NHPP Models Research Articles

NON-HOMOGENEOUS POISSON PROCESS OF A QUADRATIC TRANSMUTED LOG-LOGISTIC MODEL

In recent years, software reliability engineering has become a major topic due to rapid technological advancements, as researchers work to interpret and analyze software reliability data. Therefore, establishing new software reliability models is essential to possess reliable tools for diagnosing software systems. This paper proposes a new NHPP model based on the quadratic transmuted log-logistic (QTLL) distribution. The characteristics of the model were obtained and graphically illustrated. Three real software data sets were applied to evaluate the proposed model based on different criteria. The parameters of the NHPP QTLL were estimated using maximum likelihood estimation (MLE), and nonlinear least squares estimation (NLSE), and a comparative analysis of the two estimation methods has been performed to estimate the model parameters. Additionally, a study was carried out to compare the suggested model with other well-known NHPP models. The results indicate that NLSE outperforms MLE in parameter estimation. Furthermore, the NHPP QTLL model demonstrated superior performance across all evaluation assessments compared to other models. The graphical representation also shows that the proposed model is more effective in fitting fault data than existing models.

Development of software reliability models using a hybrid approach and validation of the proposed models using big data

This article proposes three software reliability models based on a hybrid approach combining NHPP models, Weibull model, and exponential model. The software failure is first categorised into three categories, namely pure software failures, hardware-induced software failures, and user-induced software failures. Based on the failure behaviour, NHPP models were adapted for pure software failures, Weibull model for hardware-induced failures, and exponential model for user-induced software failures. The failure intensity function, mean value function, and reliability function were determined. The proposed models are validated using big data analysis. From the data collected during the testing phase, the optimal values of parameters were estimated using maximum likelihood estimation and genetic algorithm. The expected number of failures and the cumulative number of failures were calculated, and comparison was made between the observed values to show the performance of the proposed models. A comparison criterion was also proposed to confirm the estimation accuracy. Finally, a t test was conducted to test the significance of the difference between the observed and estimated values. Experimental results confirm the better estimation accuracy of the proposed models.

Comparison of Non-Homogeneous Poisson Process Software Reliability Models in Web Applications

Software reliability is an important quality factor that effects project success. By modelling software reliability, it can be estimated when and with how much effort a project can be deployed. Consequently, this can contribute to the resource and schedule planning of a project. Therefore, software reliability models SRM are frequently used for measuring the maturity of a software. A number of studies exist in the literature that compare SRMs in terms of their modelling performance. However, there is a need of evaluating these SRMs by taking into account the software project domain. This study aims to compare the performance of SRMs in the context of Web applications. In accordance to this purpose, six different software reliability models, namely Goel-Okumoto, Musa Exponential, Inflected S-shaped, Delayed S-shaped, Yamada and Pham Nordmann Zhang Imperfect Fault Detection PNZ , are evaluated by using the defect records of four Web application projects developed by a Turkish software organization. 100%, 70% and 50% of the recorded data is used as input to the maximum likelihood parameter estimation MLPE method and the results of these three cases are investigated and commented separately in the research. The goodness of fit and the predictive validity of the models to the project data are tested by calculating Mean Square Error MSE , Mean Magnitude Relative Error MMRE , Percentage Relative Error Deviation PRED and Average Balanced Predicted Relative Error A.BPRE measures. For each NHPP model 48 separate cases which are combinations of the three defect inflow data cases 100%, 70% and 50% , four projects and four measures, are investigated and ranked. It is shown that the NHPP models can be applied to Web applications and Delayed S-shaped model displays the best results among the alternatives. However, it is understood that the Goel-Okumoto and Yamada models give identical results and that these two models converge to each other with respect to the project defect data that has been used. Combined, these two models obtain the highest ranking scores and it is concluded that these two models perform better than the other models with respect to Web based software.

