Bayesian and Classical Approaches To Monitor Process Parameters

Abstract

In this study the design structure of Shewhart }( and S2 charts have been proposed based on posterior and posterior predictive di stributions for retrospective and prospective analysis respectively for monitoring the changes in the process location and dispersion assuming the normality of the quality characteristic. The proposed design structure is based on the choice of prior distribution and posterior degree of freedom. The OC functions are calculated as a performance measure of the proposed design structures of }( and S1 charts. The proposed design structures of X and S2 charts have been compared with the frequentist or usual design structures of -"y and S2chatis with respect to (i) width of control region and (ii) least probability of not detecting a shift occurs in the parameter of the continuous process under normal process situation. This comparison reveals that the proposed design structures, which are based on Bayesian Inference, are superior to frequentist design structures of X and S2 charts for monitoring past as well as future data of continuous process 111 detecting shifts in process parameters under celiain condition. An estimator of process capability index (Splllk)' a new index proposed by Chen and Ding (2001) for any underlying distribution, based on gini's mean difference has been modified. The proposed modified estimator takes into account the process variability, departure of the process mean from the target value and the proportion of nonconformity. The comparison of the proposed mocIified estimator is made with the well known capability indicesCp'CNp and SPlllk for normal and other than normal processes and comparison reveals that the proposed estimator of process capabil ity index performs better than others capabi I ity i nd ices even for the smaller samples and any underlying distribution, which is the most practical situation.