Bayesian synthetic evaluation of multistage reliability growth with instant and delayed fix modes

In the multistage reliability growth tests with instant and delayed fix modes, the failure data can be assumed to follow Weibull processes with different parameters at different stages. For the Weibull process within a stage, by the proper selection of prior distribution form and the parameters, a concise posterior distribution form is obtained, thus simplifying the Bayesian analysis. In the multistage tests, the improvement factor is used to convert the posterior of one stage to the prior of the subsequent stage. The conversion criterion is carefully analyzed to determine the distribution parameters of the subsequent stage＇s variable reasonably. Based on the mentioned results, a new synthetic Bayesian evaluation program and algorithm framework is put forward to evaluate the multistage reliability growth tests with instant and delayed fix modes. The example shows the effectiveness and flexibility of this method.

Bayesian sequential testing for exponential life system with reliability growth

A Bayesian sequential testing method is proposed to evaluate system reliability index with reliability growth during development.The method develops a reliability growth model of repairable systems for failure censored test,and figures out the approach to determine the prior distribution of the system failure rate by applying the reliability growth model to incorporate the multistage test data collected from system development.Furthermore,the procedure for the Bayesian sequential testing is derived for the failure rate of the exponential life system,which enables the decision to terminate or continue development test.Finally,a numerical example is given to illustrate the efficiency of the proposed model and procedure.

Discrete Software Reliability Growth Modeling for Errors of Different Severity Incorporating Change-point Concept

Several software reliability growth models （SRGM） have been developed to monitor the reliability growth during the testing phase of software development. In most of the existing research available in the literatures, it is considered that a similar testing effort is required on each debugging effort. However, in practice, different types of faults may require different amounts of testing efforts for their detection and removal. Consequently, faults are classified into three categories on the basis of severity： simple, hard and complex. This categorization may be extended to r type of faults on the basis of severity. Although some existing research in the literatures has incorporated this concept that fault removal rate （FRR） is different for different types of faults, they assume that the FRR remains constant during the overall testing period. On the contrary, it has been observed that as testing progresses, FRR changes due to changing testing strategy, skill, environment and personnel resources. In this paper, a general discrete SRGM is proposed for errors of different severity in software systems using the change-point concept. Then, the models are formulated for two particular environments. The models were validated on two real-life data sets. The results show better fit and wider applicability of the proposed models as to different types of failure datasets.

RESEARCH ON RELIABILITY GROWTH FOR SYNCHRONOUSLY DEVELOPED MULTI-SYSTEMS

An advanced reliability growth model, i. e. exponential model, was presented to estimate the model parameters for multi-systems, which was synchronously tested, synchronously censored, and synchronously improved. In the presented method, the data during the reliability growth process were taken into consideration sufficiently, including the failure numbers, safety numbers and failure time at each censored time. If the multi-systems were synchronously improved for many times, and the reliability growth of each system fitted AMSAA （Army Material Systems Analysis Activity） model, the failure time of each system could be considered rationally as an exponential distribution between two adjoining censored times. The nonparametric method was employed to obtain the reliability at each censored time of the synchronous multisystems. The point estimations of the model parameters, a and b, were given by the least square method. The confidence interval for the parameter b was given as well. An engineering illustration was used to compare the result of the presented method with those of the available models. The result shows that the presented exponential growth model fits AMSAA-BISE （ Army Material Systems Analysis Activity-Beijing Institute of Structure and Environment） model rather well, and two models are suitable to estimate the reliability growth for the synchronously developed multi-systems.

Reliability Growth Modeling and Optimal Release Policy Under Fuzzy Environment of an N-version Programming System Incorporating the Effect of Fault Removal Efficiency

Failure of a safety critical system can lead to big losses. Very high software reliability is required for automating the working of systems such as aircraft controller and nuclear reactor controller software systems. Fault-tolerant softwares are used to increase the overall reliability of software systems. Fault tolerance is achieved using the fault-tolerant schemes such as fault recovery （recovery block scheme）, fault masking （N-version programming （NVP）） or a combination of both （Hybrid scheme）. These softwares incorporate the ability of system survival even on a failure. Many researchers in the field of software engineering have done excellent work to study the reliability of fault-tolerant systems. Most of them consider the stable system reliability. Few attempts have been made in reliability modeling to study the reliability growth for an NVP system. Recently, a model was proposed to analyze the reliability growth of an NVP system incorporating the effect of fault removal efficiency. In this model, a proportion of the number of failures is assumed to be a measure of fault generation while an appropriate measure of fault generation should be the proportion of faults removed. In this paper, we first propose a testing efficiency model incorporating the effect of imperfect fault debugging and error generation. Using this model, a software reliability growth model （SRGM） is developed to model the reliability growth of an NVP system. The proposed model is useful for practical applications and can provide the measures of debugging effectiveness and additional workload or skilled professional required. It is very important for a developer to determine the optimal release time of the software to improve its performance in terms of competition and cost. In this paper, we also formulate the optimal software release time problem for a 3VP system under fuzzy environment and discuss a the fuzzy optimization technique for solving the problem with a numerical illustration.

