Optimal Cusum Control Chart for Censored Reliability Data with Log-logistic Distribution

Abstract

The goal of this work is to detect any potentially harmful change in a process. The reliability tests are assumed to generate type-I right-censored data following a log-logistic distribution with scale parameter (η) and shape parameter (β). For this purpose, we have constructed a likelihood ratio based simultaneous cumulative sum (CUSUM) control chart that targets changes in both the failure mechanism and the characteristic life (the simultaneous CUSUM chart for detecting shifts in the shape and the scale parameters). This control chart displays best performance for combinations with larger positive or negative shifts in the shape parameter, signaling on average in 5 samples in an out-of-control situation, while targeting an in-control average run length of 370. The simultaneous CUSUM chart’s performance is highly dependent on the values of β, and on the interaction between them and the censoring rates and shift sizes.