On stochastic comparisons ofk-out-of-nsystems with Weibull components

Abstract

In this paper we prove that a parallel system consisting of Weibull components with different scale parameters ages faster than a parallel system comprising Weibull components with equal scale parameters in the convex transform order when the lifetimes of components of both systems have different shape parameters satisfying some restriction. Moreover, while comparing these two systems, we show that the dispersive and the usual stochastic orders, and the right-spread order and the increasing convex order are equivalent. Further, some of the known results in the literature concerning comparisons of k-out-of-n systems in the exponential model are extended to the Weibull model. We also provide solutions to two open problems mentioned by Balakrishnan and Zhao (2013) and Zhao et al. (2016).

A complex multi-state k-out-of-n: G system with preventive maintenance and loss of units

“…Li and Zuo (2008) extended these systems for modelling complex engineering systems with weighted k-out-of-n systems. Recently, Balakrishnan et al (2018) extends known results in the literature concerning comparisons of k-out-of-n systems in the exponential model to the Weibull model. Kumar and Ram (2017) have investigated the simultaneous effect of k-out-of-n: G/F and parallel redundancy in a complex industrial system by using Markov processes from a classical point of view.…”

“…As it has been mentioned above a comparison between the system with and without preventive maintenance is carried out. Firstly the proportional time in each macro-state up to a certain time has been calculated for both systems (with and without preventive maintenance) in transient and stationary case from (1)(2)(3)(4). It is shown in Table 5.…”

Reliability analyses of linear two-dimensional consecutive k-type systems

“…Redundant systems, such as k -out-of- n systems [2, 4, 11] and consecutive k -out-of- n systems [5, 7, 27], play an important role in reliability applications. The finite Markov chain imbedding approach (FMCIA), as the most efficient method for calculating reliabilities of these systems, was first proposed by Fu and Koutras [12], and subsequently named as such by Koutras [20].…”

Some conditional reliability properties of k-out-of-n system composed of different types of components with discrete independent lifetimes

“…It fails if n − k + 1 or more components fail. Two important particular cases of k-out-of-n systems are parallel and series ones corresponding to k = 1 and k = n. In the literature, many authors paid attention to the reliability and aging properties of k-out-of-n systems and their variants and extensions, see, for example Eryilmaz (2011Eryilmaz ( , 2012Eryilmaz ( , 2013, Navarro and Duarte (2017), , Misra and Francis (2018), Zhang et al (2018), Balakrishnan et al (2018) and Salehi et al (2019). Most of these results have been restricted to the case when the component lifetimes are independent and identically distributed.…”