Control limits for dependent observations

Abstract

Traditionally, statistical control has been utilised in attempting to detect variation in quality of process-output for which it was assumed statistically independent observations were obtained over time. In practice, this convenient assumption is rarely valid (for real life phenomena and forecasting and control technology is required for dependent time series data. Although the literature abounds with references to control systems for independent measurements the only reference to control of dependent data emphasized the total inadequacy of traditional control limits and the need for more realistic values, but offered no alternative methodology. To partially meet this need for control techniques for dependent observations, several models assuming some degree of dependency have been proposed and illustrated with practical applications. The models chosen represent observations generated by moving averages, the linear autoregressive mechanism, a two -state Markov chain and the number of renewals for selected ordinary and Markov renewal processes.