Exponential order statistic models of software reliability growth

Failure times of a software reliabilty growth process are modeled as order statistics of independent, nonidentically distributed exponential random variables. The Jelinsky-Moranda, Goel-Okumoto, Littlewood, Musa-Okumoto Logarithmic, and Power Law models are all special cases of Exponential Order Statistic Models, but there are many additional examples also. Various characterizations, properties and examples of this class of models are developed and presented

Confidence intervals for reliability growth models with small sample sizes

Fully Bayesian approaches to analysis can be overly ambitious where there exist realistic limitations on the ability of experts to provide prior distributions for all relevant parameters. This research was motivated by situations where expert judgement exists to support the development of prior distributions describing the number of faults potentially inherent within a design but could not support useful descriptions of the rate at which they would be detected during a reliability-growth test. This paper develops inference properties for a reliability-growth model. The approach assumes a prior distribution for the ultimate number of faults that would be exposed if testing were to continue ad infinitum, but estimates the parameters of the intensity function empirically. A fixed-point iteration procedure to obtain the maximum likelihood estimate is investigated for bias and conditions of existence. The main purpose of this model is to support inference in situations where failure data are few. A procedure for providing statistical confidence intervals is investigated and shown to be suitable for small sample sizes. An application of these techniques is illustrated by an example

An Empirical analysis of Open Source Software Defects data through Software Reliability Growth Models

The purpose of this study is to analyze the reliability growth of Open Source Software (OSS) using Software Reliability Growth Models (SRGM). This study uses defects data of twenty five different releases of five OSS projects. For each release of the selected projects two types of datasets have been created; datasets developed with respect to defect creation date (created date DS) and datasets developed with respect to defect updated date (updated date DS). These defects datasets are modelled by eight SRGMs; Musa Okumoto, Inflection S-Shaped, Goel Okumoto, Delayed S-Shaped, Logistic, Gompertz, Yamada Exponential, and Generalized Goel Model. These models are chosen due to their widespread use in the literature. The SRGMs are fitted to both types of defects datasets of each project and the their fitting and prediction capabilities are analysed in order to study the OSS reliability growth with respect to defects creation and defects updating time because defect analysis can be used as a constructive reliability predictor. Results show that SRGMs fitting capabilities and prediction qualities directly increase when defects creation date is used for developing OSS defect datasets to characterize the reliability growth of OSS. Hence OSS reliability growth can be characterized with SRGM in a better way if the defect creation date is taken instead of defects updating (fixing) date while developing OSS defects datasets in their reliability modellin

Prediction intervals for reliability growth models with small sample sizes

Engineers and practitioners contribute to society through their ability to apply basic scientific principles to real problems in an effective and efficient manner. They must collect data to test their products every day as part of the design and testing process and also after the product or process has been rolled out to monitor its effectiveness. Model building, data collection, data analysis and data interpretation form the core of sound engineering practice.After the data has been gathered the engineer must be able to sift them and interpret them correctly so that meaning can be exposed from a mass of undifferentiated numbers or facts. To do this he or she must be familiar with the fundamental concepts of correlation, uncertainty, variability and risk in the face of uncertainty. In today's global and highly competitive environment, continuous improvement in the processes and products of any field of engineering is essential for survival. Many organisations have shown that the first step to continuous improvement is to integrate the widespread use of statistics and basic data analysis into the manufacturing development process as well as into the day-to-day business decisions taken in regard to engineering processes.The Springer Handbook of Engineering Statistics gathers together the full range of statistical techniques required by engineers from all fields to gain sensible statistical feedback on how their processes or products are functioning and to give them realistic predictions of how these could be improved

Statistical modelling of software reliability

During the six-month period from 1 April 1991 to 30 September 1991 the following research papers in statistical modeling of software reliability appeared: (1) A Nonparametric Software Reliability Growth Model; (2) On the Use and the Performance of Software Reliability Growth Models; (3) Research and Development Issues in Software Reliability Engineering; (4) Special Issues on Software; and (5) Software Reliability and Safety

Generalized Exponentiated Moment Exponential Distribution

Moment distributions have a vital role in mathematics and statistics, in particular in probability theory, in the perspective research related to ecology, reliability, biomedical field, econometrics, survey sampling and in life-testing. Hasnain (2013) developed an exponentiated moment exponential (EME) distribution and discussed some of its important properties. In the present work, we propose a generalization of EME distribution which we call it generalized EME (GEME) distribution and develop various properties of the distribution. We also present characterizations of the distribution in terms of conditional expectation as well as based on hazard function of the GEME random variable

Computational Methods in Survival Analysis

Survival analysis is widely used in the fields of medical science, pharmaceutics, reliability and financial engineering, and many others to analyze positive random phenomena defined by event occurrences of particular interest. In the reliability field, we are concerned with the time to failure of some physical component such as an electronic device or a machine part. This article briefly describes statistical survival techniques developed recently from the standpoint of statistical computational methods focussing on obtaining the good estimates of distribution parameters by simple calculations based on the first moment and conditional likelihood for eliminating nuisance parameters and approximation of the likelihoods. The method of partial likelihood (Cox, 1972, 1975) was originally proposed from the view point of conditional likelihood for avoiding estimating the nuisance parameters of the baseline hazards for obtaining simple and good estimates of the structure parameters. However, in case of heavy ties of failure times calculating the partial likelihood does not succeed. Then the approximations of the partial likelihood have been studied, which will be described in the later section and a good approximation method will be explained. We believe that the better approximation method and the better statistical model should play an important role in lessening the computational burdens greatly. --

Estimation in a discrete tail rate family of recapture sampling models

In the context of recapture sampling design for debugging experiments the problem of estimating the error or hitting rate of the faults remaining in a system is considered. Moment estimators are derived for a family of models in which the rate parameters are assumed proportional to the tail probabilities of a discrete distribution on the positive integers. The estimators are shown to be asymptotically normal and fully efficient. Their fixed sample properties are compared, through simulation, with those of the conditional maximum likelihood estimators