Performance Evaluation of Shiryaev–Roberts and Cumulative Sum Schemes for Monitoring Shape and Scale Parameters in Gamma-Distributed Data Under Type I Censoring

This paper proposes two process monitoring schemes, namely the Shiryaev–Roberts (SR) procedure and the cumulative sum (CUSUM) procedure, to detect shifts in the shape and scale parameters of Type I right-censored Gamma-distributed lifetime data. The performance of the proposed schemes is compared with that of an exponentially weighted moving average (EWMA) control chart based on deep learning networks. The performance of the proposed schemes is evaluated under various censoring rates using Monte Carlo simulations, with the average run length (ARL) as the primary metric. Furthermore, the SR and CUSUM schemes are compared for both zero-state and steady-state shifts. Simulation results indicate that the SR and CUSUM procedures exhibit superior performance, with the SR scheme showing particular advantages when the actual shift is small, while the CUSUM chart proves more effective for identifying larger shifts. The shape parameter has a significant effect on the performance of the control charts such that a reduction in the shape parameter effectively improves the ability to capture early offsets. Increased censoring rates reduce detection sensitivity. To maintain ARL0= 370, control limits h adapt differentially. The SR and CUSUM charts with different censoring rates need to recalibrate the parameter to mitigate performance losses under higher censoring conditions. The monitoring performance of the SR and CUSUM chart is enhanced by an increase in sample size. Finally, a practical example is provided to illustrate the application of the proposed monitoring schemes.