Estimating capability index in multivariate processes using bootstrap sequential sampling procedures

Capability indices in both univariate and multivariate processes are extensively employed in quality control to assess the quality status of production batches before their release for operational use. It is traditionally a measure of the ratio of the allowable process spread and the actual spread. In this paper, we will adopt a bootstrap and sequential sampling procedures to determine the optimal sample size for estimating a multivariate capability index introduced by Pearns et. al. [12]. Bootstrap techniques have the distinct advantage of placing very minimum requirement on the distributions of the underlying quality characteristics, thereby rendering them more relevant under a wide variety of situations. Finally, we provide several numerical examples where the sequential sampling procedures are evaluated and compared.