In this paper, we construct a software availability model considering the number of restoration actions. We correlate the failure and restoration characteristics of the software system with the cumulative number of corrected faults. Furthermore, we consider an imperfect debugging environment where the detected faults are not always corrected and removed from the system. The time-dependent behavior of the system alternating between up and down states is described by a Markov process. From this model, we can derive quantitative measures for software availability assessment considering the number of restoration actions. Finally, we show numerical examples of software availability analysis.

We develop a software availability model incorporating software failure-occurrence and fault-correction times, under the assumption that the hazard rate for software failure-occurrence decreases geometrically with the progress in fault-removal process. Considering that the software system alternates two states, i.e. the operational state that a system is operating and the maintenance state that a system is inoperable due to the fault-correction activity, we model the time-dependent behavior of the system with a Markov process. Expressions for several quantities of software system perfomance are derived from this model. Finally, numerical examples are presented for illustration of software availability measurement.

Software development managers and users have been interested in software availability for the software operational phase. It is of great importance to assess software reliability and performance during the operation phase. Therefore, we discuss software availability measurement based on software reliability growth models which describe behavior of software errors detected during the testing and operation phase. These models are formulated by nonhomogeneous Poisson processes (NHPP). The software availability index is defined as the possible system utilization factor which means the percentage of time that the software system will be available for operation. We show numerical examples on software availability measurement for actual software error data.

Modeling of software reliability growth for a software error detection process is one of key objectives in software reliability. Most of software reliability growth models proposed in the existing literature have adopted a calendar time or machine execution time as the unit of error detection period. This paper investigates a software reliability growth model which uses the number of test runs or executed test cases as the unit of error detection period. The model is discussed by assuming a nonhomogeneous Poission process (NHPP) in which the random variable is defined as the number of software errors detected out of n test runs (n0, 1, 2, ). The NHPP model has a mean value function showing an exponential growth curve. A set of actual software error data is analyzed, and the maximum likelihood estimates of the unknown parameters and the related quantitative indices for software reliability assessment are obtained. The goodness-of-fit test shows that the observed data well-fit the NHPP model. Finally, a software release problem based on a reliability criterion is discussed.

In this paper existing software reliability growth models are reviewed by an error detection rate theory which is based on a nonhomogeneous Poisson process. The underlying concept of a software reliability growth model is summarized under general conditions. And the related software reliability measures and the maximum likelihood estimation of the model parameters are presented. The error detection rate theory is developed on the summary above of a software reliability growth model. As a software reliability growth index the error detection rate per error playes an important role in reviewing and classifying existing software reliability growth models. The models discussed here are the exponential, modified exponential, delayed S-shaped, and inflection S-shaped reliability growth models. Numerical illustrations for actual software error data are presented to show the relationship between the software reliability growth and the error detection rate.

Many software reliability growth models have been proposed in the last decade, based on software error data observed during testing phase in the software development. However, the existing models are insufficient to represent the time-dependent behavior of testing-effort expenditures in the actual environment of the software testing. For this reason we develop and investigate a testing-effort dependent reliability model incorporating the testing-effort spent on software testing into the software reliability growth. The model is described by a non-homogeneous Poisson process, assuming that the error detection rate to the amount of testing-effort spent at an arbitrary testing time is proportional to the current error content. The time-dependent behavior of testing-effort expenditures is described by a Weibull curve due to the flexibility. From this model, the quantitative software reliability measures are derived. The estimations for the testing-effort parameters and the reliability growth parameters in the model are given by a method of least-squares and by a method of maximum-likelihood, respectively. Then, statistical inferences on the model parameters and the software reliability measures, and analyses of actual software error data and studied.

This paper discusses an optimal software release problem, based on a software reliability growth model incorporating the time-dependent behavior of testing-effort expenditures in the software testing. The problem presents an optimum release time when to stop testing and to be ready for release to the user. In particular, we consider a penalty cost due to delay in the scheduled software delivery time. Using a testing-effort function described a Weibull curve, a software reliability growth process in the error detection phenomenon in software testing is modeled based on a nonhomogeneous Poisson process. The testing-effort parameters and the reliability growth parameters in the model are estimated by a modified least-squares estimation and by a maximum-likelihood estimation, respectively. Based on the software reliability growth mode, the optimal software release problem is formulated by using the total expected software cost to be minimized. Further, numerical examples are presented for illustrations.

