Lifetimes Of Parallel Systems Research Articles

Stochastic Comparisons of Lifetimes of Series and Parallel Systems with Dependent Heterogeneous MOTL-G Components under Random Shocks

To measure the magnitude among random variables, we can apply a partial order connection defined on a distribution class, which contains the symmetry. In this paper, based on majorization order and symmetry or asymmetry functions, we carry out stochastic comparisons of lifetimes of two series (parallel) systems with dependent or independent heterogeneous Marshall–Olkin Topp Leone G (MOTL-G) components under random shocks. Further, the effect of heterogeneity of the shape parameters of MOTL-G components and surviving probabilities from random shocks on the reliability of series and parallel systems in the sense of the usual stochastic and hazard rate orderings is investigated. First, we establish the usual stochastic and hazard rate orderings for the lifetimes of series and parallel systems when components are statistically dependent. Second, we also adopt the usual stochastic ordering to compare the lifetimes of the parallel systems under the assumption that components are statistically independent. The theoretical findings show that the weaker heterogeneity of shape parameters in terms of the weak majorization order results in the larger reliability of series and parallel systems and indicate that the more heterogeneity among the transformations of surviving probabilities from random shocks according to the weak majorization order leads to larger lifetimes of the parallel system. Finally, several numerical examples are provided to illustrate the main results, and the reliability of series system is analyzed by the real-data and proposed methods.

A comprehensive result on stochastic comparison for parallel systems in terms of hazard rate order

In this paper, we investigate ordering properties of lifetimes of parallel systems consisting of two components with respect to hazard rate order. By a uniform method, we provide a relatively comprehensive sufficient condition for hazard rate ordering between the lifetimes of two parallel systems. The result established in this paper extends most results known in the literature this far.

Stochastic comparisons of parallel systems with exponentiated Weibull components

The exponentiated Weibull (EW) distribution is the first generalization of the two-parameter Weibull distribution to accommodate nonmonotone hazard rates, including the bathtub shaped hazard rate. In this paper, we discuss stochastic comparisons of parallel systems with exponentiated Weibull components in terms of the usual stochastic order, dispersive order and the likelihood ratio order. We give some sufficient conditions for stochastic comparisons between lifetimes of parallel systems.

On the right spread ordering of parallel systems with two heterogeneous components

This article discusses the variability ordering of lifetimes of parallel systems with two independent heterogeneous exponential components in terms of the right spread order. It is proved, among others, that the reciprocal majorization order between the two hazard rate vectors implies the right spread order between the lifetimes of two parallel systems. The result is then extended to the proportional hazard rate model as well. The results established here extend and enrich those known in the literature.

On hazard rate ordering of parallel systems with two independent components

This note builds a sufficient condition for the hazard rate ordering between lifetimes of parallel systems with two independent components having proportional hazard rates. Some comparisons on lifetimes of such systems with general components are also obtained.