Cusum Charts for Monitoring the Characteristic Life of Censored Weibull Lifetimes

Companies routinely perform life tests on their products. Each of these life tests typically involves testing several units simultaneously with interest in the times to failure. Two aspects often associated with lifetime data that make the development of a control-charting procedure more demanding are that the data tend to be nonnormally distributed and censored. In this paper, one-sided lower and upper likelihood-ratio-based cumulative sum (CUSUM) control charting procedures are developed for Type I right-censored Weibull lifetime data to monitor changes in the scale parameter, also known as the characteristic life, for a fixed value of the Weibull shape parameter. Because a decrease in the characteristic life indicates a decrease in the mean lifetime of a product, a one-sided lower CUSUM chart is the main focus. We illustrate the development and implementation of the chart and evaluate its properties through a simulation study. The proposed CUSUM chart is compared with an exponentially weighted moving-average (EWMA) chart using the steady-state average run length (ARL) performance. The CUSUM chart is shown to perform better than the EWMA chart in detecting shifts for which it is designed.