The Studty Of Process Capability Index And The Two Transformation Methods

Traditional process capability index is based on a fundamental assumption that the process data are normal. However, in many conditions the process data are non-normal. So it is necessary to implement non-normal transformation or provide a new method for calculating process capability index for non-normal processes. This paper brings in two types of method for calculating the data of the given cases: Johnson Conversion and Box-Cox Conversion, which can be applied to the transformation of non-normal data.For the study of process capability index, many people attempt to study the inferential aspects of the index. Most of the existing work in this area has been devoted to classical frequenters theory but the frequency distributions of these estimators are often very complicated which means that the calculation of exact confidence intervals will be difficult. Bayesian approaches overcome the difficulty.This paper devotes to the following work:First, it Shows the process capability index and the relational model for percent defective,illustration the importance of the test of the process.Second, it discusses some important transformation methods for non-normal process capability, which are Johnson transformation and Box-Cox transformation methods, does some comparisons with these two methods, studies on the best transformation parameter, and analyzes some cases. All of these methods can be used directly in practice.And last, it studies the process capability index C_p~k for averages of observations from new batches in the case of the balanced random effects model using Bayesian method, and inference the process performance index P_p~ l′, it can use for the averages of the new observations, and illustrate the validity by the instance.