Bi-objective Reliability Optimization of Switch-Mode k-out-of-n Series–Parallel Systems with Active and Cold Standby Components Having Failure Rates Dependent on the Number of Components

The redundancy allocation problem (RAP) of non-repairable series-parallel systems considering cold standby components and imperfect switching mechanism has been traditionally formulated with the objective of maximizing a lower bound on system reliability instead of exact system reliability. This objective function has been considered due to the difficulty of determining a closed-form expression for the system reliability equation. But, the solution that maximizes the lower bound for system reliability does not necessarily maximize exact system reliability and thus, the obtained system reliability may be far from the optimal reliability. This article attempts to overcome the mentioned drawback. Under the assumption that component time-to-failure is distributed according to an Erlang distribution and switch time-to-failure is exponentially distributed, a closed-form expression for the subsystem cold standby reliability equation is derived by solving an integrodifference equation. A semi-analytical expression is also derived for the reliability equation of a subsystem with mixed redundancy strategy. The accuracy and the correctness of the derived equations are validated analytically. Using these equations, the RAP of non-repairable series-parallel systems with a choice of redundancy strategies is formulated. The proposed mathematical model maximizes exact system reliability at mission time given system design constraints. Unlike most of the previous formulations, the possibility of using heterogeneous components in each subsystem is provided so that the active components can be of one type and the standby ones of the other. The results of an illustrative example demonstrate the high performance of the proposed model in determining optimal design configuration and increasing system reliability.

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A Gibbs-type Phenomenon in the Failure Rates of Parallel Systems

Technometrics ◽

10.1080/00401706.1971.10488832 ◽

1971 ◽

Vol 13 (3) ◽

pp. 692-695 ◽

Cited By ~ 1

Author(s):

Maurice C. Bryson

Keyword(s):

Parallel Systems ◽

Failure Rates

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Analysis of Availability and Reliability for Repairable Parallel Systems with Different Failure Rates

Asian Journal of Information Technology ◽

10.3923/ajit.2010.231.237 ◽

2010 ◽

Vol 9 (4) ◽

pp. 231-237 ◽

Cited By ~ 7

Author(s):

M.A. El-Damcese ◽

N.S. Temraz

Keyword(s):

Parallel Systems ◽

Failure Rates

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The Robust Cold Standby Redundancy Allocation in Series-Parallel Systems With Budgeted Uncertainty

IEEE Transactions on Reliability ◽

10.1109/tr.2015.2416214 ◽

2015 ◽

Vol 64 (2) ◽

pp. 799-806 ◽

Cited By ~ 20

Author(s):

Mohammad Javad Feizollahi ◽

Roya Soltani ◽

Hadi Feyzollahi

Keyword(s):

Parallel Systems ◽

Redundancy Allocation ◽

Cold Standby ◽

In Series ◽

Budgeted Uncertainty

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COMBINED SERIES AND PARALLEL SYSTEMS SUBJECT TO INDIVIDUAL VERSUS OVERARCHING DEFENSE AND ATTACK

Asia Pacific Journal of Operational Research ◽

10.1142/s021759591250056x ◽

2013 ◽

Vol 30 (02) ◽

pp. 1250056 ◽

Cited By ~ 8

Author(s):

KJELL HAUSKEN

Keyword(s):

Parallel Systems ◽

Series System ◽

Number Of Components ◽

Unit Costs ◽

Special Cases ◽

In Series ◽

Individual Protection ◽

Overarching Protection ◽

Series Systems ◽

Analytical Expressions

A system of components can be in series, parallel, or combined series/parallel. The components and system are protected individually and overarchingly by a defender, and attacked individually and overarchingly by an attacker. Both layers of protection have to be breached for an attack to be successful. Each component, and the system as a whole, have vulnerabilities determined by individual and overarching protection and attack. The agents choose their effort variables simultaneously and independently to maximize their utilities. Each component and the system have unit costs of protection and attack, and a contest intensity. We show for both the parallel and series systems that the defender always prefers overarching and individual protection and attack, while the attacker always prefers individual protection and attack. Analytical expressions are developed for the agents' effort variables, each individual component's vulnerability, and the system vulnerability. The expenditure ratio, between individual protection and attack, and overarching protection and attack, is shown to increase in the number of components for the parallel system, and decrease in the number of components for the series system. Special cases are considered and interpreted. Comparisons are made with only individual protection and attack. The model is applicable to determine how the defender and attacker should strike the balance between choosing efforts to protect and attack components individually versus overarchingly.

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