Regressing sample quantiles to perform nonparametric capability analysis

Capability analysis corresponds to a set of methods used to estimate and test the ability of an in-control process to provide a specific output. When there is only one quality characteristic that behaves as a continuous random variable, indices like C_p and C_pk can be used to measure how well requirements are met. Under normality, variation is indicated using 3−sigma limits; otherwise, the corresponding quantiles are used. Distribution fitting and transformations to normality can be used to estimate quantiles by finding an overall fit to the data available. However, by giving the same weight to all observations, the best possible fit of extreme values can be lost. To address this issue, a regression approach is proposed to fit functions over maximum likelihood estimates of probabilities of extreme values. A case study from the automotive industry is used to illustrate the proposed approach. To evaluate the performance, extensive Monte Carlo simulation is used, and the results are compared with the corresponding approach using the Clements method. The proposed nonparametric technique shows smaller MAD when high levels of skewness exist. Practitioners with basic knowledge of regression analysis may find the approach useful to estimate capability indices without the need of a specific probability distribution.