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The purpose of this paper is to explore new ways and lay a solid foundation to solve the problem of reliability growth analysis of major aerospace equipment with various uncertainty data through propose new concepts of general uncertainty data (GUD) and general uncertainty variable (GUV) and build the operation system of GUVs.

The characteristics of reliability growth data of major aerospace equipment and the limitations of current reliability growth models have been analyzed at first. The most commonly used uncertainty system analysis methods of probability statistics, fuzzy mathematics, grey system theory and rough set theory have been introduced. The concepts of GUD and GUV for reliability growth data analysis of major aerospace equipment are proposed. The simplified form of GUV based on the “kernel” and the degree of uncertainty of GUV is defined. Then an operation system of GUVs is built.

(1) The concept of GUD; (2) the concept of GUV; (3) The novel operation rules of GUVs with simplified form.

The method exposed in this paper can be used to integrate complex reliability growth data of major aerospace equipment. The reliability growth models based on GUV can be built for reliability growth evaluation and forecasting of major aerospace equipment in practice. The reliability evaluation example of a solid rocket motor shows that the concept and idea proposed in this paper are feasible. The research of this paper opens up a new way for the analysis of complex uncertainty data of reliability growth of major aerospace equipment. Moreover, the operation of GUVs could be extended to the case of algebraic equation, differential equation and matrix which including GUVs.

The new concepts of GUD and GUV are given for the first time. The novel operation rules of GUVs with simplified form were constructed.

When performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating discrete (one-shot) reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. The purpose of this paper is to present an application of a modified GM(1,1) model for handling system-level testing constrained by small sample sizes.

The paper presents a methodology for incorporating failure data into a modified GM(1,1) model for systems with failures following a poly-Weibull distribution. Notional failure data are generated for complex systems and characterization of reliability growth parameters is performed via both the traditional AMSAA model and the GM(1,1) model for purposes of comparing and assessing performance.

The modified GM(1,1) model requires less complex computational effort and provides a more accurate prediction of reliability growth model parameters for small sample sizes and multiple failure modes when compared to the AMSAA model. It is especially superior to the AMSAA model in later stages of testing.

This research identifies cost-effective methods for developing more accurate reliability growth parameter estimates than those currently used.

The purpose of this paper is to present a novel GREY‒ASMAA model for reliability growth evaluation in the large civil aircraft test flight phase.

As limited data are collected during the large civil aircraft test flight phase, which are not enough to meet the requirements of the ASMAA model for reliability growth, four basic GM(1, 1) models, even grey model, original difference grey model, even difference grey model and discrete grey model, are presented. Then both forward and backward grey models GM(1,1) are built to forecast and obtain virtual test data on left and right sides. Then the ASMAA model for reliability growth evaluation can be built based on original and virtual test data.

Aiming at the background of poor information data during the large civil aircraft test flight phase, first, a novel GREY‒ASMAA model, which was combined by the grey model GM(1,1) with the ASMAA model, has been put forward in this paper.

The GREY‒ASMAA model for reliability growth evaluation can be used to solve the problem of reliability growth evaluation with poor information data during the large civil aircraft test flight phase, and it has been used in reliability evaluation of C919 at the test flight stage.

This paper presents two new definitions of forward grey model GM(1,1) and backward grey model GM(1,1), as well as a novel GREY‒ASMAA model for reliability growth evaluation of large civil aircraft during test flight phase.

The purpose of this research is to incorporate the exponentiated Weibull testing‐effort functions into software reliability modeling and to estimate the optimal software release time.

This paper suggests a software reliability growth model based on the non‐homogeneous Poisson process (NHPP) which incorporates the exponentiated Weibull (EW) testing‐efforts.

Experimental results on actual data from three software projects are compared with other existing models which reveal that the proposed software reliability growth model with EW testing‐effort is wider and effective SRGM.

This paper presents a SRGM using a constant error detection rate per unit testing‐effort.

Software reliability growth model is one of the fundamental techniques to assess software reliability quantitatively. The results obtained in this paper will be useful during the software testing process.

The present scheme has a flexible structure and may cover many of the earlier results on software reliability growth modeling. In general, this paper also provides a framework in which many software reliability growth models can be described.

