How this calculator works
Cp compares the specification width with six process standard deviations. Cpk uses the distance from the mean to the nearer limit, penalising poor centring. Cpm also penalises distance from the target. Interpretation assumes a stable process, representative independent measurements and a suitable approximately normal model. Supply a within-process SD for capability; substituting overall long-term SD changes the interpretation toward performance indices.
Formula
Cp = (USL - LSL)/(6sigma); Cpu = (USL - mu)/(3sigma); Cpl = (mu - LSL)/(3sigma); Cpk = min(Cpu,Cpl); Cpm = (USL - LSL)/(6sqrt(sigma² + (mu - target)²)).
Worked example
With limits 0 and 12, mean 6, target 6 and SD 2, Cp, Cpk and Cpm all equal 1. Moving the mean to 8 leaves Cp at 1 but reduces Cpk to 2/3.
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Frequently asked questions
Can Cpk be negative?
Yes. A mean outside a specification limit gives a negative distance to that limit and therefore negative capability.
Are specification limits the same as control limits?
No. Specifications come from requirements; control limits describe expected process behaviour. Capability needs a process already shown to be stable.
Does a threshold guarantee product quality?
No. A numeric index depends on data quality and distribution assumptions, and does not replace process monitoring or customer requirements.