Properties of Residual Cumulative Sharma–Taneja–Mittal Model and Its Extensions in Reliability Theory with Applications to Human Health Analysis and Mixed Coherent Mechanisms

The entropy measure of residual cumulative Sharma-Taneja-Mittal is an alternative measure of uncertainty for residual cumulative entropy. This study investigates further theoretical properties and develops nonparametric estimation procedures for the proposed measure. The performance of the estimator is evaluated through simulation experiments, and its practical relevance is illustrated using a real-world dataset on malignant tumor cases. Moreover, we investigate the properties of its dynamic version, including stochastic comparisons and its connections with the hazard rate function, mean residual function, and equilibrium random variables. Moreover, we introduce an alternative version of dynamic residual cumulative Sharma-Taneja-Mittal entropy and examine its monotonic properties. Additionally, we discuss this alternative version and its conditional form in the circumstances of record values. We introduce this alternative expression for the residual lifespan of upper record quantities in general distributions, characterizing it as a measure of upper record quantities derived from a distribution of uniform. Since Sharma-Taneja-Mittal entropy measures uncertainty, we also investigate its use in determining the entropy of the lifespan of mixed and coherent mechanisms, in which the lives of its constituent components are identically distributed and independent.