Construction of optimal reliability test plans for binary type multi-state strongly coherent systems

Abstract

The concept of Binary Type Multi-State Strongly Coherent System (BTMSCS) or Multi-State Coherent System of Type 2 (MCS of type 2) has been defined by Natvig (1982). In this research article component based optimal reliability test plans for BTMSCS have been proposed. Here it is assumed that these systems are made up of n components, and the random variables representing lifetimes of systems and their components take values in set $S=\{0,1,2,\dots ,(M-1),M\} \text{with} M\ge 2.$ The construction of reliability test plans for BTMSCS is based on the use of (i) multivariate counting processes with marginal counting processes being homogeneous Poisson processes and (ii) positively upper orthant dependent property of the associated renewal processes. The applicability of the proposed reliability test plans has been demonstrated using all the three BTMSCSs made up of two components and one system consisting of three components with $S=\{0,1,2\}$ under the assumption that $(T_{i1},T_{i2}),$ a bivariate random vector representing times spent by the ith component in states 1 and 2, follows Farlie-Gumbel-Morgenstern distribution with exponential marginals.

Keywords:

• Binary type multi-state coherent system
• Farlie-Gumbel-Morgenstern distribution
• multivariate point processes
• positively quadrant dependent
• reliability test plan