Confidence Interval for Cp of Non-normal Distributions Using an Adjusted Confidence Interval for Standard Deviation

Abstract

The capability index Cp is widely used to give a quick indication of process capability in a format that is easy to use and understand (Kotz and Lovelace, [8], pp. 40-41). In this paper a new confidence interval is derived for Cp.  The method is based on an adjusted confidence interval for the standard deviation for non-normal data. AMonte Carlosimulation has been used to investigate the coverage probabilities of the new confidence interval for small samples of sizes 10, 25, 50 and 100 for data from a range of non-normal distributions.  The simulations show that, for all non-normal distributions studied, the new confidence interval for Cp provides higher values for the coverage probabilities than the confidence interval from Kotz and Lovelace and that for most of the distributions the new coverage probabilities are greater than a nominal value of 0.95.