Gauge

Process capability

Do the readings fit the limits?

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Cp, Cpk, Pp and Ppk. Paste the readings, or a mean and a standard deviation. One limit is enough.

Cpk0.857Jump to result

Readings

Choose whether to type every measurement, or to type the average and the spread you already worked out.More detail. Raw readings also feed the histogram, the QQ plot, and the Anderson–Darling check. Summary mode does not.
One number per line. 1,5 is read as 1.5. A header row is fine.
Lower specification limit. Blank for an upper-only limit.
Upper specification limit. Blank for a lower-only limit.
Advanced

The 1.5 sigma shift is an old factory habit added on top of the score. It is not part of your measurements. Leave it off unless someone asked for that habit.

Some people add 1.5 to the sigma score, an old factory habit. It is not part of your measurements. Leave it off unless someone asked for that habit.More detail. Optional Motorola shift. The reported level becomes 3 × Cpk + 1.5, or 3 × Ppk + 1.5.

Indices

The boss, looking glum
Cpk
0.857
The lower limit sets this number. A wider upper limit does not change it. Under 1.
Ppk
0.962
Under 1
Cp
0.902
Within spread
Pp
1.013
Overall spread
More indices
Mean
11.8000
n = 10
Count
10
Readings used
Overall SD
1.3166
Divisor n − 1
Within SD
1.4775
Moving range / 1.128
Cpl
0.857
Lower side, within
Cpu
0.948
Upper side, within
Ppl
0.962
Lower side, overall
Ppu
1.063
Upper side, overall
Expected ppm, overall
2,660 ppm
Expected ppm, within
7,296 ppm
Observed ppm
0.00 ppm
0 outside the limits
Sigma level, within
2.57
3 × Cpk
Sigma level, overall
2.89
3 × Ppk

Cp = (16.0000 − 8.0000) / (6 × 1.4775) = 0.902

Cpk = 0.857, Cpl = 0.857, Cpu = 0.948. Ppk = 0.962.

Under 1, from 1 up to 1.33, or 1.33 or above. Use the specification, not only the colour.

Cpk under 1 means there is less than three standard deviations between the average and the nearer limit. That side is tight.

p = 0.5745 vs α = 0.05: no evidence against normality

Shapiro–Wilk matches JMP. Anderson–Darling matches Minitab.

Normality, histogram, and QQ plot
Shapiro–Wilk asks how straight the readings would look on a bell-curve plot. W near 1 means a good fit, like dots sitting on a ruler. A small p means the line is too bent to ignore.More detail. Royston’s 1995 algorithm (Applied Statistics AS R94), the Shapiro-Wilk W used by JMP. W is the squared correlation of the ordered sample with the normal weights. The p-value is Royston’s approximation, exact at n = 3. Valid for n from 3 to 5000.A² is a score of how badly the readings miss a bell curve. Bigger means a worse fit.More detail. Anderson–Darling A² using the sample mean and sample standard deviation. A²* is Stephens’ small-sample adjustment.
Significance levelAlpha is how surprised you need to be before you say the shape looks off. At 0.05, a p-value has to be rarer than about 1 time in 20. Like calling a coin unfair only after a run of heads that would be unusual if the coin were fair.More detail. The verdict is evidence of non-normality only when p < α. A p-value equal to alpha is not evidence against normality. Alpha must be greater than 0 and less than 0.5. The same alpha is used for Shapiro–Wilk and Anderson–Darling. It does not change W, A², or the p-value.

Shapiro–Wilk matches JMP; Anderson–Darling matches Minitab.

p = 0.5745 vs α = 0.05: no evidence against normalityShapiro–Wilk asks how straight the readings would look on a bell-curve plot. W near 1 means a good fit, like dots sitting on a ruler. A small p means the line is too bent to ignore.More detail. Royston’s 1995 algorithm (Applied Statistics AS R94), the Shapiro-Wilk W used by JMP. W is the squared correlation of the ordered sample with the normal weights. The p-value is Royston’s approximation, exact at n = 3. Valid for n from 3 to 5000.
Shapiro–Wilk W = 0.9419, p = 0.5745. A large p-value is not proof of a bell curve, especially with a short run of data.
Shapiro–Wilk W
0.9419
Shapiro–Wilk p-value
0.5745
p = 0.5745 vs α = 0.05: no evidence against normality

Showing example readings. These are not measurements.

Assumptions and references

Assumptions

  • The indices, the curve, and the expected ppm assume a normal distribution. The observed ppm is a count and does not.
  • Within-process sigma is the average moving range of successive values, divided by 1.128. That assumes the paste order is production order.
  • Overall sigma is the sample standard deviation with divisor n − 1.
  • If one standard deviation is used for both, Cp equals Pp and Cpk equals Ppk.
  • Sigma level here is 3 × Cpk (within) and 3 × Ppk (overall). The 1.5 shift is the old Motorola convention and stays off unless you tick it.
  • This is not a control chart, a gauge study, or a customer requirement.

How this is calculated

  • Cp = (USL − LSL) / (6 × σ_within). Pp swaps in σ_overall.
  • Cpk = min[(USL − mean) / (3 × σ_within), (mean − LSL) / (3 × σ_within)]. Ppk uses σ_overall.
  • With one limit, Cpk or Ppk is that side only, and Cp and Pp are left blank.
  • Expected ppm = 1,000,000 × [Φ((LSL − mean) / σ) + 1 − Φ((USL − mean) / σ)].
  • Shapiro–Wilk W is the default. It uses Royston’s 1995 algorithm and is shown from 3 readings up to 5,000. Anderson–Darling A² uses the sample standard deviation. Its p-value is Stephens’ approximation, shown from 8 readings up. The verdict uses the alpha you pick, 0.05 unless you change it, and it says there is evidence of non-normality only when p is below that alpha.
  • The QQ plot uses Blom positions, (i − 0.375) / (n + 0.25).
Methods and references
  • Cp = (USL − LSL) / (6σ) and Cpk = min[(USL − μ) / (3σ), (μ − LSL) / (3σ)]. These are the definitions in the NIST/SEMATECH e-Handbook, section 6.1.6, and the same definitions used in the AIAG SPC Reference Manual (2nd ed.) and ISO 22514-2. Montgomery’s Introduction to Statistical Quality Control uses the same indices.
  • The within standard deviation is the average moving range divided by d2 = 1.128, the individuals-chart estimator in the AIAG SPC manual. The overall standard deviation is the sample standard deviation with divisor n − 1, the Pp / Ppk convention in that same manual.
  • The NIST worked example (USL 20, LSL 8, mean 16, s = 2) gives Cp = 1 and Cpk = 0.6667. This page reproduces that when the same standard deviation is used for both indices.
  • Shapiro–Wilk uses Royston, P. (1995), Remark AS R94, Applied Statistics, 44, 547–551, which is the algorithm behind JMP’s Shapiro-Wilk W and R’s shapiro.test. It extends Royston, P. (1982), Algorithm AS 181, Applied Statistics, 31, 176–180.
  • Anderson–Darling uses the case where the mean and variance are estimated, with Stephens’ A²* adjustment and p-value approximation as given in D’Agostino, R. B. and Stephens, M. A. (1986), Goodness-of-Fit Techniques, and Stephens, M. A. (1974), Journal of the American Statistical Association, 69, 730–737. That is the Anderson–Darling test Minitab reports for normality.
  • The normal curve and the expected ppm use the standard normal distribution, as the NIST handbook states these indices assume. The QQ positions are Blom’s (i − 0.375) / (n + 0.25).