International Journal of Reliability, Quality and Safety Engineering

During the last two decades many researchers have analyzed the reliability growth of software during the testing and operational phases and proposed the mathematical models to estimate and predict the reliability measures. During the software testing on the detection of a failure the fault that has caused the failure is isolated and removed. Most of the existing research in this area considers that similar testing efforts and strategy are required on each debugging effort. However this may not be true in practice. Different faults may require different amount of testing efforts and testing strategy for their removal. In software reliability modeling in order to incorporate this phenomenon faults are classified into different categories as simple, hard and/or complex faults. This categorization is also extended to n-types of faults. Some of the existing research incorporates this phenomenon considering that the fault removal rate is different for different types of faults and remains constant during the overall period of testing. However this assumption may not apply in general testing environment in practice. It is a common observation that as the testing progresses the fault detection and/or removal rate changes. This change can be due to a number of reasons. The changing testing environment, testing strategy, skill, motivation and constitution of the testing and debugging personnel etc. are some of the major reasons behind this change. In this paper we have formulated the model for the software system developed for safety critical application under a specific testing environment. The model is validated on real life data sets.

The paper presents a heuristic for series-parallel system, exhibiting multi-state behavior, with the objective to minimize the cost in order to provide a desired level of reliability. System reliability is defined as the ability to satisfy consumers demand and is presented as a piecewise cumulative load curve. The components are binary and chosen from the list of products available in the market, and are being characterized by their feeding capacity, reliability and cost. The solution approach makes use of heterogeneous collection of components to provide redundancy in a subsystem. The algorithm has been applied to power systems from the literature for various levels of reliability requirement. The heuristic offers a straightforward analysis and efficiency over genetic algorithm (GA) existing in the literature. Keeping in view the computational efficiency and the observed solution quality the proposed heuristic is appealing. As such, the heuristic developed is attractive and can be easily and efficiently applied to numerous real life systems.

Fortunately traditional reliability theory, where the system and the components are always described simply as functioning or failed, is on the way to being replaced by a theory for multistate systems of multistate components. In this paper, we treat the consecutive k-out-of-n systems. Such systems have caught the attention of many engineers and researchers because of their wide range of application. We define a multistate consecutive k-out-of-n system: G as follows: Each component and the system can be in 1 of M + 1 possible states: 0, 1, 2, …, M. The system is in state ≥ j iff at least k_j consecutive components are in state ≥ j. The value of k_j can be different for different required minimum system state levels. We propose a method based on the combinatorial approach for computing the system's reliability and we give examples to illustrate this method.

In this paper the reliability of a repairable k-out-of-n system is studied. Repair times of components follow a phase type distribution. In addition, the service facility offers service to external customers which arrive according to a MAP. An external customer, who finds an idle server on its arrival, is immediately selected for service. Otherwise, the external customer joins the queue in a pool of postponed work of infinite capacity with probability 1 if the number of failed components in the system is < M (M ≤ n - k + 1) and if the number of failed components ≥ M it joins the pool with probability γ or leaves the system forever. Repair times of components of the system and that of the external customers have independent phase type distributions. At a service completion epoch if the buffer has less than L customers, a pooled customer is taken for service with probability p, 0 < p < 1 If at a service completion epoch no component of the system is waiting for repair, a pooled customer, if any waiting, is immediately taken for service.

We obtain the system state distribution under the condition of stability. A number of performance characteristics are derived. A cost function involving L, M, γ and p is constructed and its behaviour investigated numerically.

An "r-consecutive-k-out-of-n: F system" consists of n linearly ordered components. The system fails if and only if at least r non-overlapping sequences of k consecutive components fail. In this paper we examine this system in the case where the failure probability of a given component depends upon the state (good or failed) of the preceding one i.e. the states of the components form a Markov chain. First we give a recursive formula of the failure probability of such a system when the transition probabilities q_i,0,q_i,1 are not identical where q_i,0 (respectively q_i,1) is the probability that component i fails given that the preceding one fails (respectively works), for i = 1, 2, …, n. Secondly we treat a special case of the same system where q_j,0 = q_i,0 and q_j,1 = q_i,1 for j = mk + i (1 ≤ i ≤ k), and we call such a system an r-consecutive-k-out-of-n: F system with cycle (or period) k with Markov-dependent components, and in this case also we give a formula of the failure probability of the system.