The inflection S-shaped software reliability growth model (SRGM) proposed by Ohba (1984) is one of the well- known SRGMs. This paper deals with the optimal software release problem with regard to the expected software cost under this model based on the Bayesian approach. To reflect the effect of the learning experience for the updated software system, we consider several improvement factors to adjust the values of parameters characterizing the inflection S-shaped SRGM. Appropriate prior distributions are assumed for such factors and the expected total software cost is formulated. The optimal release time is shown to be finite and uniquely determined. Because of the flexibility of prior distributions, the proposed Bayesian methods may be applied in many different situations. Numerical results are presented on the basis of the real data.

In this paper, we propose a new software reliability growth model which is the mixture of two exponential reliability growth models, one of which has the reliability growth and the other one does not have the reliability growth after the software is released upon completion of testing phase. The mixture of two such models is characterized by a weighted factor p, which is the proportion of reliability growth part within the model. Firstly, this paper discusses an optimal software release problem with regard to the expected total software cost incurred during the warranty period under the proposed software reliability growth model, which generalizes Kimura, Toyota and Yamada's (1999) model with consideration of the weighted factor. The second main purpose of this paper is to apply the Bayesian approach to the optimal software release policy by assuming the prior distributions for the unknown parameters contained in the proposed software reliability growth model. Some numerical examples are presented for the purpose of comparing the optimal software release policies depending on the choice of parameters by the non-Bayesian and Bayesian methods.

In this paper we propose a discrete program-size dependent software reliability growth model flexibly describing the software failure-occurrence phenomenon based on a discrete Weibull distribution. We also conduct model comparisons of our discrete SRGM with existing discrete SRGMs by using actual data sets. The program size is one of the important metrics of software complexity. It is known that flexible discrete software reliability growth modeling is difficult due to the mathematical manipulation under a conventional modeling-framework in which the time-dependent behavior of the cumulative number of detected faults is formulated by a difference equation. Our discrete SRGM is developed under an existing unified modeling-framework based on the concept of general order-statistics, and can incorporate the effect of the program size into software reliability assessment. Further, we discuss the method of parameter estimation, and derive software reliability assessment measures of our discrete SRGM. Finally, we show numerical examples of discrete software reliability analysis based on our discrete SRGM by using actual data.

In this paper, we discuss software performability evaluation considering the real-time property; this is defined as the attribute that the system can complete the task within the stipulated response time limit. We assume that the software system has two operational states from the viewpoint of the end users: one is operating with the desirable performance level according to specification and the other is with degraded performance level. The dynamic software reliability growth process with performance degradation is described by the extended Markovian software reliability model with imperfect debugging. Assuming that the software system can process the multiple tasks simultaneously and that the arrival process of the tasks follows a nonhomogeneous Poisson process, we analyze the distribution of the number of tasks whose processes can be completed within the processing time limit with the infinite server queueing model. We derive several software performability measures considering the real-time property; these are given as the functions of time and the number of debugging activities. Finally, we illustrate several numerical examples of the measures to investigate the impact of consideration of the performance degradation on the system performability evaluation.

We discuss software reliability assessment considering multiple changes of software fault-detection phenomenon. The testing-time when the characteristic of the software failure-occurrence or fault-detection phenomenon changes notably in the testing-phase of a software development process is called change-point. It is known that the occurrence of the change-point influences the accuracy for the software reliability assessment based on a software reliability growth models, which are mainly divided into software failure-occurrence time and fault counting models. This paper discusses software reliability growth modeling frameworks considering with the effect of the multiple change-point occurrence on the software reliability growth process in software failure-occurrence time and fault counting modeling. And we show numerical illustrations for the software reliability analyses based on our models by using actual data.

In this paper, we propose a plausible software reliability growth model by applying a mathematical technique of stochastic differential equations. First, we extend a basic differential equation describing the average behavior of software fault-detection processes during the testing phase to a stochastic differential equation of ItÔ type, and derive a probability distribution of its solution processes. Second, we obtain several software reliability measures from the probability distribution. Finally, applying a method of maximum-likelihood we estimate unknown parameters in our model by using available data in the actual software testing procedures, and numerically show the stochastic behavior of the number of faults remaining in the software system. Further, the model is compared among the existing software reliability growth models in terms of goodness-of-fit.

