DETECTION OF RELIABLE SOFTWARE USING SPRT

Abstract

In Classical Hypothesis testing volumes of data is to be collected and then the conclusions are drawn which may take more time. But, Sequential Analysis of statistical science could be adopted in order to decide upon the reliable / unreliable of the developed software very quickly. The procedure adopted for this is, Sequential Probability Ratio Test (SPRT). In the present paper, we have proposed the performance of SPRT on Time domain data using exponential imperfect debugging model and analyzed the results by applying on 5 data sets. The parameters are estimated by using Maximum Likelihood Estimation. Wald's procedure is particularly relevant if the data is collected sequentially. Sequential Analysis is different from that of Classical Hypothesis Testing where the number of cases tested or collected, is fixed at the beginning of the experiment. In Classical Hypothesis Testing, the data collection is executed without analysis and consideration of the data. After all the data is collected the analysis is done, conclusions are drawn. However, in Sequential Analysis every case is analyzed directly after being collected, the data collected up to that moment is then compared with certain threshold values, incorporating the new information obtained from the freshly collected case. This approach allows one to draw conclusions during the data collection, and a final conclusion can possibly be reached at a much earlier stage as is the case in Classical Hypothesis Testing. The advantages of Sequential Analysis is easily seen. As data collection can be terminated after fewer cases and decisions taken earlier, the savings in terms of human life and misery, and financial savings, might be considerable. In the analysis of software failure data, we often deal with either Time Between Failures or failure count in a given time interval. If it is further assumed that the average number of recorded failures in a given time interval is directly proportional to the length of the interval and the random number of failure occurrences in the interval is explained by a Poisson process, then we know that the probability equation of the stochastic process representing the failure occurrences is given by a homogeneous poisson process with the expression     ! n