On Stress-Strength Interval-System Reliability with Applications in Heart Conditions

Abstract

The random variable X represents the stress placed on the system by the operating environment and random variable Y represents the strength of the system. A system is able to perform its intended function if its strength is greater than the stress imposed upon it. Reliability of the system is defined as the probability that the system is strong enough to overcome the stress. That is, R = P(Y >X). In other words, reliability is the probability that the strengths of the unit are greater than the stresses. The stress-strength model has found interests in many applications include mechanical engineering and human heart monitoring conditions. The interval-system is defined as a system with a series of chance events that occur in a given interval of time. A k-out-of-n interval-system is a system with a series of n events in a given interval of time which successes (or functions) if and only if at least k of the events succeed (function). In short, the k-out-of-n interval-system is an interval-system which successes if and only if at least k of n events succeeds. The stress-strength reliability inference of the interval-system with a series of n independent events that occurs in a given interval of time is considered. The reliability of the interval-system is the probability that at least k out of n events in a given interval of time succeed. This paper derives uniform minimum variance unbiased and maximum likelihood reliability estimates of k-out-of-n interval-system based on stress-strength inference events where X (stress) and Y (strength) are independent two-parameter exponential random variables. An application in human heart conditions to illustrate the results is discussed.