Bayesian Analysis And Application Based On Process Capability Index

Statistical process quality control is a useful and effective means in product quality control of mechanical process, process capability indices (PCIS) are single-number measure for the capability of a process in meeting specification limits. These indices have been widely used in manufacturing industrial. The individualized demand for the products increase constantly, and the small batch manufacturing has already become the main mode that enterprises manage gradually. It is a great challenge undoubtedly for PCIS. To probe the PCIS method that is suitable for the small batch manufacturing become a heavy focus of controlled field about present quality already. This paper mainly focuses on the most widely used PCIS C_p , C_pk,C_pm by Bayesian method.Firstly we analyzed the three types of process capability indices C_p , C_pk,C_pm in the traditional frequentist statistical theory of the point estimator and confidence intervals. and the percentage non-conforming(NC) associated with PCIS. The most commonly recommended estimator of PCIS is biased , we derived its unbiased factor..Secondly we studied of data normal assumptions and use Johnson curve-fitting of non-normal data transformation. Thus we also can make reasonable estimators. under the condition that the process capability indices are non-normal distribution. It proved that the method is more simple and the results more accurate and reliable.Furthermore we the researched the problem of Bayesian estimator and the lower Bayesian confidence limit on the process capability index C_p. We derived conditional expectation and the highest posterior estimator of PCIS C_p by using non-informative and conjugate prior distributions respectively. It showed through. using Bayesian methods than traditional frequentist statistical methods of calculation of process capability index can reflected the actual productions situation. more truly.Finally we studied the problem of the lower Bayesian confidence limit on the process capability index C_pm The Jeffreys'non-informative prior distribution depending on Fisher's information is explored. The posterior distribution of C_pmis conducted. The lower Bayesian confidence limit designed is based on the posterior distribution of C_pm combined with the application of highest posterior density. This method resolved the difficulty that the posterior density is unimodal and asymmetric. Through simulation of MATLAB, it showed that the lower limit more accurately reflected process capability and more exactly estimated index and could provide the basis of probability for more effective uses of the index.