What does Process Capability Formula Sheet · LSS.WIKI explain?

A tiered reference sheet for Cp, Cpk, Pp, Ppk, sigma estimators, DPMO, Cpm, and the rest of the process-capability toolkit.

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Continue through the related NEWMETH topic pages or open the corresponding workspace tool.

FH01 · REFERENCE SHEET

流程能力公式总表 Process Capability Formula Sheet

把 Cp／Cpk、Pp／Ppk、σ 估计、DPMO、Cpm 与非正态能力放在同一张速查表中。自上而下重要度递减：先背 T1，再熟练 T2，最后按需查 T3。 One working sheet for Cp/Cpk, Pp/Ppk, sigma estimators, DPMO, Cpm, and non-normal capability. Importance drops as you move down: memorize T1, work fluently with T2, and pull T3 when the job calls for it.

覆盖范围Coverage

T1 → T3

核心能力工具链core capability stack

必背 · 报告能力前必须会Memorize · Know These Before Reporting Capability

6 张核心卡6 core cards

T1-1

Cp 潜在能力Potential Capability

PC06 深潜 →PC06 deep dive →

Cp = (USL − LSL) / 6σ̂_within

读作：规格的门有多宽，除以过程的钟有多胖。Read it as: How wide the spec door is, divided by how fat the process bell is.

USL / LSL规格上限／规格下限upper and lower specification limits
σ̂_within组内标准差估计estimated within-subgroup standard deviationCpk 配组内 σ。Pair Cpk with within-subgroup σ.

何时用：Use it when: 双侧规格、只问“过程瘦不瘦”、不看居中。You have two-sided specs and need the spread-only potential, independent of centering.

⚠ ✗ 把高 Cp 当成过程已经合格 → ✓ 同时检查 Cpk，确认均值没有偏向规格限。✗ Treat a high Cp as proof that the process is capable → ✓ Check Cpk as well to verify the mean is not crowding a spec limit.

T1-2

Cpk 实际能力Actual Capability

PC07 深潜 →PC07 deep dive →

Cpk = min[(USL − μ)/3σ̂_within, (μ − LSL)/3σ̂_within]

读作：均值到最近规格限的距离够不够三个 σ——取更差的一侧。Read it as: How many three-sigma widths fit between the mean and the nearest spec limit—use the worse side.

min[(USL − μ)/3σ̂_within距上限几个3σThree-sigma widths to the upper limit , (μ − LSL)/3σ̂_within]距下限几个3σ，取更差侧Three-sigma widths to the lower limit; take the worse side

μ过程均值process mean
min取靠近规格限一侧的能力the capability on the side nearest a spec limit

何时用：Use it when: 既看胖瘦又看偏心，正式报告过程能力时用它。You need the reportable capability index that includes both spread and off-center drift.

⚠ ✗ 用 Cpk 报告却拿 σ_overall 计算 → ✓ Cpk 配组内 σ，Ppk 配整体 σ。✗ Report Cpk while calculating with σ_overall → ✓ Pair Cpk with within-subgroup σ and Ppk with overall σ.

T1-3

σ̂_within 组内估计Within-Subgroup Sigma Estimate

PC15 深潜 →PC15 deep dive → PC17 常数 →PC17 constants →

σ̂_within = R̄/d₂ | s̄/c₄

读作：子组内的极差（或标准差）平均后除以查表常数，估出短期波动。Read it as: Average the within-subgroup ranges (or standard deviations), then divide by the table constant to estimate short-term variation.

R̄子组极差均值average subgroup range
d₂, c₄与子组大小 n 有关的常数constants determined by subgroup size n

何时用：Use it when: 有合理子组，需要估计短期波动。Rational subgroups are available and you need short-term variation.

⚠ ✗ 不看子组大小就套 d₂ 或 c₄ → ✓ 按 n 查对应常数后再估计 σ̂_within。✗ Drop in d₂ or c₄ without checking subgroup size → ✓ Select the constant for n before estimating σ̂_within.

T1-4

Pp／Ppk 长期能力Long-Term Performance

PC08 深潜 →PC08 deep dive → PC09 深潜 →PC09 deep dive →

Pp = (USL − LSL)/6σ_overall
Ppk = min[(USL − μ)/3σ_overall, (μ − LSL)/3σ_overall]

读作：和 Cp/Cpk 同一副骨架，只是把 σ 换成包含漂移的整体 σ。Read it as: Same framework as Cp/Cpk, but replace sigma with overall sigma so drift is included.