Bayesian Reliability——Growth Analysis for Statistical of Diverse Population Based on Non-homogeneous Poisson Process

New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process（NHPP） corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.

Two new multi-phase reliability growth models from the perspective of time between failures and their applications

Aviation products would go through a multi-phase improvement in reliability performance during the research and development process.In the literature,most of the existing reliability growth models assume a constant failure intensity in each test phase,which inevitably limits the scope of the application.To address this problem,we propose two new models considering timevarying failure intensity in each stage.The proposed models borrow the idea from the accelerated failure-time models.It is assumed that time between failures follow the log-location-scale distribution and the scale parameters in each phase do not change,which forms the basis for integrating the data from all test stages.For the test-find-test scenario,an improvement factor is introduced to construct the relationship between two successive location parameters.Whereas for the test-fix-test scenario,the instantaneous cumulative time between failures is assumed to be consistent with Duane model and derive the formulation of location parameter.Likelihood ratio test is further utilized to test whether the assumption of constant failure intensity in each phase is suitable.Several applications with real reliability growth data show that the assumptions are reasonable and the proposed models outperform the existing models.

COMMENTS ON AMSAA-BISE RELIABILITY GROWTH MODEL (Ⅰ)

From 1986 to 1991,based on AMSAA model, ZHOU Yuan_quan and WENG Zhao_xi presented AMSAA_BISE model to estimate reliability growth for multiple systems development, for the case that more than one system of the same type is put into reliability growth test, once a Type B failure mode is seen during test, corrective action will be taken to all systems. It is shown that there is something wrong with AMSAA_BISE model. According to AMSAA_BISE model, the maximum likelihood estimation of MTBF for multiple systems reliability growth test is much larger than that according to AMSAA model for a single system; The more systems is put into test, the larger the estimation of MTBF. An example is given, and an approximate method is presented.

Estimation in Discrete Reliability Growth,a Growth Model with Coefficient Condition

This paper considers the well known problem of estimating reliability in discrete reliability growth context with sequence of dichotomous success-failure outcomes. More precisely, the authors generalize the simple order relationship constraint with some coefficients. The authors prove that under some mild conditions, the generalized constraint MLE problem can be transformed to a traditional isotonic problem. The authors also study the lower confidence limit estimation of reliability with sample space ranking method. A simulation is conducted to illustrate the superiority of the proposed method.

Reliability Growth Test Planning and Verification of Commercial Vehicles

Reliability and durability are two important technical indicators in automobile research and development.A research-and-design and testing organization can increase inherent quality attributes by adopting a systematic approach based on statistical tools and clearly defined processes.The process affects the design phase,validation through testing,and quality assurance in production.On the basis of reliability growth theory and the Duane model,this study established an estimation method for the definition of the target mileage and specific test cycles in reliability growth testing.A construction method for defin-ing test conditions was proposed that adopts the theory of the design of experiments.The simulation was conducted under a variety of typical test conditions including differing operation times,loads,and logistics modes to predict customer use and detect failures.Failure cases were then analyzed in detail.At the same time,a reliability growth prediction model was established on the basis of the initial test data and used for test process tracking and risk control.

Incorporating S-shaped testing-effort functions into NHPP software reliability model with imperfect debugging

Testing-effort（TE） and imperfect debugging（ID） in the reliability modeling process may further improve the fitting and prediction results of software reliability growth models（SRGMs）. For describing the S-shaped varying trend of TE increasing rate more accurately, first, two S-shaped testing-effort functions（TEFs）, i.e.,delayed S-shaped TEF（DS-TEF） and inflected S-shaped TEF（IS-TEF）, are proposed. Then these two TEFs are incorporated into various types（exponential-type, delayed S-shaped and inflected S-shaped） of non-homogeneous Poisson process（NHPP）SRGMs with two forms of ID respectively for obtaining a series of new NHPP SRGMs which consider S-shaped TEFs as well as ID. Finally these new SRGMs and several comparison NHPP SRGMs are applied into four real failure data-sets respectively for investigating the fitting and prediction power of these new SRGMs.The experimental results show that：（i） the proposed IS-TEF is more suitable and flexible for describing the consumption of TE than the previous TEFs;（ii） incorporating TEFs into the inflected S-shaped NHPP SRGM may be more effective and appropriate compared with the exponential-type and the delayed S-shaped NHPP SRGMs;（iii） the inflected S-shaped NHPP SRGM considering both IS-TEF and ID yields the most accurate fitting and prediction results than the other comparison NHPP SRGMs.

