Interpretation & Calculations
Why do the non-normal process capability analyses max out at a Cpk value of 2.500?
David W., Manufacturing Engineer
When a normal distribution is assumed, the capability indices are conveniently calculated using the algebraic formula (provided in Chapter 3). The arithmetic allows for calculation of any value, down to several decimal places. However, when the Johnson distribution is used, an approximate distribution is fit to the data, and the distribution is interpolated at the specifications. When the specification lie far from the process centerline, in the far tails of the distribution, it is nonsensical to estimate beyond a capability index of 2.5, given that a capability index of 2.5 corresponds to a z-value of 7.5 (beyond the 99.99999999999 percentile of the distribution).
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).