Page 1 - SUBHARADEV SEN AND AHMED

IAPQR Transactions

IAPQR Transactions
Vol. 43, No. 1, 2018

FINITE RANGE LIFE DISTRIBUTIONS OF COHERENT
DEPENDENT SYSTEMS

SUBHRADEV SEN* AND AHMED Z. AFIFY**
*Alliance School of Business, Alliance University, Bangalore, India
**Department of Statistics, Mathematics and Insurance, Benha University, Egypt

ABSTRACT: Opposed to the general theory of infinite upper limit for lifetime
distributions, Mukherjee and Islam ([4], 1983) proposed and studied a finite range
distribution considering the fact that designed lifetime of equipment is actually
finite. It is quite rational to consider interdependency of multi-component systems in
analyzing reliability characteristics. In this article, we consider two-component
coherent dependent systems by developing bivariate finite range distribution
following the method of Farlie-Gumbel-Morgenstern copula. We investigate and
study different reliability characteristics, such as mean time to system failure,
system reliability and failure rate functions for finite range coherent dependent
systems. We also compare the dependent finite range systems with independent
finite range systems for mentioned reliability characteristics.

Keywords and Phrases: Finite range distribution, coherent dependent systems,
reliability characteristics.

1. INTRODUCTION

Most of the univariate lifetime distributions, prescribed in the literature,
have been defined over the range (0, ∞). However, the designed lifetime of
equipment may not be infinite always in view of life tests that are usually
censored or truncated. In fact, it is sometimes appropriate to consider the
lifetime (time-to-event) of equipment over a finite range. Owing to this
fact, Mukherjee and Islam ([4], 1983) introduced and studied a finite range

* Correspondence E-mail: subhradev.stat@gmail.com
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