Web software reliability modeling with random impulsive shocks

As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth models （SRGMs）, including those combined with multiple change-points （CPs）, have been available, these conventional SRGMs cannot be directly applied to web soft- ware reliability analysis because of the complex web operational profile. To characterize the web operational profile precisely, it should be realized that the workload of a web server is normally non-homogeneous and often observed with the pattern of random impulsive shocks. A web software reliability model with random im- pulsive shocks and its statistical analysis method are developed. In the proposed model, the web server workload is characterized by a geometric Brownian motion process. Based on a real data set from IIS server logs of ICRMS website （www.icrms.cn）, the proposed model is demonstrated to be powerful for estimating impulsive shocks and web software reliability.

NHPP-based software reliability model considering testing effort and multivariate fault detection rate

In recent decades,many software reliability growth models（SRGMs） have been proposed for the engineers and testers in measuring the software reliability precisely.Most of them is established based on the non-homogeneous Poisson process（NHPP）,and it is proved that the prediction accuracy of such models could be improved by adding the describing of characterization of testing effort.However,some research work indicates that the fault detection rate（FDR） is another key factor affects final software quality.Most early NHPPbased models deal with the FDR as constant or piecewise function,which does not fit the different testing stages well.Thus,this paper first incorporates a multivariate function of FDR,which is bathtub-shaped,into the NHPP-based SRGMs considering testing effort in order to further improve performance.A new model framework is proposed,and a stepwise method is used to apply the framework with real data sets to find the optimal model.Experimental studies show that the obtained new model can provide better performance of fitting and prediction compared with other traditional SRGMs.

An Imperfect-debugging Fault-detection Dependent-parameter Software

Software reliability growth models （SRGMs） incorporating the imperfect debugging and learning phenomenon of developers have recently been developed by many researchers to estimate software reliability measures such as the number of remaining faults and software reliability. However, the model parameters of both the fault content rate function and fault detection rate function of the SRGMs are often considered to be independent from each other. In practice, this assumption may not be the case and it is worth to investigate what if it is not. In this paper, we aim for such study and propose a software reliability model connecting the imperfect debugging and learning phenomenon by a common parameter among the two functions, called the imperfect-debugging fault-detection dependent-parameter model. Software testing data collected from real applications are utilized to illustrate the proposed model for both the descriptive and predictive power by determining the non-zero initial debugging process.

The AMSAA-BISE Model with Gap Intervals

In this paper, the AMSAA-BISE model with missing data is discussed. The ML estimates of model parameters and current MTBF are given, and the chi-squared test and a plot for cumulative number of failures versus cumulative testing time are used to test the goodness of fit for the model. This paper concludes with a numerical example to verify the model.

An Energy Model of a Failure Mechanism and its Application

The energy expression is presented for a failure mechanism, and it is appliedin an Accelerated Life Test (ALT) and an Accelerated Reliability Growth Test (ARGT). The conditionsof the common failure mechanism are obtained. The essential relationship between the conditions andthe Accelerated Factor (A_f) is proposed by using the energy model.

An Improved NHPP Model with Time-Varying Fault Removal Delay

In this paper, an improved NHPP model is proposed by replacing constant fault removal time with time-varying fault removal delay in NHPP model, proposed by Daniel R Jeske. In our model, a time-dependent delay function is established to fit the fault removal process. By using two sets of practical data, the descriptive and predictive abilities of the improved NHPP model are compared with those of the NHPP model, G-O model, and delayed S-shape model. The results show that the improved model can fit and predict the data better.

A Study of Quantitative Progress Evaluation Models for Open Source Projects

Open source software (OSS) has become an indispensable part of society, not only for personal use but also for corporate use. Projects developed and operated by OSS are called open source projects, and the number of such projects is increasing. On the other hand, because anyone can participate in an open source project, the progress of the project is uncertain due to differences in project members’ skills, development environments, and time zones of activity. Therefore, many users and companies need to understand the development and operation status of open source project. Then, the developers carefully make decisions on upgrading or installing new OSS. In this paper, we focus on the maintenance effort estimation for open source projects considering uncertainty. Also, we evaluate the project quantitatively using Earned Value Management (EVM). Moreover, we examine the appropriateness of the model for predicting the maintenance effort expeditures. Furthermore, we discuss the appropriateness of this EVM method.

Data-driven reliability analysis of Boeing 787 Dreamliner

The Boeing 787 Dreamliner,launched in 2011,was presented as a game changer in air travel.With the aim of producing an efficient,mid-size,wide-body plane,Boeing initiated innovations in product and process design,supply chain operation,and risk management.Nevertheless,there were reliability issues from the start,and the plane was grounded by the U.S.Federal Aviation Administration(FAA)in 2013,due to safety problems associated with Li-ion battery fires.This paper chronicles events associated with the aircraft’s initial reliability challenges.The manufacturing,supply chain,and organizational factors that contributed to these problems are assessed based on FAA data.Recommendations and lessons learned are provided for the benefit of engineers and managers who will be engaged in future complex systems development.