Component-Wise Adaptive Joint EWMA Monitoring of Lifetime Quantiles and Entropy

Statistical monitoring of lifetime processes is commonly based on a single process characteristic, which may fail to detect distributional changes that affect different aspects of process behavior. This study proposes a component-wise adaptive joint exponentially weighted moving average (EWMA) control chart for simultaneously monitoring a Weibull lower quantile and Shannon entropy. Unlike conventional joint monitoring schemes that apply a common smoothing mechanism, the proposed framework preserves the quantile and entropy as separate standardized components, adaptively updates each according to its own departure, and subsequently combines them through a correlation-adjusted quadratic statistic that retains their dependence. Control limits are calibrated by Monte Carlo simulation to achieve a target in-control average run length of approximately 370. Extensive simulations consider scale, shape, and combined Weibull parameter shifts, together with quantile-preserving and entropy-preserving alternatives specifically designed to isolate changes in the individual characteristics. Comparisons with single-component Q-EWMA and H-EWMA charts and a fixed joint EWMA chart demonstrate that the proposed procedure maintains the desired in-control performance while providing robust and balanced detection across heterogeneous process changes. Its advantage is particularly evident when one monitored characteristic remains relatively stable while the other changes substantially, a setting in which single-characteristic charts may become insensitive. Practical applicability is demonstrated through two complementary real-data applications involving medical rehabilitation length-of-stay data and rolling-contact fatigue-life data under different lubrication conditions. In both settings, the proposed chart successfully identifies meaningful distributional departures, while the component-wise adaptive mechanism responds selectively to the relative magnitudes of quantile and entropy changes. Overall, the proposed framework provides a robust and flexible monitoring strategy for heterogeneous lifetime-process changes without requiring prior knowledge of whether deterioration will primarily affect lower-tail performance, distributional uncertainty, or both.