Abstract

The application of the concept of cost elasticity of reliability was extended from the parallel system to the partially redundant or k-out-of-n:G(F) system (or k-out-of-n system, for short). An expression for the cost elasticity of reliability was derived for a general k-out-of-n system. The expression yielded acceptable results for a wide range of values for k, n, and component reliability. For systems of practical interest characterized by good components, the expression became highly susceptible to round-off errors, and catastrophic cancellations took place. These numerical problems seemed unavoidable as they were inherently associated with the definition of the cost-elasticity-of-reliability metric itself. We introduced another metric, the cost elasticity of the Mean Time To Failure (MTTF), which measures the relative change in the life expectancy that can be obtained for a given relative change in cost. We believe the cost-elasticity-of-MTTF metric is a more tangible and a more cumulative measure than the cost-elasticity-of-reliability metric. We derived a very simple expression for the cost elasticity of MTTF for a k-out-of-n system and showed that it is a function of only k and n, i.e. it is independent of component characteristics such as component failure rate or component reliability. This expression is insensitive to round-off errors since it is a purely additive formula. We provided charts for the cost elasticity of MTTF that can be used to assess the cost incurred in achieving a certain life expectancy for a k-out-of-n system. These charts can be used with any coherent system, since the MTTF for a coherent system can be approximated by that of a k-out-of-n system.

Highlights

  • An important goal for reliability engineering is to achieve cost minimization [1]

  • The k-out-of-n system plays a central role for the general class of coherent systems, as it can be used to approximate the reliability of such systems [7]

  • We derive a very simple expression for ∈T,C for a k-out-of-n:G system and show that it is a function of only k and n, i.e. it is independent of component characteristics such as component failure rate or component reliability

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Summary

Introduction

An important goal for reliability engineering is to achieve cost minimization [1]. This goal has rarely been achieved, primarily because of the lack of suitable mathematical models or metrics [2]. A recently introduced metric that captures the value of reliability from a financial viewpoint is the cost elasticity of reliability [3], defined as. We extend this study by applying this new metric to a k-out-of-n:G(F) system. The k-outof-n:G(F) system is a system of n components that functions (fails) if at least k out of its n components function (fail) Situations in which this system serves as a useful model are frequently encountered in practice [6]. While virtually all nontrivial network reliability problems are known to be NP-hard for general networks, the regular structure of the k-out-of-n system allows the existence

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