A generalized JM model with applications to imperfect debugging in software reliability

For their nice mathematical properties, state space models have been widely used, especially for forecasting. Over the last decades, the study of tracking software reliability by statistical models has attracted scientists’ attention. However, most of models focus on perfect debugging although practically imperfect debugging arises everywhere. In this paper, a non-Gaussian state space model is modified to predict software failure time with imperfect debugging. In fact, this model is very flexible so that we can modify the system equation in this model to satisfy the various situations. Besides, this model is suitable for tracking software reliability, and applied to two well known datasets on software failures.     

An imperfect debugging model with two types of hazard rates for software reliability measurement and assessment

We propose a software reliability model which assumes that there are two types of software failures. The first type is caused by the faults latent in the system before the testing; the second type is caused by the faults regenerated randomly during the testing phase. The former and latter software failure-occurrence phenomena are described by a geometrically decreasing and a constant hazard rate, respectively. Further, this model describes the imperfect debugging environment in which the fault-correction activity corresponding to each software failure is not always performed perfectly. Defining a random variable representing the cumulative number of faults successfully corrected up to a specified time point, we use a Markov process to formulate this model. Several quantitative measures for software reliability assessment are derived from this model. Finally, numerical examples of software reliability analysis based on the actual testing data are presented.     

Continuous model for software reliability demonstration testing considering damage size of software failures

This study proposes a continuous model for software reliability demonstration testing, which takes the damage size of software failures into consideration. In the proposed procedure, the software being tested is accepted if the number of software failures does not exceed a prespecified value, s and if the total damage size of software failures is less than another prespecified value, d. Based on the producer's and consumer's risks, an algorithm for designing a software reliability demonstration test is discussed.     

Effect of change point and imperfect debugging in software reliability and its optimal release policy

This article presents a software reliability growth model based on non-homogeneous Poisson process. The main focus of this article is to deliver a method for software reliability modelling incorporating the concept of time-dependent fault introduction and fault removal rate with change point. Also in this article, a cost model with change point has been developed. Based on the cost model optimal release policy with change point has been discussed. Maximum likelihood technique has been applied to estimate the parameters of the model. The proposed model has been validated using some real software failure data. Comparison has been made with models incorporating change point and without change point. The application of the proposed cost model has been shown using some numerical examples.     

Transient solutions of a software model with imperfect debugging and generation of errors by two servers

In this paper, we obtain the transient solution of probabilities of error in the software, mean number of faults and the expected number of failures remaining at time t, under the assumption that the number of faults is finite, the failure rate is proportional to the number of faults present in the software at any time, debugging is imperfect and error generation will never lead the software to have infinite errors. Moreover, the software is tested by two servers with the first M errors being debugged by first server and the remaining errors (M +1 ≤n ≤N) by the second server. Also, when a failure occurs, instantaneously repair starts with the following probabilities.

• 1.(a) The fault content is reduced by one by the first (second) server with probability μ₁(μ₂),μ₂ ≥μ₁
• 2.(b) The fault content remains unchanged with probability Ψ.
• 3.(c) The fault content is increased by one by the first (second) server with probability λ₁(λ₂), λ₁ ≥λ₂ where μ₁ + Ψ + λ₁ = 1, μ₂ + Ψ + λ₂ = 1, μ₁ ⪢ Ψ ⪢ λ₁, μ₂ ⪢ Ψ ⪢ λ₂. Finally, a numerical example is presented for the transient probabilities for the number of errors in the software, mean number of faults and the expected number of failures remaining in the software.

     

A cost model for N-version programming with imperfect debugging

One of the challenging problems for software companies is to find the optimal time of release of the software so as to minimize the total cost expended on testing and potential penalty cost due to unresolved faults. If the software is for a safety critical system, then the software release time becomes more important. The criticality of a failure caused by a fault also becomes an important issue for safety critical software. In this paper we develop a total cost model based on criticality of the fault and cost of its occurrence during different phases of development for N-version programming scheme, a popular fault-tolerant architecture. The mathematical model is developed using the reliability growth model based on the non-homogeneous Poisson process. The models for optimal release time under different constraints are developed under the assumption that the debugging is imperfect and there is a penalty for late release of the software. The concept of Failure Mode Effects and Criticality Analysis is used for measuring criticality.     

Flexible software reliability growth model with testing effort dependent learning process

A lot of importance has been attached to the testing phase of the Software Development Life Cycle (SDLC). It is during this phase it is checked whether the software product meets user requirements or not. Any discrepancies that are identified are removed. But testing needs to be monitored to increase its effectiveness. Software Reliability Growth Models (SRGMs) that specify mathematical relationships between the failure phenomenon and time have proved useful. SRGMs that include factors that affect failure process are more realistic and useful. Software fault detection and removal during the testing phase of SDLC depend on how testing resources (test cases, manpower and time) are used and also on previously identified faults. With this motivation a Non-Homogeneous Poisson Process (NHPP) based SRGM is proposed in this paper which is flexible enough to describe various software failure/reliability curves. Both testing efforts and time dependent fault detection rate (FDR) are considered for software reliability modeling. The time lag between fault identification and removal has also been depicted. The applicability of our model is shown by validating it on software failure data sets obtained from different real software development projects. The comparisons with established models in terms of goodness of fit, the Akaike Information Criterion (AIC), Mean of Squared Errors (MSE), etc. have been presented.     

