Developing New Multivariate Process Capability Indices for Autocorrelated Data

Traditionally, the process capability index is developed assuming that the process output data are independent and follow normal distribution. However, in most environmental cases, the process data have more than one quality characteristic and exhibit property of autocorrelation. We propose two novel multivariate process capability indices for autocorrelated data, NMAC_p and NMAC_pm, for the nominal‐the‐best case. For the smaller‐the‐better case, Γ(0) is used to modify the ND index and a new multivariate autocorrelated process capability index NMAC_pu is derived. Furthermore, a simulation study is conducted to compare the performance of the various multivariate autocorrelated indices. The simulation results show that the actual nonconforming rates can be correctly reflected by our proposed indices, which outperform the previous C_p^m, MC_p, MC_pm, NMC_p, NMC_pm, and ND indices under different time series models. Thus, our proposed capability indices can be used in evaluating the performance of multivariate autocorrelated processes. Finally, a realistic example in hydrological application further demonstrates the usefulness of our proposed capability indices. Copyright © 2013 John Wiley & Sons, Ltd.