Empirical Bayes estimation of software failures

The empirical Bayes estimator is applied to software failures production. The time between failures data registered up to a given time, are used in order to estimate the probability of failure appearance dur- ing the next interval time. This method is similar to the estimation of n-grams in natural language processing. A modi ed expression to the estimator usually used in language and speech processing is introduced in order to follow the failures production curve. Results of simulations comparing well with experimental data are also shown.Sociedad Argentina de Informática e Investigación Operativa (SADIO

On the asymptotic analysis of Littlewood's reliability model for modular software

International audienceWe consider a Markovian model, proposed by Littlewood, to assess the reliability of a modular software. Speci cally , we are interested in the asymptotic properties of the corresponding failure point process. We focus on its time-stationary version and on its behavior when reliability growth takes place. We prove the convergence in distribution of the failure point process to a Poisson process. Additionally, we provide a convergence rate using the distance in variation. This is heavily based on a similar result of Kabanov, Liptser and Shiryayev, for a doubly-stochastic Poisson process where the intensity is governed by a Markov process

Empirical Bayes estimation of software failures

The empirical Bayes estimator is applied to software failures production. The time between failures data registered up to a given time, are used in order to estimate the probability of failure appearance dur- ing the next interval time. This method is similar to the estimation of n-grams in natural language processing. A modi ed expression to the estimator usually used in language and speech processing is introduced in order to follow the failures production curve. Results of simulations comparing well with experimental data are also shown.Sociedad Argentina de Informática e Investigación Operativa (SADIO

Compound and Non Homogeneous Poisson Software Reliability Models

The efficiency of two Software Reliability growth models are analyzed. The most popular based on a non homogeneous Poisson process and the less known based on a compound Poisson process. Several experimental data are used in order to analyze the goodness of fit of both models. The importance of the estimation method for the parameters involved is also analyzed.Sociedad Argentina de Informática e Investigación Operativ

Critical Fault-Detecting Time Evaluation in Software with Discrete Compound Poisson Models

Software developers predict their product’s failure rate using reliability growth models that are typically based on nonhomogeneous Poisson (NHP) processes. In this article, we extend that practice to a nonhomogeneous discrete-compound Poisson process that allows for multiple faults of a system at the same time point. Along with traditional reliability metrics such as average number of failures in a time interval, we propose an alternative reliability index called critical fault-detecting time in order to provide more information for software managers making software quality evaluation and critical market policy decisions. We illustrate the significant potential for improved analysis using wireless failure data as well as simulated data

Software Reliability Modeling

International audienceSoftware Reliability Modelin

COMPOUND-POISSON SOFTWARE-RELIABILITY MODEL

The probability density estimation of the number of software failures in the event of clustering or clumping of the software failures is the subject of this paper. A discrete compound Poisson (CP) prediction model, as opposed to a Poisson (P) process, is proposed for the random variable (rv) X(rem), which is the remaining number of software failures. The compounding distributions, which are assumed to govern the failure sizes at Poisson arrivals, are respectively taken to be geometric when failures are forgetful and logarithmic-series (LSD) when failures are contagious. The expected value (mu) of X(rem) of CP is calculated as a function of the time-dependent Poisson and compounding distribution based on the failures experienced. Also, the q (variance/mean) parameter for the remaining number of failures, q(rem) is best estimated by q(past) from the failures already experienced. Then, one obtains the pdf of the remaining number of failures estimated by CP(mu,q). The CP model suggests that the CP is superior to Poisson where clumping of failures exists. Its predictive validity is comparable to Musa-Okumoto's (MO) Log-Poisson Model for certain software failure data with q > 1 when software failures clump within the same CPU second or unit time

Alternative parameter estimation methods for the compound poisson software reliability model with clustered failure data

The 'compound Poisson' (CP) software reliability model was proposed previously by the first named author for time-between-failure data in terms of CPU seconds, using the 'maximum likelihood estimation' (MLE) method to estimate unknown parameters; hence, CPMLE. However, another parameter estimation technique is proposed under 'nonlinear regression analysis' (NLR) for the compound Poisson reliability model, giving rise to the name CPNLR. It is observed that the CP model, with different parameter estimation methods, produces equally satisfactory or more favourable results as compared to the Musa-Okumoto (M-O) model, particularly in the event of grouped or clustered (clumped) software failure data. The sampling unit may be a week, day or month within which the failures are clumped, as the error recording facilities dictate in a software testing environment. The proposed CPNLR and CPMLE yield comparatively more favourable results for certain software failure data structures where the frequency distribution of the cluster (clump) size of the software failures per week displays a negative exponential behaviour. Average relative error (ARE), mean squared error (MSE) and average Kolmogorov-Smirnov (K-S Av.Dn) statistics are used as measures of forecast quality for the proposed and competing parameter-estimation techniques in predicting the number of remaining future failures expected to occur until a target stopping time. Comparisons on five different simulated data sets that contain weekly recorded software failures are made to emphasize the advantages and disadvantages of the competing methods by means of the chronological prediction plots around the true target value and zero per cent relative error line. The proposed generalized compound Poisson (MLE and NLR) methods consistently produce more favourable predictions for those software failure data with negative exponential frequency distribution of the failure clump size versus number of weeks. Otherwise, the popularly used competing M-O log-Poisson model is a better fit for those data with a uniform clump size distribution to recognize the log-Poisson effect while the logarithm of the Poisson equation is a constant, hence uniform. The software analyst is urged to perform exploratory data analysis to recognize the nature of the software failure data before favouring a particular reliability estimation method. © 1997 by John Wiley & Sons, Ltd