Capability-analysis laboratory

Learning objectives

• Run a capability analysis in a free spreadsheet.
• Compute mean, standard deviation, Cp, Cpk, Pp and Ppk step by step.
• Report capability honestly against the tolerance.

Data first, formulas second

Before any capability number is calculated the data must be from a stable process. Plot the values in order of production and confirm there is no trend or step change. Only then does capability tell an honest story.

Spreadsheet steps

• Column A: measurement values.
• Column B: MOVING RANGE between consecutive rows for a within estimate.
• Cell for mean: =AVERAGE(A2:A31).
• Cell for overall standard deviation: =STDEV.S(A2:A31).
• Cell for within standard deviation: =AVERAGE(B3:B31)/1.128 (moving-range estimator).
• Ppk = MIN((USL−mean),(mean−LSL))/(3×overall sd).
• Cpk = MIN((USL−mean),(mean−LSL))/(3×within sd).

Garment-factory example

Thirty polo chest widths from one shift give mean 52.15 cm and overall standard deviation 0.28 cm with tolerance 52 ± 1 cm. Ppk = min(0.85, 1.15) ÷ (3 × 0.28) ≈ 1.01. Reporting only Ppk without the stability plot would hide that a mechanic change caused a step in the middle of the shift.

Method

1. Plot data in production order first; treat capability as invalid if unstable.
2. Report Ppk and Cpk together with sample size and tolerance.
3. Recompute after every improvement to confirm the gain is real.

Common mistakes

• Using =STDEV.P on a sample instead of =STDEV.S.
• Reporting a single capability number without showing the stability plot.