Sequential testing of process capability indices

A Process Capability Index (PCI) is a numeric summary that compares the behaviour of a product or process characteristics with engineering specifications. We propose a sequential procedure for testing whether two processes are equally capable by using the PCI (C-pm). We employ a non-sequential Wald-type statistic and provide its sequential version by Brownian motion approximations. We point out that, as a byproduct, the non-sequential Wald-type statistic used here provides an easily computable alternative to Boyels' approximate F-test [Boyels, The Taguchi Capability Index, J. Quality Technol. 23 (1991), pp. 17-26]. We give an algorithm for conducting the sequential test and we examine its performance by using Monte Carlo simulations. Finally, we illustrate the method by testing capability improvement of an industrial process before and after calibration based on published data.