A comparison of Process Capability Measures for Seasonal and Non-Seasonal Autoregressive Auto-Correlated Data

The process capability indices give a measure of how a process suits within the specification limits. Traditionally, the main assumptions are used in calculating these indices that the measurements for the specified characteristic are independent and normally distributed. In this paper we investigated the distributional properties in terms of Bias, MSE and empirical distribution for the sample version of the most common three process capability measures namely;  when the process data are autocorrelated following seasonal or non-seasonal first-order autoregressive process. We have found that the characteristics of those estimators are negatively affected by the autocorrelation data, especially for the multiplicative seasonal AR model. Besides, we found that the empirical distributions of the three sample capability measures are positively skewed and leptokurtic, a fact which is true when the data are independent and normal.