Optimal Redundancy Allocation in Homogeneous Multi-State Coherent Systems

SYNOPTIC ABSTRACT

Reliability improvement and enhancing system performance through redundancy allocation are often discussed in the context of binary systems, where at any time the systems can be found in one of two states: either fully (perfectly) working or completely failed. But, in practice, the engineered systems might not always be binary. It is rather realistic to assume more than two possible states for components, as well as for the entire system. When the systems and their constituent components are no longer binary, the performance of a system depends on the particular state or level of functioning, and handling of any issues, including system definition and performance evaluation, become much more complex. Here, a performance measure of a multi-state system based on the performance probabilities at different functioning states is proposed. Not much work has been found in the literature about redundancy allocation in multi-state systems in order to improve the performance of such systems. The present work studies a homogeneous multi-state coherent system, develops basic results and relations, and provides an optimal solution to a redundancy allocation problem. The method derived here can be applied to any complex coherent multi-state system with non-overlapping or overlapping critical subsystems. Numerical examples are added to demonstrate the applicability of the proposed method.

KEY WORDS AND PHRASES:

• Homogeneous system
• multi-state system
• redundancy
• stochastic order
• system performance probability