CUSUM charts with transformed exponential data

It has been stressed by some authors that when the process fraction nonconforming is very small, monitoring the time between events (TBE) is an effective approach other than monitoring the fraction nonconforming directly. Some control charts have been designed for monitoring exponentially distributed TBE data, e.g. the CQC chart, exponential CUSUM, and exponential EWMA chart. Another possible approach is to transform the TBE data to normal, and then apply the well developed schemes for the approximate normal data. Since Cumulative Sum (CUSUM) chart is very effective in detecting small and persistent shifts because of its inherent ability of accumulate deviations for successive observations, it can also be used for the transformed data. The purpose of this paper is to investigate the design and performance of CUSUM chart with transformed exponential data. Different transformation methods such as Nelson's method, Double SQRT transformation, and log transformation were examined in order to find the most appropriate transformation method. The Average Run Length (ARL) performance of the CUSUM chart was discussed. Comparisons between the transformed CUSUM, the X-MR chart and the CQC chart were also conducted. The optimal design procedures of optimal CUSUM chart were proposed. This study provides another possible alternative for monitoring TBE data with easy design procedures and relatively good performance.