On a software availability model with imperfect maintenance

In this paper we consider a general software availability model and derive compound availability measures, such as the joint probability of software availability and the remaining number of errors. The results given here generalize the results given in Kim et al. (1982).     

An inventory model with reliability in an imperfect production process

The paper analyzes an economic manufacturing quantity (EMQ) model with price and advertising demand pattern in an imperfect production process under the effect of inflation. If the machine goes through a long-run process, it may shift from in-control state to out-of-control state. As a result, the system produces imperfect items. The imperfect items are reworked at a cost to make it as new. The production of imperfect quality items increases with time. To reduce the production of the imperfect items, the systems have to more reliable and the produced items depend on the reliability of the machinery system. In this direction, the author considers that the development cost, production cost, material cost are dependent on reliability parameter. Considering reliability as a decision variable, the author constructs an integrated profit function which is maximized by control theory. A numerical example along with graphical representation and sensitivity analysis are provided to illustrate the model.     

A redundant repairable system with imperfect coverage and fuzzy parameters

This paper proposes a procedure to construct the membership functions of the system characteristics of a redundant repairable system with two primary units and one standby in which the coverage factor is the same for an operating unit failure as that for a standby unit failure. Times to failure and times to repair of the operating and standby units are assumed to follow fuzzified exponential distributions. The α-cut approach is used to extract from the fuzzy repairable system a family of conventional crisp intervals for the desired system characteristics, determined with a set of parametric nonlinear programs using their membership functions. A numerical example is solved successfully to illustrate the practicality of the proposed approach. Because the system characteristics are governed by the membership functions, more information is provided for use by management, and because the redundant system is extended to the fuzzy environment, general repairable systems are represented more accurately and the analytic results are more useful for designers and practitioners.     

A discrete time model for software reliability with application to a flight control software

This work is motivated by a particular software reliability problem in a unit of flight control software developed by the Indian Space Research Organization (ISRO), in which the testing of the software is carried out in multiple batches, each consisting of several runs. As the errors are found during the runs within a batch, they are noted, but not debugged immediately; they are debugged only at the end of that particular batch of runs. In this work, we introduce a discrete time model suitable for this type of periodic debugging schedule and describe maximum likelihood estimation for the model parameters. This model is used to estimate the reliability of the software. We also develop a method to determine the additional number of error‐free test runs required for the estimated reliability to achieve a specific target with some high probability. We analyze the test data on the flight control software of ISRO. Copyright © 2011 John Wiley & Sons, Ltd.     

Sensitivity analysis of release time of software reliability models incorporating testing effort with multiple change-points

To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis.     

Comparative analysis of the machine repair Problem with imperfect coverage and service pressure condition

In this paper we analyze the warm-standby M/M/R machine repair problem with multiple imperfect coverage which involving the service pressure condition. When an operating machine (or warm standby) fails, it may be immediately detected, located, and replaced with a coverage probability c by a standby if one is available. We use a recursive method to develop the steady-state analytic solutions which are used to calculate various system performance measures. The total expected profit function per unit time is derived to determine the joint optimal values at the maximum profit. We first utilize the direct search method to measure the various characteristics of the profit function followed by Quasi-Newton method to search the optimal solutions. Furthermore, the particle swarm optimization (PSO) algorithm is implemented to find the optimal combinations of parameters in the pursuit of maximum profit. Finally, a comparative analysis of the Quasi-Newton method with the PSO algorithm has demonstrated that the PSO algorithm provides a powerful tool to perform the optimization problem.     

An optimal statistical testing policy for software reliability demonstration of safety-critical systems

When software reliability demonstration of safety-critical systems by statistical testing is treated as a Test, Analyse and Fix (TAAF) process, an optimal testing policy can be found, which maximises the probability of success of the whole process, over a pre-determined period of time. The optimisation problem is formulated, solved by stochastic dynamic programming, and demonstrated by two numerical examples.     

A consumption model with separability and imperfect decision makers

A consumption model is considered, where agents may have a simplified image of reality and a simplified way of reaching decisions. Some rules of behaviour are assumed, considering, in particular, the decision-theoretic ideas of decentralization and price aggregation. The consumers have a price-independent relative income distribution. The existence and unicity of temporary equilibria are investigated.      

Optimal software release policies with simultaneous cost and reliability requirements

A cost-reliability optimal software release problem is investigated for three existing software reliability growth models. The decision policies on the optimum software release times are discussed by evaluating both software cost and software reliability criteria simultaneously.     

Estimation of the number of missing observations with applications to software reliability

In this paper, starting from an important and interesting problem of software reliability prediction, we arrive at a rather unusual problem of estimation of the number of missing observations in a truncated sample. For different types of truncation we present some easily calculated estimates and discuss their properties. Added to the English translation