On Designing CUSUM and Adaptive CUSUM Charts for Monitoring Scale Parameter of Birnbaum–Saunders Distribution

Statistical process control (SPC) is extensively applied to track and enhance process quality by minimizing variability. Control charts are the best available tool in SPC, useful to identify changes in process parameters over time. Classical control charts require normality assumption of variable of interest, while numerous industrial processes and environmental processes exhibit skew distributions like Birnbaum–Saunders (BS) distribution. In such a scenario, traditional charts tend to give deceptive results and are not able to spot changes effectively. Hence, the design of such specific charts is required to effectively monitor skew and non‐normal processes. This study develops cumulative sum (CUSUM) and adaptive CUSUM control charts for tracking the scale parameter of the BS distribution. The adaptive chart adjusts dynamically according to process data, providing greater sensitivity compared to the traditional alternative. Performance of the new charts is evaluated via Monte Carlo simulation under varying process conditions. Comparative findings indicate that adaptive BS‐CUSUM is more sensitive to small and moderate shifts compared to the traditional competitors. Generally, the proposed charts offer effective monitoring of BS processes with improved responsiveness guaranteed through the adaptive mechanism and practical implementation.