Monotonicity Properties of Residual Lifetimes of Parallel Systems and Inactivity Times of Series Systems With Heterogeneous Components

Abstract

Here, we discuss the stochastic comparison of residual lifetimes of parallel systems and inactivity times of series systems by means of the reversed hazard rate order when the components of the systems are independent but not necessarily identically distributed. We also establish some monotonicity properties of such residual lifetimes of parallel systems and inactivity times of series systems. These results extend some of the recent results in this direction due to Zhao, Li, and Balakrishnan [21], Kochar and Xu [12], and Saledi and Asadi [16].

Reliability analysis of fail-safe systems with heterogeneous and dependent components subject to random shocks

“…6 Reliability analysis on k -out-of- n systems has attracted extensive attention from many scholars during the past several years. On one hand, a large amount of work has appeared on the studies of residual lifetime and inactivity time, and effects of the heterogeneity and dependence among components lifetimes on system lifetimes; see for example Ding et al 7 On the other hand, many researchers focused on their attention on reliability improvement of k -out-of- n systems by introducing redundant components; see for example Refs., 8–11 and references therein.…”

On inactivity times of failed components of coherent system under double monitoring

“…For instance, Zhao et al [43] investigated stochastic monotone properties of the inactivity time on 𝑘-out-of-𝑛 systems with the independent and nonidentically distribution. Interested readers may refer to Navarro et al [34], Li and Lu [23], Kayid and Ahmad [20], Asadi [3], Khaledi and Shaked [21], Li and Zhao [25], Li and Zhang [24], Goliforushani and Asadi [16], Ding et al [13], Balakrishnan and Zhao [4], Gupta et al [19], Navarro [31], Salehi and Tavangar [37], and Amini-Seresht et al [1]. Besides, the inactivity times of components in the coherent system are also an important topic in many practical scenarios.…”