Abstract
Any given system can be represented as a parallel arrangement of series structures. Motivated by this fact, a general family of distributions is introduced, by adding two extra parameters to a distribution (called baseline distribution),twice compounding with power series distribution. The new family can allow various hazard rate curves that compete well with other alternatives in fitting real data. We derive formal expressions for its moments, generating function, mean residual lifetime and other reliability functions. Certain characterizations of the new family are presented in terms of the ratio of two truncated moments as well as based on the hazard rate function. The maximum likelihood estimation technique is used to estimate the model parameters and a simulation study is conducted to investigate the performance of the maximum likelihood estimates. Finally, two applications of the model with real data sets are presented to illustrate the usefulness of the proposed distribution.
Highlights
The reliability of the parallel and series systems with a random number of components has extensive literature
The purpose of this paper is to introduce a new family of lifetime distributions by compounding a lifetime distribution and twice the power series distribution, which is referred to as the lifetime PS2 family of distributions
The lifetime PS2 family of distributions contains as special cases all the compounded lifetime distributions constructed by Marshall and Olkin method such as the generalized exponential geometric distribution [4], exponential power series [9], Weibull power series [22], exponentiated extended Weibull power series [32] and the inverse Weibull geometric distribution [20]
Summary
The reliability of the parallel and series systems with a random number of components has extensive literature. Throughout the last two decades, several distributions have been proposed to model the lifetime of systems with an unknown number of components. These new distributions are built by compounding a lifetime distribution and a member of the power series family of distributions in series or parallel arrangement. Let U denote the number of components in a system connected in series or parallel structures and let Xi denote the lifetime of the ith component. Marshall and Olkin [21] proposed adding a parameter to the lifetime distribution through compounding with the geometric distribution. Flores et al [15] proposed the complementary EPS distribution, complementary to the EPS distribution
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Statistics, Optimization & Information Computing
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
