与时间相关的分布模型 A1–D（ISO 22514-2）

08 — 分类 · § 9.4 · ISO 22514-2

与时间相关的分布模型

按位置和变异是恒定、随机变化、系统性变化还是两者兼有,共八个模型。给过程指定模型不涉及能力的任何判断:它不引用公差。只有 A1 和 A2 处于统计受控。

A1

In control

Location: Constant
Variation: Constant
Instantaneous: Normal
Resulting: Normal

Measured length of a part in a process in statistical control.

A2

In control

Location: Constant
Variation: Constant
Instantaneous: Non-normal, unimodal
Resulting: Non-normal, unimodal

Surface roughness: physically bounded characteristic.

B

Not in control

Location: Constant
Variation: Systematic or random
Instantaneous: Normal
Resulting: Non-normal, unimodal

Uneven spindle wear in a multi-spindle automatic with identical centering.

C1

Not in control

Location: Random (normal)
Variation: Constant
Instantaneous: Normal
Resulting: Normal

Different centering of clamping fixtures.

C2

Not in control

Location: Random (non-normal, unimodal)
Variation: Constant
Instantaneous: Normal
Resulting: Non-normal, unimodal

Fixed tools.

C3

Not in control

Location: Function-oriented
Variation: Constant
Instantaneous: Any shape
Resulting: Any shape

Wear trend, with cycle.

C4

Not in control

Location: Systematic and random
Variation: Constant
Instantaneous: Any shape
Resulting: Any shape

Tool changes or batch changes.

D

Not in control

Location: Systematic and random
Variation: Systematic and random
Instantaneous: Any shape
Resulting: Any shape

Multi-stream processes.

对控制计划的实务后果

按模型给出的选图、样本量和频次示例。表 10-2 · § 10.4。

Table 10-2 · § 10.4. Concrete numbers are calculated with chapter 10 methods; the four groups can be read as four risk levels.
Model	Analysis chart	SPC chart	Sample size	Frequency	Rationale
A1	Shewhart	Shewhart	Smaller	Lower	Near-stable process, normal.
A2	Pearson	Pearson	Smaller	Lower	Near-stable, non-normal.
B	Pearson	Shewhart	Larger	Lower	Non-constant variation: difficult to readjust; compensated with larger sample.
C	Extended Shewhart	Acceptance	Smaller	Higher	Constant variation and variable position: easily corrected on machine, not in moulds.
D	Extended Shewhart	Acceptance	Larger	Higher	Neither position nor variation constant: larger sample and higher frequency.

看选图指引 →

可交互改变子组划分策略,观察后果

实验:一张图上看四个型腔

车间里的实际过程:想象一副四腔注塑模或冲压模。每一次冲压或机器循环同时产出 4 件零件(每个型腔一件:1、2、3、4)。它们共享同一个机器循环(同样的压力、温度和材料批次),短期随机波动也相近。但由于工装的几何差异、磨损或冷却不均,每个型腔有各自的均值中心:型腔之间存在系统性偏移。

合理子组的核心一课:两种情况下物理过程和产出的零件完全相同,产出的总散布(s_total 和 P_pk)也不变。随抽样策略剧烈变化的,是每一份变异在哪里显现出来:是被吸收进子组内部(子组内变异),还是被子组之间显现出来(子组间变异)。

与 § 9.4 模型的对应关系:这个过程对应 C4 模型(各流之间位置系统性变化,短期变异恒定)。糟糕的子组划分 —— 比如把型腔混进同一个子组 —— 并不能把过程变成稳定的 A1 模型;它只是把型腔偏移稀释进 σ̂_组内,从而在 x̄ 图上制造出稳定的假象,把特殊原因藏起来而不是暴露出来。

Batch #42

subgroups of 4 cavities from the same shot (24 subgroups, n = 4) 零件完全相同;变的只是子组的划分方式(N = 96,24 次冲压 × 4 个型腔)。

按策略分组的 x̄ 图

N = 96 parts (24 shots × 4 cavities) · Batch #42

按策略分组的 s 图

σ̂ 组内0.0157

总体 s0.0145

C_wk(诊断用)1.20

P_pk(总体)1.30

Stratification by mixing in the same shot (false illusion of control). Each subgroup contains all 4 cavities from the same machine cycle: the systematic offset between cavities is trapped inside each subgroup and artificially inflates σ̂ within. Because every subgroup carries the exact same compensated mix of cavities, subgroup means x̄ barely fluctuate and the chart yields no out-of-control C1 signals: it appears in control, but this is an artifact of sampling. With σ̂ within artificially inflated by mixing cavity offsets within subgroups, C_wk can approach or even fall below P_pk, and the chart completely conceals between-cavity differences.

Control-chart signal diagnosis: C1 (outside ±3σ limits / s limits): 0 · Sequence patterns (C2–C5): 0.

C1 signals are independent of display order and comparable across strategies. Sequence patterns (C2–C5) depend on sampling order and must not be interpreted as an intrinsic subgroup quality metric.