Studies For Process Capability Indices By Generalized Inference Method

Process capability indices(PCIs) are intended to provide single-number assessment of the ability to meet the specification limits on a quality characteristic of interest. However, in the practical production, many stable processes fail to follow normal distribution simply, but the population can be formed by mixed linear model. Therefore, the inference for PCIs in mixed linear model is tremendously significant for commercial process. In this article, PCIs are studied in two kinds of mixed linear models. Mutivariate condition also be concerned. The main results are as follows:In this article, the difference of PCIs is concerned in two kinds of mixed linear model firstly. Under balance condition, we construct generalized confidence intervals on PCIs by generalized pivotal quantity method. And simulation studies show that the proposed method performs better. Under unbalance condition, in order to apply the GCI idea to derive confidence intervals for the difference of PCIs, fiducial inference is proposed to give generalized pivotal quantity for PCIs. A simulation study is conducted to compare the resulted interval with the existed generalized confidence intervals. The results indicate that generalized inference performs better than approximate method.Finally, the coefficient of variation(CV) and principal components analysis are used as different weights to synthesize the univariate capability index. We explore the possibility of applying the ideal of GCIs to get generalized confidence intervals for MPCIs. The results indicate that the models are feasible. At last, simulation study shows that GCI of CV is better.