This paper describes a segment driver IC for high-quality liquid-crystal-displays (LCDs). Major design issues in the segment driver IC are a wide signal bandwidth and excessive output-offset variation both within a chip and between chips. After clarifying the trade-off relation between the signal bandwidth and the output-offset variation originated from conventional sample-and-hold (S/H) circuits, two wide-band S/H circuits with low output-offset variation have been introduced. The basic ideas for the proposed S/H circuits are to improve timing of the sampling pulses applied to MOS analog switches and to prevent channel charge injection onto a storage capacitor when the switches turn off. The inter-chip offset-cancellation technique has been also introduced by using an additional S/H circuit. Two test chips were implemented using the above S/H circuits for demonstration purposes. The intra-chip output-offset standard deviation of 9.5 mVrms with a 3dB bandwidth of 50 MHz was achieved. The inter-chip output-offset standard deviation was reduced to 5.1 mVrms by using the inter-chip offset-cancellation technique. The evaluation of picture quality of an LCD using the chips shows the applicability of the proposed approaches to displays used for multimedia applications.

In this paper, we discuss the stochastic modeling for operational software reliability measurement, assuming that the testing environment is originally different from the user operation one. In particular, we introduce the concept of systemability which is defined as the reliability characteristic subject to the uncertainty of the field operational environment into the model. First we introduce the environmental factor to consistently bridge the gap between the software failure-occurrence characteristics during the testing and the operation phases. Then we consider the randomness of the environmental factor, i.e., the environmental factor is treated as a random-distributed variable. We use the Markovian imperfect debugging model to describe the software reliability growth phenomena in the testing and the operation phases. We derive the analytical solutions of the several operational software reliability assessment measures which are given as the functions of time and the number of debuggings. Finally, we show several numerical illustrations to investigate the impacts of the consideration of systemability on the field software reliability evaluation.

The higher a social mission of computer systems becomes, the more important developing highly reliable computer softwares becomes. During the testing phase in the software development, a developed software is repeatedly tested with a lot of test cases to remove latent software errors. Using the observed test data, it is of great interest to evaluate reliability for the developed software. In this paper, we propose and investigate a software reliability growth model for software error detection phenomena in the software testing. The useful software reliability measures are derived from the model. Using the number of test runs as the unit of software error detection period, the model is described by a nonhomogeneous Poisson process in which the random variable is the cumulative number of software errors detected by the testing. The model proposed here considers that the testing efficiency is geometrically decreasing with the progress of software testing. We apply this model to a set of actual software error data and illustrate the statistical inferences based on a method of maximum likelihood. Finally, an optimum software release problem using software reliability index is discussed as a practical application of the model.

Actual debugging actions during the testing phase in the software development and the operation phase are not always performed perfectly. In other words, all detected software faults are not corrected and removed certainly. Generally, this is called imperfect debugging. In this paper, we discuss a software reliability growth model considering imperfect debugging that faults are not always corrected/removed when they are detected. Defining a random variable representing the cumulative number of faults corrected up to a specified testing time, this model is described by a semi-Markov process. We derive various quantitative measures for software reliability assessment and show their numercal examples.

It is of great importance to propose the appropriate quantitative measures for assessing the software performance in software reliability. During the software development phase, a software system is tested to eliminate software errors, which can be detected by a test tool and corrected in accordance with standardized procedures. Then, of our interest is the following: How many statements or steps including the software errors can be corrected up to time t in a program? We consider a software failure process by describing two distinct processes, i.e., the error detection and error correction processes. That is, each software error detection takes place with the counting process on time axis and the error correction can be described by the cumulative process in which the number of the statements or steps corrected for each error detection obeys a Poisson distribution. The stochastic behavior of such a model can be analyzed by applying the theory of cumulative processes. We propose two models based on the nonhomogeneous Poisson process and the De-Eutrophication process. Several useful quantitative measures associated with the total number of statements or steps corrected up to time t are derived. The numerical examples of these measures are shown and two models are compared.