Reliability Analysis of a System Subject to Partial and Catastrophic Failures

Int J Math, Eng, Manag Sci

2019

The goal of the present study is to investigate the availability and the reliability of the system, which has two dissimilar units in the parallel network under copula. Other key parameters, such as mean time to failure (MTTF) and expected profit are also evaluated. Simultaneous malfunctioning of units, common cause failure and human fault are the causes of system breakdown. The present mathematical model is examined under the assumption that each failure rate is constant and is exponentially distributed. The system undergoes repair in the completely failed state as well as in degraded state. In the case of complete failure, the system is repaired by two repair facilities and that are tackled by utilizing Gumbel-Hougaard family copula. The present system has been studied by applying the concepts of probability theory, supplementary variable technique and Laplace transformation.

Section: Introductionmentioning

confidence: 99%

Reliability Measures of Two Dissimilar Units Parallel System Using Gumbel-Hougaard Family Copula

Chopra

Int J Math, Eng, Manag Sci

2019

“…The literature of reliability consists of bunch of studies on the reliability and cost-benefit analysis of various systems. Earlier researchers including Gupta and Agarwal (1984), Kontoleon and Kontoleon (1974), Dhillon and Yang (1992a, b, 1993) and Gupta and Sharma (1993) have reported a substantial amount of work in the field of reliability analysis, by considering complex systems with different failure and repair polices.…”

Section: Introductionmentioning

confidence: 99%

Stochastic analysis of two non-identical unit parallel system incorporating waiting time

Chopra

2017

IJQRM

Purpose The purpose of this paper is to evaluate various reliability metrics such as transition state probabilities, availability, reliability, mean time to failure and expected profit of two non-identical unit parallel system incorporating waiting time. Design/methodology/approach The present paper investigates the reliability of two non-identical unit parallel system with two types of failures: common cause failure and partial failure. Moreover, waiting time to repair, a significant aspect of reliability analysis, has also been incorporated. The considered system is assumed to function properly if at least one of the units is in operative mode. The present system is examined by using the supplementary variable technique and Laplace transformation. Findings Numerical calculation shows that the availability and the reliability of the system is minimum when the system is without partial failure and is maximum when the system is free from common cause failure. Finally, the cost analysis of the system reveals that the expected profit decreases with increase in service cost. Originality/value This paper presents a mathematical model of two dissimilar unit parallel system, through which the performance of the considered system can be improved.

“…Moreover not only the occurrence of an event is important but also the manner in which it takes place. Some earlier researchers including Yang (1992, 1993); Gupta and Sharma (1993); Pan (1997); Philip and Deans (1997); Kumar and Ram (2014) developed different mathematical models with identical unit systems, common cause failure and they computed the reliability measures such as availability, reliability, mean time to failure (MTTF), mean time between failure (MTBF) and profit function of a complex engineering system with different type of failures (Kontoleon and Kontoleon, 1974;Bao and Cui, 2010; and one type of repair. Many researchers have analysed different types of systems with different failures.…”

Section: Introductionmentioning

confidence: 99%

Reliability Measures Analysis of an Industrial System under Standby Modes and Catastrophic Failure

International Journal of Operations Research and Information Systems

Manglik

2016

The objective of this research paper is, to present the reliability measures of a model by representing an industrial system having three subsystems. Two of the subsystems have standby unit while the third one has n units in parallel configuration. The entire system can fail due to a failure in subsystems or due to the catastrophic failure. The system failure and the repair rates are assumed to be constant. Markov and supplementary variable methodologies have been used to achieve the mathematical analysis of this model. Generalized expressions of state probabilities, system availability, reliability, mean time to failure, mean time to repair, cost analysis and sensitivity analysis are developed. Graphs for the resulting expressions have been shown.