Design of Fuzzy and Neutrosophic Mixed EWMA-CUSUM control charts under failure censored lifetime test

In reliability analysis, product lifetime is a critical quality characteristic, particularly in industries where durability defines performance. Since monitoring every unit is costly, censored life tests are commonly used, followed by control charts to evaluate lifetime behavior. However, failure-time data often contain uncertainty arising from measurement errors, device limitations, or operator variability. This research proposes two new statistical monitoring toolsthe Fuzzy Mixed EWMACUSUM (Fuzzy MEC) and the Neutrosophic Mixed EWMACUSUM (Neutrosophic MEC) chartsto address lifetime monitoring under uncertainty. The charts are developed for failure-censored life tests without replacement, assuming a Weibull distribution with a fixed shape parameter and variable scale. Control limits and performance measures such as average out-of-control run lengths are obtained using Monte Carlo simulation. In the fuzzy framework, triangular fuzzy numbers model imprecise failure times, and α-cuts of 0.65 and 1 are examined using the fuzzy midrange transformation. Results indicate that the Fuzzy MEC chart with midrange at α = 0.65 provides superior detection capabilities compared to the fuzzy mode. The Neutrosophic MEC chart further improves performance, demonstrating better sensitivity than both the classic and fuzzy MEC charts when uncertainty is high.