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EWMA Charts for the Weibull Shape Parameter

This article discusses exponentially weighted moving average (EWMA) charts for monitoring the Weibull shape parameter β. The charts are based on the sample range of the logarithms of the data and an unbiased estimator of 1β. The average run length (ARL) of the proposed chart is determined by β and the sample size n. Hence, the design of a chart is based on the β of interest, n, and the desired in-control ARL. Two-sided charts are derived, as well as one-sided charts for detecting specific shifts in β. These charts are compared with the cumulative sum chart of Page (1954), which is known to have optimality properties. The EWMA schemes studied here are ARL unbiased in the sense that they are expected to detect shifts sooner than the in-control ARL. The proposed schemes are applied to monitoring the Weibull shape parameter of the strength distribution of a carbon fiber used in composite materials.