Sequential Sampling Designs for Estimating Software Reliability

Title from PDF of title page viewed August 25, 2020Dissertation advisors: Kamel Rekab and Paul RulisVitaIncludes bibliographical references (pages 58-62)Thesis (Ph.D.)--Department of Mathematics and Statistics and Department of Physics and Astronomy. University of Missouri--Kansas City, 2020For any non-trivial system, it is impossible to reach the exact reliability of software due to the complexity, cost, and time required to complete the testing. Instead, a sample of test cases can be used to estimate the overall software reliability. Our objective is to obtain the most accurate estimate of software reliability by allocating test cases among partitions. In the traditional approach, the method of allocating test cases among partitions is determined before reliability testing begins. By allocating test cases in advance, there is no opportunity to take advantage of the errors in choosing the distributions of test cases that may occur during the testing of the software. The inability to use these errors to adjust the estimate during testing is a shortcoming of a fixed sampling scheme. We applied sequential sampling schemes to make allocation decisions dynamically throughout the testing process. Under these sampling schemes, we can refine the allocation of test cases sequentially based on the information gained as the testing proceeds. Using theoretical results and Monte Carlo simulation, we have shown that the proposed sequential sampling scheme performs at least as well as the balanced sampling scheme.Introduction -- A fully sequential sampling scheme for software reliability estimation -- A Two-Stage Sampling Scheme for Software Reliability Estimation -- Summary and conclusion -- Appendi

Sequential Designs with Application in Software Engineering

Title from PDF of title page, viewed on March 31, 2014Dissertation advisor: Kamel RakabVitaIncludes bibliographical references (pages 77-81)Thesis (Ph. D.)--Dept. of Mathematics and Statistics and Dept. of Computer Science and Electrical Engineering. University of Missouri, Kansas City, 2013Presented here is a Bayesian approach to test case allocation in the software reliability estimation. Bayesian analysis allows us to update our beliefs about the reliability of a particular partition as we test, and thus, dynamically re refine our allocation of test cases during the reliability testing process. We started with a fully sequential sampling scheme to estimate the reliability of a software system using partition testing. We have shown both theoretically and through simulation that the proposed scheme always performs at least as well as fixed sampling approaches where test case allocation is predetermined, and in all but the most unlikely circumstances, outperform them. Based on the sequential allocation, a multistage sampling scheme is established, which is less time consuming and more e efficient. Meanwhile, an e efficient sampling scheme is also developed to accommodate more situations. In the last chapter, we extend our study from parallel systems to series systems. We again use a Bayesian approach to allocate test cases to estimate the reliability of a series system with two components. A second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound for the incurred Bayes risk is established theoretically and Monte Carlo simulations with several proposed sequential designs are implemented to achieve this second-order lower bound.Abstract -- List of tables -- List of notations -- Acknowledgement -- Introduction -- A fully sequential test allocation for software reliability estimation -- A multistage sequential test allocation for software reliability estimation -- An efficient test allocation for software reliability estimation -- Test allocation for estimating reliability of series systems with two components -- Summary and conclusion -- Appendix -- Tables -- Referenc

Sampling Schemes For Estimating Software Reliability

Title from PDF of title page, viewed January 4, 2023Dissertation advisors: Kamel Rekab and Elizabeth StoddardVitaIncludes bibliographical references (pages 59-63)Dissertation (Ph.D.)--Department of Mathematics and Statistics, Department of Physics and Astronomy. University of Missouri--Kansas City, 2022Any software system of non-trivial size cannot be easily and completely tested because the domain of all possible inputs is complex and very large. In this study, we use a technique called partition testing, in which we divide the input domain of all potential testing cases D into K ≥ 2 non-overlapping sub-domains. Each sub-domain can therefore be tested independently from the others. We employ two methods, a fully sequential method and two-stages method, that are based on a sample of the test cases to allocate the test cases among partitions and minimize the variance of estimated software reliability when usage probabilities are random. These methods allow us to take advantages from the previous testing as we test and, as a result, dynamically improve the distribution of test cases throughout the reliability testing process. By dynamically allocating test cases to partitions, these methods aim to minimize the variance of the reliability estimation. The variance incurred by fully sequential method and the variance incurred by two-stages method are compared with the variance incurred by the optimal and the variance incurred by the balanced sampling method. Using theoretical results and a Monte Carlo simulation, the fully sampling method and the two-stages method perform better than the balanced sampling method and are nearly optimal.Introduction -- Software reliability estimation for K partitions -- Software reliability estimation for two partitions -- Fully sequential estimation in software reliability -- Two-stage estimation in software reliability -- Monte Carlo simulations -- Summary and conclusio

Reliability demonstration for safety-critical systems

This paper suggests a new model for reliability demonstration of safety-critical systems, based on the TRW Software Reliability Theory. The paper describes the model; the test equipment required and test strategies based on the various constraints occurring during software development. The paper also compares a new testing method, Single Risk Sequential Testing (SRST), with the standard Probability Ratio Sequential Testing method (PRST), and concludes that: • SRST provides higher chances of success than PRST • SRST takes less time to complete than PRST • SRST satisfies the consumer risk criterion, whereas PRST provides a much smaller consumer risk than the requirement

On optimal designs for clinical trials: An updated review

Optimization of clinical trial designs can help investigators achieve higher qualityresults for the given resource constraints. The present paper gives an overviewof optimal designs for various important problems that arise in different stages ofclinical drug development, including phase I dose–toxicity studies; phase I/II studiesthat consider early efficacy and toxicity outcomes simultaneously; phase IIdose–response studies driven by multiple comparisons (MCP), modeling techniques(Mod), or their combination (MCP–Mod); phase III randomized controlled multiarmmulti-objective clinical trials to test difference among several treatment groups;and population pharmacokinetics–pharmacodynamics experiments. We find thatmodern literature is very rich with optimal design methodologies that can be utilizedby clinical researchers to improve efficiency of drug development