Towards a Parallel System

1983 ◽  
pp. 416-439
Author(s):  
Renato De Mori
Keyword(s):  
Parallel System

On stochastic comparisons of k-out-of-n systems with Weibull components

2018 ◽  
Vol 55 (1) ◽  
pp. 216-232 ◽  
Author(s):  
Narayanaswamy Balakrishnan ◽  
Ghobad Barmalzan ◽  
Abedin Haidari
Keyword(s):  
Weibull Model ◽  
Exponential Model ◽  
Parallel System ◽  
Stochastic Orders ◽  
Open Problems ◽  
Increasing Convex Order ◽  
Scale Parameters ◽  
Convex Transform Order ◽  
Right Spread Order ◽  
The Right

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).

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