Stochastic Modelling for a System with Two Types of Failure and Possibility of Wrong Diagnosis on Major Failure

Abstract

The present paper investigates a single-unit system where a failed system is inspected by a first repairman to see if it has a major or minor failure. Minor faults are rectified by the first repairman; however major faults require a second opinion on the type of failure from another repairman, referred to as the second repairman. The second repairman might or might not concur with the first. If the second repairman agrees with the first, the repair is completed by the second; if he does not agree, a third opinion is sought from an expert repairman. Following the third opinion, the system is repaired by an expert repairman, whether the third opinion agreed with either of the previous two opinions or contradicted with both. The Markov and regenerative processes are used to derive reliability, availability, and other system profitability measures. The system's profit equation, sensitivity functions are also determined and the derived measures are demonstrated with numerical examples.