Generally weighted moving average control chart for monitoring two-parameter exponential distribution with measurement errors

Control charts for two-parameter exponential distributions are widely used in monitoring quality and lifetime processes, and more useful and flexible than the chart for one parameter exponential distributions. In order to efficiently detect small shifts for two-parameter exponential distributions, a generally weighted moving average (GWMA) control chart is developed. Since measurement errors are inevitable in practice, and they are not considered in the existing control charts, we proposed a GWMA chart with measurement errors (GWMA-M) by two strategies: one is the GWMA chart with adjusted control limits, and the other is the GWMA chart with additive measurement error model to deal with measurement errors. The performance of the proposed GWMA-M scheme is investigated in terms of average run length (ARL) and expected ARL (EARL). Comparisons of the GWMA-M chart with the EWMA-M chart and the GWMA signed-rank (GWMA-SR) chart in the presence of measurement errors are carried out, and results show the advantage and efficiency of the GWMA-M scheme. In addition, the effect of model parameters, measurement errors and sample size on the GWMA-M chart are studied through Monte-Carlo simulation. Finally, two real examples of monitoring flood data and HPM (high-voltage metal oxide semiconductor transistor) data are given to illustrate the implementation of the proposed chart.