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.

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.

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.

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.