Concomitant of Consecutive r-Out-of-m: W System Models through Information-Theoretic Methods with Industrial Modeling Data Application

Abstract

Tsallis entropy is investigated as an uncertainty measure for the concomitants of consecutive r-out-of-m: W systems arising from the Farlie–Gumbel–Morgenstern family, a dependence model frequently encountered in reliability and engineering analyses. A series representation of the proposed entropy measure is established, and its implementation is illustrated through the log-logistic distribution. In addition, stochastic ordering results, theoretical bounds, and characterization properties are derived to reveal the uncertainty behavior of the underlying system. To facilitate practical inference, two distribution-free estimators of the proposed entropy are introduced and examined through extensive Monte Carlo simulation experiments. The usefulness of the proposed methodology is finally demonstrated by analyzing a real dataset.