Using generalized confidence Intervals to compare two processes capability indices

The first and main process capability indices (PCI), , was stated by Juran. The  process capability indices and then the  process capability indices have been formally stated by Chan et al. The  process capability indices is a combination of the  and  process capability indices and was introduced by Pearn et al. (2002). The  process capability indices are a tool for measuring process capability in production. So far, confidence intervals for the difference between process capability indices for the two processes have been obtained using the pivotal quantity method and also using the bootstrap resampling simulation method. In situations such as selecting a supplier and assessing process improvement, it is of interest to compare capability indices for two different processes or the same process before and after an adjustment. In this paper, first a generalized confidence interval for the  capability indices ratio of two different processes is presented and then this comparison is performed by performing a appropriate hypothesis test and providing an example. In addition, using simulating, the generalized confidence interval was compared with the Bootstrap confidence interval and the results showed that the generalized confidence interval works better. The  capability indices is based on the assumption that a given process can be represented by a normal probability model with mean  and standard deviation .