The Duane reliability growth model has a number of inherent limitations that make it unsuitable for monitoring reliability improvement progress. These limitations are explored and a model based on variance‐stabilizing transformation theory is explained. This model retains the ease of use while also avoiding the disadvantages of the Duane model. It represents a more useful graphical model for portraying reliability improvement at development team meetings. Computer simulations have shown that the new model provides a better fit to the data over the range of Duane slopes normally observed during a reliability growth program. The instantaneous mean time between failures (MTBF) equation for the new model is developed. Computer simulations show that its use results in higher values of instantaneous MTBF than that achieved by the Duane model. The new model also reduces the total test time for achieving a particular specified instantaneous MTBF. Finally, software failure data from an actual project illustrates the calculations and benefits of the new model.

Most of the existing software reliability models assume time between failures to follow an exponential distribution. Develops a reliability growth model based on non‐homogeneous Poisson process with intensity function given by the power law, to predict the reliability of a software. Several authors have suggested the use of the non‐homogeneous Poisson process to assess the reliability growth of software and to predict their failure behaviour. Inference procedures considered by these authors have been Bayesian in nature. Uses an unbiased estimate of the failure rate for prediction. Compares the performance of this model with Bayes empirical‐Bayes models and a time series model. The model developed is realistic, easy to use, and gives a better prediction of reliability of a software.

Software testing is needed to produce extremely reliable software products. A crucial decision problem that the software developer encounters is to ascertain when to terminate the testing process and when to release the software system in the market. With the growing need to deliver quality software, the critical assessment of reliability, cost of testing and release time strategy is requisite for project managers. This study seeks to examine the reliability of the software system by proposing a generalized testing coverage-based software reliability growth model (SRGM) that incorporates the effect of testing efforts and change point. Moreover, the strategic software time-to-market policy based on costreliability criteria is suggested.

The fault detection process is modeled as a composite function of testing coverage, testing efforts and the continuation time of the testing process. Also, to assimilate factual scenarios, the current research exhibits the influence of software users refer as reporters in the fault detection process. Thus, this study models the reliability growth phenomenon by integrating the number of reporters and the number of instructions executed in the field environment. Besides, it is presumed that the managers release the software early to capture maximum market share and continue the testing process for an added period in the user environment. The multiattribute utility theory (MAUT) is applied to solve the optimization model with release time and testing termination time as two decision variables.

The practical applicability and performance of the proposed methodology are demonstrated through real-life software failure data. The findings of the empirical analysis have shown the superiority of the present study as compared to conventional approaches.

This study is the first attempt to assimilate testing coverage phenomenon in joint optimization of software time to market and testing duration.

The software reliability models to describe the reliability growth phenomenon are formulated by any stochastic point process with state‐dependent or time‐dependent intensity function. On the other hand, to deal with the environmental data, which consists of covariates influencing times to software failure, it may be useful to apply the Cox’s proportional hazards model for assessing the software reliability. In this paper, we review the proportional hazards software reliability models and discuss the problem to determine the optimal software release time under the expected total software cost criterion. Numerical examples are devoted to examine the dependence of the covariate structure in both the software reliability prediction and the optimal software release decision.

The purpose of this paper is to develop a new software reliability growth model considering different fault distribution function before and after the change point.

In this paper, the authors have developed a framework to incorporate change-point in developing a hybrid software reliability growth model by considering different distribution functions before and after the change point.

Numerical illustration suggests that the proposed model gives better results in comparison to the existing models.

The existing literature on change point-based software reliability growth model assumes that the fault correction trend before and after the change is governed by the same distribution. This seems impractical as after the change in the testing environment, the trend of fault detection or correction may not follow the same trend; hence, the assumption of same distribution function may fail to predict the potential number of faults. The modelling framework assumes different distributions before and after change point in developing a software reliability growth model.

Studies a non‐homogeneous Poisson process software reliability model with failure rate based on Zipf’s law. Discusses the rate function, mean value function and the estimation of parameters. The proposed model can be used to analyse the reliability growth. The results of applying the proposed model and Duane model to several actual failure data sets show that the model with failure rate observed from Zipf’s law can fit not only in operating software but also in testing software. The result also indicates that the proposed model has better long‐term predictive capability than the Duane model for failure data sets with power law’s failure rates