Reliability Analysis Based on the Losses from Failures
Authors: Todinov M. T. 
Published: March 2006

The conventional reliability analysis is based on the premise that increasing the reliability of a system will decrease the losses from failures. On the basis of counterexamples, it is demonstrated that this is valid only if all failures are associated with the same losses. In case of failures associated with different losses, a system with larger reliability is not necessarily characterized by smaller losses from failures. Consequently, a theoretical framework and models are proposed for a reliability analysis, linking reliability and the losses from failures. Equations related to the distributions of the potential losses from failure have been derived. It is argued that the classical risk equation only estimates the average value of the potential losses from failure and does not provide insight into the variability associated with the potential losses. Equations have also been derived for determining the potential and the expected losses from failures for nonrepairable and repairable systems with components arranged in series, with arbitrary life distributions. The equations are also valid for systems/components with multiple mutually exclusive failure modes. The expected losses given failure is a linear combination of the expected losses from failure associated with the separate failure modes scaled by the conditional probabilities with which the failure modes initiate failure. On this basis, an efficient method for simplifying complex reliability block diagrams has been developed. Branches of components arranged in series whose failures are mutually exclusive can be reduced to single components with equivalent hazard rate, downtime, and expected costs associated with intervention and repair. A model for estimating the expected losses from early‐life failures has also been developed. For a specified time interval, the expected losses from early‐life failures are a sum of the products of the expected number of failures in the specified time intervals covering the early‐life failures region and the expected losses given failure characterizing the corresponding time intervals. For complex systems whose components are not logically arranged in series, discrete simulation algorithms and software have been created for determining the losses from failures in terms of expected lost production time, cost of intervention, and cost of replacement. Different system topologies are assessed to determine the effect of modifications of the system topology on the expected losses from failures. It is argued that the reliability allocation in a production system should be done to maximize the profit/value associated with the system. Consequently, a method for setting reliability requirements and reliability allocation maximizing the profit by minimizing the total cost has been developed. Reliability allocation that maximizes the profit in case of a system consisting of blocks arranged in series is achieved by determining for each block individually the reliabilities of the components in the block that minimize the sum of the capital, operation costs, and the expected losses from failures. A Monte Carlo simulation based net present value (NPV) cash‐flow model has also been proposed, which has significant advantages to cash‐flow models based on the expected value of the losses from failures per time interval. Unlike these models, the proposed model has the capability to reveal the variation of the NPV due to different number of failures occurring during a specified time interval (e.g., during one year). The model also permits tracking the impact of the distribution pattern of failure occurrences and the time dependence of the losses from failures.