Term | Description |
---|---|
USL | Upper specification limit |
LSL | Lower specification limit |
η | Process median |
X_{pu} | Upper empirical percentile from the tolerance |
X_{pl} | Lower empirical percentile from the tolerance |
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.
Term | Description |
---|---|
p | the percentage of data less than or equal to the desired percentile, divided by 100 |
X_{y} | the y^{th} row of the data when the data are sorted from least to greatest |
y | the truncated value of w |
w | p(N + 1) |
N | the number of rows with nonmissing data |
z | w – 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.