Convergence of MLE to MVUE of reliability for exponential class software reliability models

Abstract

Software quality has become a major concern of all software manufacturers. One such measure of software quality is the reliability, which is the probability of failure-free operation of a software in a specified environment for a specified time. If T denotes the time to failure of any software, then, the reliability of this software, denoted by R(t), is given by R(t)=P(T>t). The reliability of any software can be estimated using various methods of estimation. The simplest among these methods, is the method of maximum likelihood estimation. Even though it satisfies most of the desirable properties of a good estimator, it is still not as efficient as the minimum variance unbiased estimator. In this paper, the minimum variance unbiased estimator of R(t) for exponential class software reliability models, is obtained using a procedure called blackwellization. The error in the two estimators is obtained for a model belonging to the exponential class, viz, the Jelinski - Moranda model. It is found that as the failure time increases, the difference decreases exponentially and finally both approach zero for a very large failure time