σ_overall全体数据的整体标准差overall standard deviation across all observationsPpk 配整体 σ。Pair Ppk with overall σ.
Pp / Ppk长期潜力／长期实际表现long-term potential and actual performance

何时用：Use it when: 从客户视角评价包含漂移与批次差异的长期表现。You need the customer's long-horizon view, including drift and batch-to-batch movement.

⚠ ✗ 把 Ppk 当成 Cpk 的同义词 → ✓ 先确认使用的是整体 σ 还是组内 σ，再给指数命名。✗ Use Ppk and Cpk as interchangeable labels → ✓ Identify whether sigma is overall or within-subgroup before naming the index.

T1-5

σ_overall 整体标准差Overall Standard Deviation

PC16 深潜 →PC16 deep dive →

σ_overall = √[Σ(x_i − x̄)² / (n − 1)]

读作：所有数据对总均值的偏差平方平均后开根——经典样本标准差。Read it as: Take the square root of the average squared distance from every observation to the overall mean—the classic sample standard deviation.

n总样本量total sample size
x̄全体观测值均值mean of all observations

何时用：Use it when: 把所有数据合在一起计算长期波动。All observations must be pooled into one long-term variation estimate.

⚠ ✗ 分母用 n 计算样本标准差 → ✓ 样本估计使用 n − 1。✗ Divide by n for a sample standard deviation → ✓ Use n − 1 for the sample estimate.

T1-6

Cp 与 Cpk 的关系Cp–Cpk Relationship

PC19 深潜 →PC19 deep dive →

Cpk = Cp(1 − k)
k = |μ − M| / [(USL − LSL)/2]

读作：潜力打个折，折扣率就是偏心程度 k。Read it as: Discount the potential capability; the discount rate is the off-center ratio k.

M规格中心specification midpoint
k偏移系数，范围 0–1off-center ratio, from 0 to 1

何时用：Use it when: 判断能力差在偏心，还是差在波动太大。You need to separate the centering penalty from an inherently wide process spread.

⚠ ✗ 看到 Cpk 低就直接投资降波动 → ✓ 先比较 Cp 与 Cpk，差距大时优先重新居中。✗ Buy variation reduction as soon as Cpk looks low → ✓ Compare Cp with Cpk first; a large gap points to recentering.

常用 · 从能力指数走向不良率 Working Set · From Capability Indices to Defect Rates

7 张常用卡 7 working cards

T2-7

Z 分数（单侧距离） Z Scores for Each Spec Side

PC11 深潜 → PC11 deep dive →

Z_USL = (USL − μ)/σ ; Z_LSL = (μ − LSL)/σ

Z_USL 均值到上限的标准差个数 standard deviations from the mean to USL
Z_LSL 均值到下限的标准差个数 standard deviations from the mean to LSL

何时用： Use it when: 分别量化过程均值到每一侧规格限的距离。 You need the tail distance to each specification limit separately.

T2-8

双侧不良率 Two-Sided Defect Rate

PC18 深潜 → PC18 deep dive →

P_defect = Φ(−Z_LSL) + [1 − Φ(Z_USL)]
ppm = P_defect × 10⁶

Φ 标准正态累积分布函数 standard normal cumulative distribution function
ppm 每百万件不良数 defects per million units 上下两侧超规格尾部合并。Combine both out-of-spec tails.

何时用： Use it when: 把上下两侧超规格尾部合并为总不良率。 You need the combined out-of-spec probability from both tails.

T2-9

Z_bench 合成基准 Combined Z Benchmark

PC12 深潜 → PC12 deep dive →

Z_bench = Φ⁻¹(1 − P_total)

P_total 双侧总不良率 total two-sided defect probability
Φ⁻¹ 标准正态分布的反函数 inverse standard normal distribution

何时用： Use it when: 把双侧总不良率压缩成一个可比较的 Z 基准。 You need one comparable Z benchmark from a two-sided total defect rate.

T2-10

DPMO 与西格玛水平 DPMO and Sigma Level

PC14 深潜 → PC14 deep dive → F27 深潜 → F27 deep dive →

DPMO = D / (U × O) × 10⁶
Z_lt = Z_st − 1.5

DPMO 每百万机会缺陷数 defects per million opportunities
D / U / O 缺陷数／单位数／每单位机会数 defects / units / opportunities per unit
1.5σ 短期到长期的偏移约定 the conventional short-term to long-term shift 按 1.5σ 偏移约定换算长期西格玛水平。Use the 1.5σ shift convention for the long-term sigma level.