유연한 와이블 확장분포의 형상모수를 이용한 NHPP 소프트웨어 신뢰성 모형에 관한 비교연구

소프트웨어 고장분석을 위한 비동질적인 포아송과정에서 결함당 고장발생률이 상수이거나, 단조 증가 또는 단조 감소하는 패턴을 가질 수 있다. 본 논문에서는 수리시점에서도 고장이 발생할 상황을 반영하는 무한고장 NHPP 모형들을 비교 제시하였다. 소프트웨어 신뢰성분야에서 많이 사용되는 유연한 와이블 확장분포에 근거한 무한고장 소프트웨어 신뢰성모형에 대한 비교문제를 제시하였다. 그 결과 형상모수가 비교적 작은 경우가 효율적으로 나타났다. 그리고 모수 추정법은 최우추정법을 이용하였고 모형선택은 평균제곱오차와 결정계수를 이용하였다. 이 연구를 통하여 소프트웨어 개발자들은 형상모수에 따른 소프트웨어 고장현상을 파악하는데 어느 정도 도움을 줄 수 있을 것으로 사료된다. NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, infinite failures NHPP models that repairing software failure point in time reflects the situation, was presented for comparing property. Commonly used in the field of software reliability based on Flexible Weibull extension distribution software reliability of infinite failures was presented for comparison problem. The result is that a relatively small shaping parameter was effectively. The parameters estimation using maximum likelihood estimation was conducted and model selection was performed using the mean square error and the coefficient of determination.. In this research, software developers to identify software failure property follows shape parameter, some extent be able to help is considered.

일반화 통계량에 의존한 와이블 확장모형을 이용한 NHPP 소프트웨어 신뢰성 모형에 관한 연구

소프트웨어 고장분석을 위한 비동질적인 포아송과정에서 결함당 고장발생률이 상수이거나, 단조 증가 또는 단조 감소하는 패턴을 가질 수 있다. 본 논문에서는 수리시점에서도 고장이 발생할 상황을 반영하는 무한고장 NHPP 모형들을 비교 제시하였다. 소프트웨어 신뢰성분야에서 많이 사용되는 와이블 확장분포에 근거한 무한고장 소프트웨어 신뢰성모형에 대한 비교문제를 제시하였다. 그 결과 형상모수가 비교적 큰 경우가 효율적으로 나타났다. 그리고 모수추정법은 최우추정법을 이용하였고 모형선택은 평균제곱오차와 결정계수를 이용하였다. 이 연구를 통하여 소프트웨어 개발자들은 형상모수에 따른 소프트웨어 고장현상을 파악하는데 어느 정도 도움을 줄 수 있을 것으로 사료된다. NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, infinite failures NHPP models that repairing software failure point in time reflects the situation, was presented for comparing property. Commonly used in the field of software reliability based on Weibull extension distribution software reliability of infinite failures was presented for comparison problem. The result is that a relatively large shape parameter was effectively. The parameters estimation using maximum likelihood estimation was conducted and Model selection was performed using the mean square error and the coefficient of determination. In this research, software developers to identify software failure property follows shape parameter, some extent be able to help is considered.

Lomax 분포의 형상모수에 근거한 무한고장 NHPP 소프트웨어 신뢰성 모형에 관한 연구

NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, infinite failures NHPP models that repairing software failure point in time reflects the situation, was presented for comparing property. Commonly used in business, economics, and actuarial modeling based on Lomax distribution, software reliability of infinite failures was presented for comparison problem. The result is that a relatively large shape parameter was effectively. The parameters estimation using maximum likelihood estimation was conducted and Model selection was performed using the mean square error and the coefficient of determination. In this research, software developers to identify software failure property follows shape parameter, some extent be able to help is considered.

유한 및 무한고장 지수파우어 NHPP 소프트웨어 신뢰성모형에 대한 비교 연구

NHPP software reliability models for failure analysis can have, in the literature, exhibit either constant, monotonic increasing or monotonic decreasing failure occurrence rates per fault. In this paper, finite failure NHPP models that assuming the expected value of the defect and infinite failures NHPP models that repairing software failure point in time reflects the situation, were presented for comparing property. Commonly used in the field of software reliability based on exponential power distribution software reliability model finite failures and infinite failures were presented for comparison problem. As a result, finite fault model is effectively infinite fault models, respectively. The parameters estimation using maximum likelihood estimation was conducted. In this research, software developers to identify software failure property some extent be able to help is considered.

