EWMA control charts for the scale parameter of a Weibull control variable with fixed and variable sampling intervals

Economic Quality Control, 13 (1998), 23–46


In this paper we are concerned with EWMA control charts for the scale parameter of the three-parameter Weibull control variable, where $\eta$, $\delta$ and $\alpha$ are the location , the scale and the shape parameters, respectively, with fixed (FSI) and variable (VSI) sampling intervals. We consider lower and upper one-sided EWMA control charts and their FSI and VSI versions for jointly controlling the mean and the variance of the control variable X. The pivotal statistic of those control charts is based on the maximum likelihood estimator of $\ln(\delta^\alpha)$ of the Weibull control variable X. The design and performance of the control charts are studied, Two criteria, "comparability criteria" (or "matched criterion") under control and "primordial criterion", are imposed on their design, The performance of the control charts is measured by means of the average time to signal.