Novel Estimators of Software Reliability for Finite Failures Category Models

Abstract

The most important characteristic of the software product is its quality. One such important measure of the quality of the software is its reliability, which is the probability of failure-free operation of a computer program in a specified environment for a specified period of time. Estimating this software reliability enables the software developers to decide whether or not the user requirements are met. It also enables the users of the software to decide whether or not to accept the software. Thus, there is a strong need for estimating the reliability of the software. Software reliability models, with certain failure time distributions are used to estimate this reliability. Software reliability models are classified based on many attributes. One such classification is based on the number of failures. Depending on the number of failures, the software reliability models have been classified into two categories: (i) finite failures category models, where the number of failures is assumed to be finite and (ii) infinite failures category models, where the number of failures is assumed to be infinite. Finite failures category models are further classified into four classes, depending on the distribution of the failure times, namely, (i) Exponential class models, (ii) Weibull class models, (iii) Gamma class models and (iv) Pareto class models. Herein, the finite failures category models are considered and the reliability are estimated for the above four classes of models using the methods of Maximum Likelihood Estimation and Minimum Variance Unbiased Estimation. Further, the bias if any, present in the Maximum Likelihood Estimators (MLEs) are found using the Minimum Variance Unbiased Estimators (MVUEs). The MLEs are then improved by removing the bias present in them, thus getting the Improved Estimators of reliability. Several sample failure time data have been used to obtain these estimators, namely, MLE, MVUE and the Improved Estimators. The three estimators are then compared through the properties satisfied by these estimators. It is found that the Improved Estimator possesses most of the desirable properties of good estimators for all finite failures category models, which indicates that the Improved Estimator is most efficient and accurate as compared to MLE and MVUE. Hence, it is concluded that the software reliability can be estimated more accurately using the Improved Estimator, for any finite failures category software reliability model.