Statistical Inference For The Comparison Of Various Process Capability Indices

Process capability analysis is an important issue in industrial production and life to measure production capacity and ensure product quality.Linking process production capacity to specification limits of the production process gives an indicator of process capability,called the process capability index(PCI).Through statistical inference,the quality of the product can be improved and the customer's requirements for product quality can be satisfied.Due to the fact that there are often data unbalance in actual production data,we have conducted detailed research and analysis of PCI under unbalanced data.And in the actual production process,many stable processes do not simply obey the normal distribution,and the variance is the sum of variance components.The overall situation at this time can be represented by a mixed model.Therefore,the study of PCI under the mixed linear model is of great significance to the modern industrial production process.After this,a group of scholars emerged to develop a new measure called the Process Capability Incapability Index(PICI).PICI can reflect the inaccuracy and imprecision of the process and has better research value.Therefore,we study and analyze the theoretical nature of PICI,and statistically infer the PICI under the one-way variance component unbalanced model.In short,this paper mainly statistically infers the comparison of process capability differences under the mixed linear unbalanced model.The main contents are as follows:In the case of unbalanced data,statistical inferences were made on the one-way variance component model and the single process multi-process capability index.At the same time,the generalized pivots of PCI were given using three methods: approximation method,parameter bootstrapping and Fiducial generalized inference,and their confidence intervals were further constructed.According to the analysis of the simulation results,the model of the generalized confidence interval obtained by generalized inference is more accurate and the interval coverage is closer to the confidence level.In the extreme unbalanced data,the results are more stable and the construction method is easier than other methods.In the case of unbalanced data,the statistical inference of the difference in process capability index under the two-factor design suite model is given,and the generalized pivot value of PCI difference is given using the Fiducial generalized inference and the parameter bootstrapping is constructed respectively.According to the simulation results,the confidence interval obtained by the generalized inference is higher than the coverage of the parameter self-confidence interval,and it is closer to the confidence level.Study the theoretical nature of PICI and give the PICI estimate.In the case of unbalanced data,the Fiducial generalized inference of PICI under one-way variance components model is compared with the parameter bootstrapping method to construct its corresponding confidence interval.According to the simulation results,the confidence interval obtained by the generalized inference is higher than the coverage of the parameter self-confidence interval,and it is closer to the confidence level.