Abstract: To analyze the process capability under random parameters,a new kind of process capability index is designed in this paper. Based on the statistical model for quality variables,we explored the parameters' Bayesian point estimates and interval estimation with a diffuse prior and developed a Bayesian process capability index. Then,we considered the parameters'current posterior distribution to be their prior distribution in the next phrase when the process is capable,by which the Bayesian dynamic process capable index is established. Finally,we give an example to show how to use the method proposed in this paper. The results indicate that the accuracy of estimators for process capability indices can be improved through Bayesian dynamic statistical methods.

Key words: quality control, process capability index, bayesian method, estimation, prior distribution