It is of great importane to make a recovery action to reconstruct the logical consistency of the databese on the occasion of a system failure. Such a recovery action consists of two operations. One is UNDO operation, which rolls back the effects of all incomplete transactions from the database, and the other is REDO operation, which reflects the results of all complete transactions in the databese. In general, we limit the amount of REDO operation by generating checkpoints, in which the results of a complete transactions(s) are collected in a safe place. In this paper, we discuss evaluation for a database recovery action with periodical checkpoint generations. A new model is proposed to evaluate the recovery action in a case where a failure rate of the system changes with time. The expected recovery time and the availability for one cycle are derived under the assumption of an arbitrary failure-time distribution. In particular, we obtain analytically the optimum checkpoint interval with the maximum availability in the case of an exponential distribution. We numerically calculate the above results by assuming Weibull distributions. We further discuss the numerical results in varying the parameters that we define in our model, and show the impact of these parameters on the recovery action.

This paper proposes a statistical method to estimate the optimal software release time which minimizes the expected total software cost incurred in both testing and operation phases. It is shown that the underlying cost minimization problem can be reduced to a graphical one. This implies that the software release problem under consideration is essentially equivalent to a time series forecasting for the software fault-occurrence time data. In order to predict the future fault-occurrence time, we apply three extraordinary auto-regressive models by Singpurwalla and Soyer (1985) as the prediction devices as well as the well-known AR and ARIMA models. Numerical examples are devoted to illustrate the predictive performance for the proposed method. We compare it with the classical exponential software reliability growth model based on the non-homogeneous Poisson process, using actual software fault-occurrence time 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.

In this paper, we develop an effective smoothing technique to estimate the optimal software release schedule which minimizes the total software cost. The optimal software release problem is essentially reduced to a statistical estimation problem for the software failure rate, but the resulting estimator based on both the fault-detection time data observed in testing phase and its estimate in future is discontinuous and does not always function well for determining the optimal release schedule. We estimate the smoothed software failure rate using the usual quadratic programming approach and generate the optimal software release schedule with higher accuracy.

This paper considers a probabilistic model for a database recovery action with checkpoint generations when system failures occur according to a renewal process whose renewal density depends on the cumulative operation period since the last checkpoint. Necessary and sufficient conditions on the existence of the optimal checkpoint interval which maximizes the ergodic availability are analytically derived, and solvable examples are given for the well-known failure time distributions. Further, several methods to be needed for numerical calculations are proposed when the information on system failures is not sufficient. We use four analytical/tractable approximation methods to calculate the optimal checkpoint schedule. Finally, it is shown through numerical comparisons that the gamma approximation method is the best to seek the approximate solution precisely.

Non-homogeneous Poisson Processes (NHPP's) can be applied for analyzing reliability growth models for hardware and/or software. Evaluating the Mean Time Between Failures (MTBF's) for such processes, we can evaluate the present status (the degree of improvement). However, it is difficult to evaluate the MTBF's for such processes analytically except the simplest cases. The so-called instantaneous MTBF's which can be easily evaluated are applied in practice instead of the exact MTBF's. In this paper, we discuss both MTBF's analytically, and derive the conditions for the existence of both exact and instantaneous MTBF's. We further illustrate both MTBF's for the Weibull process and S-shaped reliability growth model numerically.

A computing system, which plays an important role in our society, should be operated with high reliability and performance. A multisystem is one of the typical fault-tolerant computing systems, and is widely used in our society because of its high reliability and performance. In this paper we discuss a multisystem composed of two processors and buffer(s), and evaluate the system taking account of the reliability, performance and computational demands simultaneously. We propose two models for the system from the viewpoint of job assignment. Applying Markov renewal and queuing theories, we obtain the reliability/performance measures for each model. Using the numerical results of our models, we compare two models and show the impact of job assignment on the evaluation measures based on our numerical examples.

This paper considers two simulation models for simple unreliable file systems with checkpointing and rollback recovery. In Model 1, the checkpoint is generated at a pre-specified time and the information on the main memory since the last checkpoint is back-uped in a secondary medium. On the other hand, in Model 2, the checkpointing is executed at the time when the number of transactions completed for processing is achieved at a pre-determined level. However, it is difficult to treat such models analytically without employing any approximation method, if queueing effects related with arrival and processing of transactions can not be ignored. We apply the generalized stochastic Petri net (GSPN) to represent the stochastic behaviour of systems under two checkpointing schemes. Throughout GSPN simulation, we evaluate quantitatively the maintainability of checkpoint models under consideration and examine the dependence of model parameters in the optimal checkpoint policies and their associated system availabilities.

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.

The software rejuvenation is one of the most effective preventive maintenance technique for operational software systems with high assurance requirement. In this paper, we propose the workload-based software rejuvenation scheme for a server type of software system, and develop stochastic models to determine the optimal software rejuvenation schedules for some dependability measures. In numerical examples, we evaluate quantitatively the performance of workload-based software rejuvenation scheme and compare it with the time-based rejuvenation scheme.

This article considers a hybrid data backup model for a file system, which combines both conventional magnetic disk (MD) and write-once, read-many optical disk (OD). Since OD recently is a lower cost medium as well as a longer life medium than the ordinary MD, this kind of backup configuration is just recognized to be important. We mathematically formulate the hybrid data backup model and obtain the closed-form average cost rate when the system failure time and the recovery time follow exponential distributions. Numerical calculations are carried out to obtain the optimal backup policy, which is composed of two kinds of backup sizes from the main memory to MD and from MD to OD and minimizes the average cost rate. In numerical examples, the dependence of the optimal backup policy on the failure and the recovery mechanism is examined.

Checkpointing is one of the most powerful tools to operate a computer system with high reliability. We should execute the optimal checkpointing in some sense. This note shows the optimal checkpoint sequence minimizing the expected loss, Numerical examples are shown for illustration.

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.