A consecutive-k-out-of-n:G system consists of n components which are arranged in a line and the system works if and only if at least k consecutive components work. This paper discusses the optimization problems for a consecutive-k-out-of-n:G system. We first focus on the optimal number of components at the system design phase. Then, we focus on the optimal replacement time at the system operation phase by considering a preventive replacement, which the system is replaced at the planned time or the time of system failure which occurs first. The expected cost rates of two optimization problems are considered as objective functions to be minimized. Finally, we give study cases for the proposed optimization problems and evaluate the feasibility of the policies.

Recently, the wavelet-based estimation method has gradually been becoming popular as a new tool for software reliability assessment. The wavelet transform possesses both spatial and temporal resolution which makes the wavelet-based estimation method powerful in extracting necessary information from observed software fault data, in global and local points of view at the same time. This enables us to estimate the software reliability measures in higher accuracy. However, in the existing works, only the point estimation of the wavelet-based approach was focused, where the underlying stochastic process to describe the software-fault detection phenomena was modeled by a non-homogeneous Poisson process. In this paper, we propose an interval estimation method for the wavelet-based approach, aiming at taking account of uncertainty which was left out of consideration in point estimation. More specifically, we employ the simulation-based bootstrap method, and derive the confidence intervals of software reliability measures such as the software intensity function and the expected cumulative number of software faults. To this end, we extend the well-known thinning algorithm for the purpose of generating multiple sample data from one set of software-fault count data. The results of numerical analysis with real software fault data make it clear that, our proposal is a decision support method which enables the practitioners to do flexible decision making in software development project management.

Non-homogeneous Poisson processes (NHPPs) have gained much popularity in actual software testing phases to estimate the software reliability, the number of remaining faults in software and the software release timing. In this paper, we propose a new modeling approach for the NHPP-based software reliability models (SRMs) to describe the stochastic behavior of software fault-detection processes. The fundamental idea is to apply the equilibrium distribution to the fault-detection time distribution in NHPP-based modeling. We also develop efficient parameter estimation procedures for the proposed NHPP-based SRMs. Through numerical experiments, it can be concluded that the proposed NHPP-based SRMs outperform the existing ones in many data sets from the perspective of goodness-of-fit and prediction performance.

The non-homogeneous Poisson process (NHPP) has been applied successfully to model nonstationary counting phenomena for a large class of problems. In software reliability engineering, the NHPP-based software reliability models (SRMs) are of a very important class. Since NHPP is characterized by its rate (intensity) function, which is known as the software failure rate of NHPP-based SRM, it is of great interest to estimate accurately the rate function from observed software failure data. In the existing work the same authors introduced a Haar-wavelet-based technique for this problem and found that the Haar wavelet transform provided a very powerful performance in estimating software failure rate. In this paper, we consider the application potentiality of a Daubechies wavelet estimator in the estimation of software failure rate, given the software failure time data. We give practical solutions by overcoming technical difficulties in applying the Daubechies wavelet estimator to the real software failure time data.

Using a matrix approach based on a Markov process, we investigate the reliability of a circular connected-(1,2)-or-(2,1)-out-of-(m,n):F lattice system for the i.i.d. case. We develop a modified linear lattice system that is equivalent to this circular system, and propose a methodology that allows the systematic calculation of the reliability. It is based on ideas presented by Fu and Hu [6]. A partial transition probability matrix is used to reduce the computational complexity of the calculations, and closed formulas are derived for special cases.

In a network topology design problem, it is important to analyze the reliability and construction cost of complex network systems. This paper addresses a topological optimization problem of minimizing the total cost of a network system with separate subsystems under a reliability constraint. To solve this problem, we develop three algorithms. The first algorithm finds an exact solution. The second one finds an exact solution, specialized for a system with identical subsystems. The third one is a heuristic algorithm, which finds an approximate solution when a network system has several identical subsystems. We also conduct numerical experiments and demonstrate the efficacy and efficiency of the developed algorithms.

A connected-(r,s)-out-of-(m,n): F system is a kind of the connected-X-out-of-(m,n): F system defined by Boehme et al. [2]. A connected-(r,s)-out-of-(m,n): F system consists of m×n components arranged in (m,n)-matrix. This system fails if and only if there exists a grid of size r×s in which all components are failed. When m=r, this system can be regarded as a consecutive-s-out-of-n: F system, and then the optimal arrangement of this system satisfies theorem which stated by Malon [9] in the case of s=2. In this study, we proposed a new algorithm for obtaining optimal arrangement of the connected-(r,2)-out-of-(m,n): F system based on the above mentioned idea. We performed numerical experiments in order to compare the proposed algorithm with the algorithm of enumeration method, and calculated the order of the computation time of these two algorithms. The numerical experiments showed that the proposed algorithm was more efficiently than the algorithm of enumeration method.

A new modeling approach for the non-homogeneous Poisson processes (NHPPs) based software reliability modeling is proposed to describe the stochastic behavior of software fault-detection processes, of which the failure rate is not monotonic. The fundamental idea is to apply the Marshall-Olkin distribution to the software fault-detection time distribution. The applicability of Marshall-Olkin distribution in software reliability modeling is studied. The data fitting abilities of the proposed NHPP-based software reliability model is compared with the existing typical ones through real software project data analysis.