
The next phase of analysis would not focus on operators or machines.
It would examine storage, handling, and environmental interaction.
The 4M investigation had not concluded.
It had advanced.
Reading Comprehension Questions
Verification of Discipline: Stratification and the Trap of the Charts
⸻
Question 1
What was the main purpose of Sakurako’s X̄–R Control Chart?
(A) To calculate financial losses
(B) To determine whether the process was statistically stable
(C) To verify customer specifications
(D) To compare maintenance performance
⸻
Question 2
What did Nishino’s comparison test reveal?
(A) Machine precision solved the instability
(B) Operator error was the dominant factor
(C) Changing the Machine factor did not stabilize the output
(D) The dies were improperly installed
⸻
Question 3
Why did Sakurako avoid discussing process capability (Cpk) at this stage?
(A) She lacked supplier data
(B) The maintenance records were incomplete
(C) Capability requires a stable process
(D) The customer tolerances were unknown
⸻
Question 4
What relationship did the Scatter Diagram suggest?
(A) No correlation between variables
(B) A positive relationship between exposure time and dimensional variance
(C) A negative relationship between machine speed and defects
(D) A direct link between shift and customer complaints
⸻
Question 5
Why does Sakurako move her analysis to the “Materials” branch of the 4M framework?
(A) The warehouse staff admitted an error
(B) The machines were proven defective
(C) Evidence indicated instability linked to material behavior
(D) Management ordered a new investigation
証明ではなく、分離
この章で示されたのは「犯人」ではありません。
Machineは切り分けられました。
しかしそれは免罪でも断罪でもありません。
管理図は叫びません。
ただ境界を示します。
安定していない工程に能力指数は語れません。
感情が強いほど、順序は守られなければなりません。
層別は疑いを増やすためではなく、
仮説を削るためにあります。
Man。
Machine。
そして残るのは Materials。
証明はまだ終わっていません。
しかし分析は前進しています。
問題は派手な不正かもしれませんし、
単なる環境応答かもしれません。
いずれにせよ、答えは構造の中にあります。
