Research On Non-Homogeneous Poisson Process Software Reliability Process Under Imperfect Debugging

As the rapid development of information technology, software systems havepenetrated into all aspects of human production and living and play an increasinglyimportant role. Software system quality attributes are tightly related to businessfunction and non-function attributes and have received constant attention. As one ofthe most important attributes, reliability research as the core has been got muchattention by lots of researchers and continued to grow. Due to reliability oftendefined as a function of time and a variety of random factors, reliability processresearches based on variable failure intensity NHPP(Non-Homogeneous PoissonProcess) are becoming one of the most important aspects in current researches. Inthe software life cycle, test stage is an important part for improving reliability. Dueto uncertainty and randomness in test environment, software debugging presentsimperfect features. But, more perfect assumptions made during the existing researchdiverge from reality. So, imperfect debugging should be incorporated into reliabilityresearches. To meet the actual requirement describing software reliability in the realtesting process, this paper starts with imperfect debugging dependent SRGM,proposes a unified and flexible SRGM framework considering imperfect debuggingand then illustrates optimal release policy containing testing effort. And on this basis,reliability analysis is extended to fault detection and correction stochasticsub-processes during CBS(Component-Based Software) integration testing, andreliability process analysis model incorporating imperfect debugging and manyother practical problems is summarized in this paper.Imperfect debugging describes the real debugging during test or operation stagefor black box software and exists in many forms. But, existing research does notgive sufficient consideration to imperfect debugging. Firstly, this paper builds theunified imperfect debugging dependent SRGM framework incorporating incompletedebugging, introduction of new faults and testing effort. The proposed frameworkexplicitly describes the quantitative relationship among fault detection, correctionand introduction. Moreover, the framework has strong flexibility and supportsmultiple function parameters setting according to actual testing environment.Furthermore, a special SRGM incorporating an improved S-shaped Logistictesting-effort function(TEF) with not zero initialization and the same S-shaped faultdetection rate function into imperfect debugging modeling is proposed, calledSRGM-GTEID describing multiple actual situations. The proposed SRGM closer toreal software testing has better descriptive and predictive power of reliability growththan other models.The main purpose of software testing is to continuously detect and repair fault,improve reliability, and realize the optimal software release under the anticipatedgoal. In this paper, optimal release policy for SRGM with imperfect debugging isproposed. First, based on the imperfect debugging dependent SRGM framework, aspecial SRGM: IDTEDM with S-shaped trend failure rate function showing firstlyan increase and then a decrease variation is built. From the viewpoint of the wholesoftware life cycle, cost model considering imperfect debugging is illustrated andoptimal release model with expected reliability is also presented. Hereon, testingcosts initialization is quantified in the cost model to avoid uncertainty brought bysubjective setting. Actual testing cost(ATC) may have a serious deviation fromexpected testing cost(ETC), namely, there is a risk that ATC may be larger ETC.Thus, optimal release model containing cost risk analysis and regulation isintroduced. So, on the basis of considering imperfect debugging, life cycle costconstruct and cost overruns risk controls, optimal release time algorithm:ORP-BEVRA is summarized. Imperfect debugging SRGM dependent optimal releasepolicy considering the real situation is closer to actual testing process, and providesimportant decision-making support for cost- reliability optimum control.Considering internal architecture, reliability process research of CBS is morecomplicated than SRGM for black box software. Against the deficiencies of CBSreliability modeling and analysis, for instance, importing too many assumptions,paying less attention to debugging process, without adequately consideringimperfect debugging and change-point(CP) problems, an approach of CBSreliability process analysis is proposed incorporating the imperfect debugging andCP. An imperfect debugging dependent infinite server queuing model is presented tosketch the integration test process of CBS. Due to imperfect debugging, there is afeedback between fault detection and correction process in the proposed queuingmodel. And on this basis, quantitative analysis on fault correction before and afterthe CP is undertaken, imperfect debugging is also incorporated into analysis, and thecumulative number of fault detection and correction during CBS integration test arededuced finally. Analytical equation obtained describes imperfect debugging and CPmodels the growth of CBS reliability during testing. Moreover, a theorem about thegrowth acceleration in fault removal rate by change-point is presented that provestest efficiency can be improved with change-point caused by improving testenvironment. Numerical example verifies the validity of the proposed model:IDCP-CBSRGM.The assumption that the faults detected during testing go through the samecorrection process is not consistent with the actual situation in existing research. Todo this, a CBS reliability process analysis model is proposed incorporatingdebugging delay and imperfect debugging in this paper. The CBS test queuingmodel built explicitly incorporates fault allocation process that make the faults withdifferent severity go through different correction process. A unified fault correctionprocess is sketched, given debugging delay. Furthermore, the diversities of faultsdebugging processing for serious and simple faults are illustrated, and the impacts ofimperfect debugging on fault detection and correction are explicitly elaborated.Thus, reliability analysis model considering debugging delay and imperfectdebugging is built that sketches the cumulative number of fault detection andcorrection. Mainly due to the fact that more practical details are considered inanalysis, the proposed model is closer to real imperfect testing process. Finally, theresults of numerical experiments verify the effectiveness and rationality of theproposed model.