Methods and formulas for overall capability measures in Nonparametric Capability Analysis

Overall capability measures

Cnpk = min{Cnpl, Cnpu}


USLUpper specification limit
LSLLower specification limit
ηProcess median
XpuUpper empirical percentile from the tolerance
XplLower empirical percentile from the tolerance

Empirical percentiles

The analysis uses the empirical percentiles to estimate the spread of the process. First, the analysis uses the tolerance to find the percentiles to calculate.

where Z is a percentile from the standard normal distribution and T is the tolerance. For example, if the tolerance is 6, then pU = P(Z < 3) = 0.99865. If the tolerance is 6, then pL = P(Z < −3) = 0.00135. For a process with 2 specification limits, a tolerance of 6 covers approximately 99.7% of the data.

Next, the analysis calculates the empirical percentiles from the data.

p the percentage of data less than or equal to the desired percentile, divided by 100
Xy the yth row of the data when the data are sorted from least to greatest
ythe truncated value of w
wp(N + 1)
Nthe number of rows with nonmissing data
zw – y


McCormack, D. W., Harris, I. R., Hurwitz, A., M., & Spagon, P. D. (2000). Capability indices for non-normal data. Quality Engineering, 12(4), 489-495.