从直觉开始：Cp 量宽度、Cpk 量居中

00 — 入门 · 不含公式

从直觉开始

拖动滑块,看会发生什么。第 01 章之后全部内容,都是把这里用眼睛能看到的东西精确算出来的公式。示例:一个 Ø20.0 +0.2/0 mm 的孔,所以公差从 20.000 到 20.200 mm。

可交互改变居中位置和散布,看指数怎么变

1. C_p 量的是宽度。C_pk 量的是它待在哪。

蓝色带是公差:它永远不动,是图纸定死的。钟形曲线是你的过程。红色的是废品。

The machine is good, the setting is not. C_p is high (the process fits inside the tolerance with room to spare) but C_pk is low because it is off-centre. This is fixed by moving the mean, not by buying a new machine.

过程居中位置 20.178 mm 过程散布(s) 0.009 mm

C_p · 宽度3.70

C_pk · 位置0.81

超差零件7,254 ppm · 1 bad part in every 138

可交互改变样本量,对比单值和均值

2. 控制限不是规格限

这是头号误解。公差管的是每一件零件。控制限管的是样本均值,而样本均值的波动小得多。改变样本量,看橙色钟形曲线怎么收窄。

With n = 10, the control limits sit 3.16 times closer to the centre than the spread of individual parts. A sample average that falls outside the orange limits can correspond to parts that are all within tolerance: the chart warns before scrap is produced. That is what prevention means.

每样本件数(n) 10 parts

宽度 ±u·σ±0.0660

宽度 ±u·σ/√n±0.0209

图纸用的是 ±3σ 限。手册给出同一个例子的另一种常见参数化:单值用 ±2.58σ,样本量为 5 时变成 ±1.15σ。常数变了,道理没变:永远要除以 √n。§ 10.3.3.2

3. 四个总被搞混的概念

误解

"过程受控,所以零件是好的"

受控只意味着过程是可预测的:只有随机变异在起作用。它对零件是否符合图纸只字未提。一个过程可以完全稳定,同时 100% 的零件都超差。

正确的看法:稳定性和能力是两个独立的问题。手册因此采用四象限矩阵:第 III 象限就是"稳定但没能力"。§ 10.4

误解

"我把公差限画到操作工的控制图上"

操作工一旦在图上看到规格限,就不会再对控制限作出反应,而是等着公差逼近。也就是说,他不再做 SPC 了。

正确的看法:线边的那张图(控制回路 1)上从不画规格限。与公差的关联放在回路 2 和回路 3,用来决定围堵措施。§ 10.3.1

误解

"那个值离公差十万八千里,是离群值:我把它删了"

数值离得远,并不使它成为离群值。离群值是指不属于所研究这个过程的值:测量错误、同一零件测了两次、调机测量。

正确的看法:要去论证这个值为什么不可能来自该过程。而且它不是被删掉:是标记为无效、排除在计算之外,并追查原因。§ 7.6

误解

"有一个点出界了:我去调机器"

在确认这个数据点是否可靠之前就调整,会把变异注入到一个本来可能没有任何变异的过程中。这就是过度调整,只会让过程更糟。

正确的看法:失控行动计划(OCAP)规定的顺序是:重测或再取一个样本 —— 再查过程参数 —— 再查过程要素,最后用一个新样本验证有效性。§ 10.2.3

4. 检验自己

八个真实的车间场景。选一个答案,就会看到为什么是这样。

正确 7 of 8 · 8 of 8 answered

Situation 1 of 8

You have had 30 consecutive samples with no point outside the control limits. Production tells you that 3 % of parts are being rejected at final inspection. Is that possible?

Correct. Control limits come from the process itself, not from the drawing. A process can be perfectly predictable and still be centred on a value that does not conform, or simply be too wide. This is quadrant III of the matrix: stable but not capable. The fix is not tighter control, it is a better process. § 10.4 · four-quadrant matrix

Situation 2 of 8

You are designing the control chart the operator will see at the machine. Do you draw the tolerance limits on it?

Correct. If the operator sees the tolerance, they will stop reacting to the control limits and wait until the drawing limit is close. As a rule in this guide (see § 10.3.1): the chart at the line carries only control limits; the tolerance is handled in loops 2 and 3, to decide containment. § 10.3.1 · p. 74

Situation 3 of 8

You have measured 125 parts from a series process and calculated the indices, but nobody has assessed stability with a chart. What are the indices called in your report?

Correct. The arithmetic is exactly the same, but the letter changes what you may claim. C is used only when stability is demonstrated. If it has not been investigated, cannot be investigated, or the process is out of control, it is P. P_m/P_mk is reserved for machine studies. § 7.2 · Table 7-1

Situation 4 of 8

On an x̄/s chart, which of the two plots do you review first?

Correct. The control limit of the averages chart is calculated from σ̂, which comes from the variation chart. If the variation is out of control, the limits on the averages chart are not valid, and assessing it first leads you to false conclusions. First s, correct it, then x̄. § 10.3.3.2 · p. 81

Situation 5 of 8

A value appears in your data that is clearly outside the tolerance. Is it an outlier?

Not that one. How large a value is does not make it an outlier. An outlier is one that does not belong to the population under study: a measurement error, a part measured twice, a setup measurement. And outlier tests only check the fit to a distribution model, so at most they give an indication. It is also not deleted: it is flagged as invalid and the cause is investigated. § 7.6 · p. 36

Situation 6 of 8

You calculate C_wk = 1.85 and P_pk = 0.95 on the same data. What is that difference telling you?

Correct. C_wk uses only the within-subgroup variation, that is, what the machine does at a single instant. P_pk uses the total variation, which includes what moves between subgroups. A large difference means the process jumps from one sample to the next: batch changes, wear, shifts. And note: C_wk is diagnostic, it is not reported. § 7.8.2.5 · p. 43

Situation 7 of 8

How is sample size handled in a final process study?

Correct. The final edition allows adjusted targets with 75 ≤ N < 125 and uses the base target from N = 125. The typical strategy in § 9.2 is 25 subgroups of 5 parts, but it must not be presented as an absolute minimum. Temporal representativeness and the sufficiency of the chart are reviewed separately. § 9.2 and § 9.5 · p. 57, 65–66

Situation 8 of 8

A supplier sends you a report that says only "C_pk = 1.45". What do you ask for before accepting it?

Correct. Without the .G or .Z suffix you do not know which method produced it, and under non-normal distributions the two do not agree. Without proof of stability it cannot be called C. Without the distribution model you do not know whether 1.45 means anything. And without n you cannot judge the confidence interval: a C_pk of 1.45 from 30 parts can have a lower bound below 1.00. ch. 12 · report elements 15–19

7 of 8. Good going.

The basics are there. Review the clauses flagged below and try the calculator in section 06 with your own data.

To review:

Situation 5 — § 7.6 · p. 36

00 从直觉开始：Cp 量的是宽度，Cpk 量的是它待在哪