何时用： Use it when: 单位含多个缺陷机会，并需按 1.5σ 偏移约定换算长期西格玛水平。 Each unit has multiple defect opportunities and the 1.5σ shift convention is part of the reporting system.

T2-11

Cpk ↔ ppm 速查 Cpk-to-ppm Lookup

PC20 深潜 → PC20 deep dive →

1.00 → 2700 · 1.33 → 63 · 1.67 → 0.57 · 2.00 → 0.002 ppm

约定Assumption 双侧、居中、无偏移约定 two-sided, centered, with no shift convention
ppm 两侧合计每百万件不良数 combined two-tail defects per million units 双侧、居中、无偏移约定。Two-sided, centered, with no shift convention.

何时用： Use it when: 在明确假设下快速把居中的 Cpk 映射为 ppm。 You need a quick centered-process ppm estimate under the stated assumptions.

T2-12

Cpm 田口指数 Taguchi Capability Index

PC10 深潜 → PC10 deep dive → F26 深潜 → F26 deep dive →

Cpm = (USL − LSL) / [6·√(σ² + (μ − T)²)]

σ²波动项 σ²Variation term σ² (μ − T)²偏靶惩罚 (μ−T)²Off-target penalty (μ−T)²

T 目标值 target value
μ − T 偏离目标造成的损失项 off-target penalty term

何时用： Use it when: 偏离目标本身会带来损失，而不仅仅关心是否越过规格限。 Missing the target carries a loss even while output remains inside the spec limits.

T2-12b

DPU／FTY／RTY DPU, FTY, and RTY

F28 深潜 → F28 deep dive →

DPU = D/U ; FTY = e^(−DPU) ; RTY = ∏FTY_i

DPU 单位缺陷数 defects per unit
D / U 缺陷数／单位数 defect count / unit count
RTY 多工序首次通过率连乘，揭示“隐藏工厂” rolled throughput yield across steps, exposing the hidden factory

何时用： Use it when: 分析多工序首次通过率，以及返工掩盖的真实损失。 You need the true multi-step yield that rework and final inspection can hide.

进阶 · 特殊规格与非正态场景Advanced · Special Specs and Non-Normal Data

4 张进阶卡4 advanced cards

T3-13

单边规格One-Sided Specifications

PC05 深潜 →PC05 deep dive →

Cpu = (USL − μ)/3σ ; Cpl = (μ − LSL)/3σ
Cpk = Cpu | Cpl

Cpu只有上限时的单侧能力upper-side capability when only USL exists
Cpl只有下限时的单侧能力lower-side capability when only LSL exists

何时用：Use it when: 只有一个真实规格限，此时 Cpk 就等于对应的单侧值。Only one specification limit is physically meaningful; Cpk is that single-side value.

T3-14

非正态 Percentile 法Non-Normal Percentile Method

PC21 深潜 →PC21 deep dive →F29 深潜 →F29 deep dive →

Pp = (USL − LSL) / (P_99.865 − P_0.135)

P_99.865经验或拟合的 99.865% 分位数empirical or fitted 99.865th percentile
P_0.135经验或拟合的 0.135% 分位数empirical or fitted 0.135th percentile

何时用：Use it when: 数据明显非正态，需要用经验或拟合分位数定义过程宽度。The distribution is materially non-normal and process width must come from empirical or fitted percentiles.

T3-15

离散数据等价 CpkEquivalent Cpk for Discrete Data

PC22 深潜 →PC22 deep dive →

P% → Z = Φ⁻¹(1 − P) → Cpk_eq = Z/3

P观测到的不良率observed defect proportion
Z/3换算后的等价能力指数converted equivalent capability index

何时用：Use it when: 输入只有合格／不合格等离散结果，需要换算为等价 Cpk。The output is pass/fail or otherwise discrete and must be expressed as an equivalent Cpk.

T3-16

全家桶关系图Capability Index Relationship Map

F25 深潜 →F25 deep dive →

Cp ≥ Cpk ; Pp ≥ Ppk
Δ_μ = Cp − Cpk ; Δ_σ = Cp − Pp

Cp / Cpk组内短期能力short-term, within-subgroup capability
Pp / Ppk整体长期表现long-term, overall performance

何时用：Use it when: 快速诊断差距来自偏心，还是短期与长期波动不同。You need a fast read on whether the gap comes from centering or from short- versus long-term variation.