Conditional confidence intervals of process capability indices following rejection of preliminary tests

Finding an ordinary confidence interval of an unknown parameter is well known, but finding a conditional confidence interval following rejection of a preliminary test is not so noted, especially for finding a conditional confidence interval of the process capability indices Cp or Cpk following rejection of some preliminary tests. This dissertation will provide some basic theories and computational methods for finding such conditional confidence intervals of the two process capability indices. The most basic method used in this dissertation is the general method for finding a confidence interval of an unknown parameter. Numerical methods are also used for finding the values of these conditional confidence limits. The conditional confidence intervals of the process capability index Cp and Cpk are obtained. Computational programming code and other useful information and methods are provided.