测量能力指数 Cg 计算器

Measurement Capability Index Cg

Compute Cg = (USL − LSL)/(6·s) from specification limits and measurement process standard deviation; Cg ≥ 1.33 is generally required.

📐 计算公式
测量能力指数 Cg(本页代码口径):Cg=(USL−LSL)÷(6×s)(公差带宽度÷6 倍测量标准差);联动量:公差带宽度=USL−LSL;6σ 占公差比=6s÷(USL−LSL||1)(带宽为 0 时分母按 1 兜底)。校验:三项输入空值/非法值即提示并中止。判据:代码无分支,deep-dive 口径 Cg≥1.33 表示测量系统可接受(6σ 测量散布落入公差带且有余量)。

输入上/下规格限与测量标准差 s,求 Cg。

Formula & Standard References

Item Formula / Note Source / Standard
Measurement capability index Cg = tolerance / (K · sigma_m), commonly with K = 6 ISO 22514-7:2012, Statistical methods in process management - Capability of measurement processes
Twenty percent rule Measurement variation should generally not exceed 20% of the tolerance AIAG, Measurement Systems Analysis (MSA) Reference Manual, 4th ed. (2010)
Acceptance criterion Cg ≥ 1.33 is commonly required to accept the measurement process ISO 22514-7:2012, Statistical methods in process management - Capability of measurement processes
Relation to capability indices Formally parallels the process capability index Cp, applied to the measurement process ISO 22514-7:2012, Statistical methods in process management - Capability of measurement processes
📌 计算说明
  • Cg≥1.33 通常表示测量系统合格。
  • (10−0)/(6×1) → 1.667。

📚 深度解析:测量系统能力 Cg

💡 常见使用场景

公式
Cg = (USL-LSL)/(6*sigma_measure)(或 0.2*(USL-LSL) 约束式)。例:公差 0.1、sigma_m=0.008,Cg=0.1/(6*0.008)=2.08。
USL=8,LSL=2,s=0.25
Cg=(8−2)/(6×0.25)=4.000,远高于 1.33 的门槛,说明量具分辨能力对这条公差带绰绰有余。

❓ 常见问题(FAQ)

判据?
Cg≥1.33 通常可接受。
与 Cpk?
Cg 看测量系统自身,Cpk 看过程。