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, NMACp and NMACpm for the-nominal-the-best case. For the-smaller-the-better case, Γ(0) is used to modify the ND index proposed by Niverthi and Dey 1 and a new multivariate autocorrelated process capability index NMACpu 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 non-conforming rates can be correctly reflected by our proposed indices, which outperform the previous Cp m , MCp, MCpm, NMCp, NMCpm 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.