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

Abstract

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.

Optimal designs of the side sensitive synthetic chart for the coefficient of variation based on the median run length and expected median run length

“…Designs based on the MRL are available for several charts in the literature, among some of the more recent ones are studies on the MRL performance of the synthetic � X chart by Hu et al [27], optimal designs based on the MRL and/or EMRL for the one-sided exponential CUSUM chart [28], one-sided exponential EWMA chart [29], EWMA-γ chart [30], EWMA � X chart [31], variable sample size � X chart [32], synthetic np chart [33], multivariate synthetic |S| chart [34], double sampling � X chart [35], and many others. However, the design of the side sensitive synthetic-γ chart is not available in the literature.…”

Economic statistical model of the np chart for monitoring defectives

“…Even though Shewhart charts assess the expenses implicitly by selecting n and h, the resultant charts are not guaranteed to be economically optimal.The performance of statistically designed charts is typically determined in terms of the Average Run Length (ARL) or Average Time to Signal (ATS) where ATS = ARL × h 8,9 . The out-of-control ARL can be defined as the average number of samples required to detect a process shift after it occurs [10][11][12] . Similarly, the out-of-control ATS can be defined as the average time required to detect a process shift after it occurs [13][14][15] .…”