Cpk fixes the blind spot in Cp by measuring the distance from the process average (x̄, pronounced x-bar) to the nearest specification limit. It computes two half-indices. The upper one is (USL − x̄) / 3σ. The lower one is (x̄ − LSL) / 3σ. Cpk is the smaller of the two, because the nearest limit is the one that will bite first.
When the process sits exactly in the middle of the tolerance, both halves are equal and Cpk equals Cp. As the average drifts toward one limit, that half shrinks and Cpk falls below Cp. The gap between Cp and Cpk is therefore a direct measure of how far off centre the process is. A big gap means a centring problem; a small gap means the process is centred and any shortfall is pure spread.
Key Concept
Cpk = min[(USL − x̄) / 3σ, (x̄ − LSL) / 3σ], and the gap between Cp and Cpk is the cost of being off centre.
Practical Example
The drive shaft process averages x̄ = 25.02 mm with σ = 0.012 mm, so 3σ = 0.036 mm. Upper half: (25.05 − 25.02) / 0.036 = 0.03 / 0.036 = 0.83. Lower half: (25.02 − 24.95) / 0.036 = 0.07 / 0.036 = 1.94. Cpk is the smaller value, 0.83. Cp was 1.39, so the gap of 0.56 says the problem is centring, not spread: the lathe is cutting shafts 0.02 mm oversize on average.
Standard Procedure
- 1Calculate the process average x̄ from all the subgroup data.
- 2Multiply the short-term sigma by 3.
- 3Compute (USL − x̄) / 3σ and (x̄ − LSL) / 3σ.
- 4Take the smaller of the two as Cpk.
- 5Compare Cpk with Cp: a large gap points to centring, a small gap points to spread.
Lesson Summary
- ✓Cpk looks at the nearest specification limit, so it reflects actual performance.
- ✓Cpk can never exceed Cp; it equals Cp only when the process is perfectly centred.