Conditional analysis of Phase II exponential chart for monitoring times to an event. Issue 3 (3rd May 2020) - Kumar, Nirpeksh
ABSTRACT: It is now well known that the error in estimating parameter(s) adversely affects the performance of control charts. The charts with estimated control limits are usually assessed by some of characteristics of unconditional run length (URL) distribution. However, it is now under criticism because the unconditional analysis based on URL does not give the full impression of the chart's performance conditioning on a given Phase I sample. In recent years, the focus has been shifted from unconditional performance analysis to conditional analysis which is carried out in terms of conditional run length (CRL) and its associated characteristics and provides deep understanding of conditional performance of the chart given a Phase I sample. In this article, Phase II exponential charts are considered to monitor times to an event and their performance are examined conditional on given Phase I sample by considering several indicators based on conditional average run length (CARL) distribution. In this respect, the exact expressions of the distribution functions of C A R L for the estimated exponential control charts are derived and several statistical constants are computed which could be helpful in evaluating and designing the chart.