Optimal design of one-sided exponential cumulative sum charts with known and estimated parameters based on the median run length

As a useful tool in statistical process control (SPC), the exponential control chart is more and more popular for monitoring high-quality processes. Considering both known and estimated parameter cases, the one-sided exponential cumulative sum (CUSUM) charts are studied in this paper through a Markov chain approach. Because the shape of the run length (RL ) distribution of the one-sided exponential CUSUM charts is skewed and it also changes with the mean shift size and the number of Phase I samples used to estimate the process parameter, the median run length (MRL ) is employed as a good alternative performance measure for the charts. The optimal design procedures based on MRL of the one-sided exponential CUSUM charts with known and estimated parameters are discussed. By comparing the MRL performance of the chart with known parameters with the one of the chart with estimated parameters, we investigate the effect of estimated process parameters on the properties of the chart. Finally, an application is illustrated to show the implementation of the chart.