New EWMA control charts for monitoring the Weibull shape parameter

Abstract

Abstract In this article, we first propose a new exponentially weighted moving average (EWMA ) chart for monitoring the shape parameter of the Weibull distribution. The proposed chart is developed based on the EWMA of the normal random variable, which is transformed from the easy‐to‐understand chi‐squared random variable. In contrast, the existing EWMA charts for monitoring the shape parameter use the sample range or the unbiased estimator of the shape parameter. Unfortunately, the EWMA chart generated from sample ranges is inefficient in detecting changes due to its lack of sufficiency, whereas the one produced using unbiased estimators of the shape parameter has a highly complicated distribution that is difficult to manipulate. Simulation studies are conducted to compare the effectiveness of the proposed EWMA chart and the two existing EWMA charts. Also, a maximum likelihood estimation method is employed to estimate the change point in the process for the proposed EWMA chart once an out‐of‐control (OC) signal has been triggered. Further, to reduce the time for detecting the OC signal, an EWMA chart with variable sampling intervals (VSIs) for monitoring the shape parameter is developed based on the proposed EWMA chart. This EWMA chart with VSIs is studied, and its performance is evaluated. Finally, an example to demonstrate the applicability and implementation of the proposed charts is provided.

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