A New Software Reliability Growth Model: Genetic-Programming-Based Approach

A variety of Software Reliability Growth Models (SRGM) have been presented in literature. These models suffer many problems when handling various types of project. The reason is; the nature of each project makes it difficult to build a model which can generalize. In this paper we propose the use of Genetic Programming (GP) as an eVolutionary computation approach to handle the software reliability modeling problem. GP deals with one of the key issues in computer science which is called automatic programming. The goal of automatic programming is to create, in an automated way, a computer program that enables a computer to solve problems. GP will be used to build a SRGM which can predict accumulated faults during the software testing process. We evaluate the GP developed model and compare its performance with other common growth models from the literature. Our experiments results show that the proposed GP model is superior compared to Yamada S-Shaped, Generalized Poisson, NHPP and Schneidewind reliability models.

The Comparative Study of Software Optimal Release Time Based on Burr Distribution

It is great practical interest to decide when to stop testing a software system in development phase and transfer it to the user. This problem is called as the optimal software release policies. In this research, it was studied about this software release problem. Because of the possibility of introducing new faults when correcting or modifying the software, infinite failure NHPP models presented and propose an optimal release policies of the life distribution applied Burr distribution which makes out efficiency application for software reliability. In this paper, discuss optimal software release policies which minimize a total software cost of development and maintenance under the constraint of satisfying a software reliability requirement. In a numerical example, after trend test applied and estimated the parameters using maximum likelihood estimation of inter-failure time data (Lyu, M. R. [13]), make out estimating software optimal release time.

Software Reliability Growth Models Incorporating Change Point With Imperfect Fault Removal and Error Generation

The number of faults removed need not always be same as the number of failures observed in real software development environment. If number of failures observed is more than number of faults removed then we have the case of imperfect debugging. Due to complexity of software system and incomplete understanding of software, testing team may not be able to remove the fault perfectly on detection of failure and the original fault may remain leading to imperfect fault removal, or get replaced by another fault/error causing error generation. Attempts have been made to study the above cases separately. Most of the SRGMs are based upon constant or monotonically increasing fault detection rate (FDR). In practice, as testing grows, so does skill and efficiency of the testers. With introduction of new testing strategies and new test cases, there comes a change in FDR. The time point where the change in removal curve appears is termed as “change point”. In this paper, we incorporate the concept of change point in software reliability growth in presence of imperfect fault removal and error generation. The models have been validated, evaluated and compared with other existing NHPP models by applying it on actual failure/fault removal data sets cited from real software development projects.

Reliability Analysis of Component Software in Wireless Sensor Networks Based on Transformation of Testing Data

We develop an approach of component software reliability analysis which includes the benefits of both time domain, and structure based approaches. This approach overcomes the deficiency of existing NHPP techniques that fall short of addressing repair, and internal system structures simultaneously. Our solution adopts a method of transformation of testing data to cover both methods, and is expected to improve reliability prediction. This paradigm allows component-based software testing process doesn’t meet the assumption of NHPP models, and accounts for software structures by the way of modeling the testing process. According to the testing model it builds the mapping relation from the testing profile to the operational profile which enables the transformation of the testing data to build the reliability dataset required by NHPP models. At last an example is evaluated to validate and show the effectiveness of this approach.

Adaptive functional mixed NHPP models for the analysis of recurrent event panel data

An adaptive semi-parametric model for analyzing longitudinal panel count data is presented. Panel data refers here to data collected as the number of events occurring between specific followup times over a period or disjoint periods of observation of a subject. The counts are assumed to arise from a mixed nonhomogeneous Poisson process where frailties account for heterogeneity common to this type of data. The generating intensity of the counting process is assumed to be a smooth function modeled with penalized splines. A main feature is that the penalization used to control the amount of smoothing, usually assumed to be time homogeneous, is allowed to be time dependent so that the spline can more easily adapt to sharp changes in curvature regimes. Splines are also used to model time dependent covariate effects. Penalized quasi-likelihood (PQL; [Breslow, N.E., Clayton, D.G., 1993. Approximate inference in generalized linear mixed models. Journal of the American Statistical Association 88, 9–25]) is used to derive estimating equations for this adaptive spline model so that only low moment assumptions are required for inference. Both jackknife and bootstrap variance estimators are developed. The finite sample properties of the proposed estimating functions are investigated empirically by simulation. Comparisons with a model assuming a time homogeneous penalty are made. The methods are used in an analysis of data from an experiment to test the effectiveness of pheromones in disrupting the mating pattern of the cherry bark tortrix moth. Recommendations are provided on when the simpler model with a time homogeneous penalty may provide a fair approximation to data and where such an approach will be lacking, calling for the more complicated adaptive methods.

