Process Capability Analysis in the Presence of Autocorrelation

The classical method of process capability analysis necessarily assumes that collected data are independent; nonetheless, some processes such as biological and chemical processes are autocorrelated and violate the independency assumption. Many processes exhibit a certain degree of correlation and can be treated by autoregressive models, among which the autoregressive model of order one (AR (1)) is the most frequently used one. In this paper, we discuss the effect of autocorrelation on the process capability analysis when a set of observations are produced by an autoregressive model of order one. We employ a multivariate regression model to modify the process capability estimated from the classical method, where the AR (1) parameters are utilized as regression explanatory variables. Finally, the performance of the presented method is investigated using a Monte Carlo simulation.