Design of Exponential Distributed Median Chart with Unknown Parameters

Abstract

Abstract-It is recommended to monitor the time between events(TBE) when the defect rate is very low. An unbiased median chart is proposed to monitor exponential distributed TBE data and some design parameters are provided for ease of application. For the parameter is usually unknown, the effects of estimation on the chart performance are evaluated in terms of conditional false alarm rate and the conditional average run length(ARL) distribution. It is find that the median statistical can significantly reduce the "practitioner-to-practitioner" variability, and less number of reference samples are needed in phase I control chart. Moreover, the median chart ensures the sensitivity of the process shift to a certain extent. It is shown that the median statistical is an alternative one to monitor the exponential distributed TBE data.