Non-Normal Distributions - Non-Normal Process Capability Indices (Percentile Method)

Process capability indices are generally computed to evaluate the quality of a process, that is, to estimate the relative range of the items manufactured by the process (process width) with regard to the engineering specifications.

For the standard, normal-distribution-based, process capability indices, the process width is typically defined as 6 times sigma, that is, as plus/minus 3 times the estimated proces1s standard deviation. For the standard normal curve, these limits ( zl = -3 and zu = +3) translate into the 0.135 percentile and 99.865 percentile, respectively. In the non-normal case, the 3 times sigma limits as well as the mean ( zM = 0.0) can be replaced by the corresponding standard values, given the same percentiles, under the non-normal curve. This procedure is described in detail by Clements (1989).

Process capability indices

Shown below are the formulas for the non-normal process capability indices:

C_p = (USL-LSL)/( U_p-L_p)

C_pL = (M-LSL)/(M-L_p)

C_pU = (USL-M)/(U_p-M)

C_pk = Min(C_pU, C_pL)

In these equations, M represents the 50'th percentile value for the respective fitted distribution, and Up and Lp are the 99.865 and .135 percentile values, respectively, if the computations are based on a process width of ±3 times sigma. Note that the values for Up and Lp may be different, if the process width is defined by different sigma limits (e.g., ±2 times sigma).

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