Discrete software reliability assessment with discretized NHPP models

A software reliability growth model is one of the fundamental technique to assess software reliability quantitatively. The software reliability growth model is required to have a good performance in terms of goodness-of-fit, predictability, and so forth. In this paper, we propose discretized software reliability growth models. As to the software reliability growth modeling, discretized nonhomogeneous Poisson process models are investigated particularly for accurate software reliability assessment. We show that the discrete nonhomogeneous Poisson process models have better performance than discretized deterministic software reliability growth models which have been proposed so far.

NHPP models for categorized software defects

AbstractWe develop NHPP models to characterize categorized event data, with application to modelling the discovery process for categorized software defects. Conditioning on the total number of defects, multivariate models are proposed for modelling the defects by type. A latent vector autoregressive structure is used to characterize dependencies among the different types. We show how Bayesian inference can be achieved via MCMC procedures, with a posterior prediction‐based L‐measure used for model selection. The results are illustrated for defects of different types found during the System Test phase of a large operating system software development project. Copyright © 2005 John Wiley & Sons, Ltd.

Superposition of Power-Law Models for Hardware/Software System Reliability Data Analysis

One of the widely used NHPP models in reliability is the so-called power-law model, also known as the Duane model. A power-law model can be applied in analyzing failure data of both software and hardware systems. Nevertheless, the power-law model is no longer applicable to describe the failure behavior when a hardware/software embedded system is concerned since the failures can come from both hardware and software. How to analyze the failure data of this type is still a problem to study and a new type of model is needed to develop. In this paper, we consider the superposition of the power-law models (SPLM) as one candidate to describe the failure behaviors of hardware/software systems. The characteristics of SPLMs are thoroughly studied. It is shown that an SPLM has the intensity function that can be increasing, decreasing, increasing-then-decreasing or decreasing-then-increasing. Specifically, the identification method of the superposition of power-law processes is provided by using the TTT-plot technique. The TTT-transform of a superposition of power-law processes is DFR-like. Therefore, the conditional TTT-plot should present a convex pattern if the system failures follow a superposition process by a few power-law processes. This provides us an easy way to identify the model when the testing data is available.

The role of NHPP models in the practical analysis of maintenance failure data

The analysis of failure data is an important facet in the development of maintenance strategy for equipment. Only by properly understanding the mechanism of failure, through the modelling of failure data, can a proper maintenance plan be developed. This is normally done by means of probabilistic analysis of the failure data. From this, conclusions can be reached regarding the effectiveness and efficiency of preventive replacement (and overhaul) as well as that of predictive maintenance. The optimal frequency of maintenance can also be established by using well developed optimisation models. These optimise outputs, such as profit, cost and availability. The problem with this approach is that it assumes that all repairable systems are repaired to the ‘good-as-new’ condition at each repair occasion. Maintenance practice has learnt, however, that in many cases equipment slowly degrades even while being properly maintained (including part replacement and periodic overhaul). The result of this is that failure data sets often display degradation. This renders conventional probabilistic analysis useless. During the last two decades, a few researches applied themselves to the solution of this problem. This paper briefly examines the present state of the theoretical foundation of repairable systems analysis techniques and then develops two formats of the Non-Homogeneous Poisson Process model (NHPP model) for practical use by the maintenance analyst. This includes an identification framework, goodness-of-fit tests and optimisation modelling. The model is tested on two failure data sets from literature and one from industry.

Estimation of parameters of yamada et al. model and modification of the model

Yamada, Ohba and Osaki (1983) suggested an important NHPP model for software failure phenomenon. So far little work has been done on the problem of estimating its parameters. We present here some conditions for the likelihood estimates to be finite, positive and unique. We also suggest a modification of the model. The performance measures and statistical inferences of the modified model are discussed here. The modified model is applied to software failure data and the results are compared with Jelinski-Moranda [4] and some existing important NHPP models

Rationale for a Modified Duane Model

The Duane model for reliability growth involves a rate function which is an inverse power law and has an ``infinite'' value at t = 0. The model is usually motivated entirely empirically. Here a probabilistic rationale is proposed via a reliability growth model involving the removal of design faults. This rationale results in a modified power law rate, finite at the origin. A wider class of rate functions should be investigated for NHPP models of reliability growth.