Pp is the performance twin of Cp. It divides the tolerance width by six times the overall sigma: Pp = (USL − LSL) / (6σ overall). It answers the question of whether the full long-term spread of the process, including every lot change and setup, could fit inside the specification if the average were perfectly centred.
Like Cp, Pp takes no notice of where the average actually sits. It is a statement about width only. A Pp of 1.25 means the long-term spread fits into the tolerance 1.25 times. Because the overall sigma is usually bigger than the short-term sigma, Pp is usually smaller than Cp for the same process. If you ever see Pp noticeably larger than Cp, check the data, because something has gone wrong in the calculation or the sampling.
Key Concept
Pp = (USL − LSL) / 6σ overall measures long-term potential width, ignoring centring.
Practical Example
A moulded housing has a weight specification of 42.0 ±1.5 g, so LSL = 40.5 g, USL = 43.5 g and the tolerance width is 3.0 g. Over six weeks the overall sigma from 480 individual weights is 0.40 g, so 6σ = 2.40 g. Pp = 3.0 / 2.40 = 1.25. The long-term spread would fit the tolerance with a modest margin if the average were held at 42.0 g.
Standard Procedure
- 1Calculate the tolerance width, USL minus LSL.
- 2Multiply the overall sigma by 6.
- 3Divide the tolerance width by that spread to obtain Pp.
- 4Record Pp alongside the study window and the number of readings used.
Lesson Summary
- ✓Pp uses the same structure as Cp but with the overall sigma in the denominator.
- ✓Pp is about width only; it says nothing about whether the process is centred.