International Journal of Reliability, Quality and Safety Engineering

The geometric Poisson model for software reliability and debugging was introduced by P. B. Moranda to deal with the situation when one is collecting grouped data on faults (say for example the number of faults detected weekly or monthly) in a new piece of software. In this model one assumes that the number of faults or bugs detected in subsequent intervals of equal length of time in testing a piece of software are independent Poisson random variables with respective Poisson parameters which form a decreasing geometric sequence. An important problem in software reliability testing is to decide when to stop testing and release software for commercial use. In this paper we determine the optimal time T* to release software under the geometric Poisson model with a cost structure for repairing or fixing faults by minimizing the expected cost. We consider both the situation where one is interested in the software performing well until some fixed software life-cycle time t, and for the case where we want the software to function well for an additional τ units of (mission) time after release. Solutions are obtained both when parameter estimates are available as well as in the Bayesian framework when prior information on these parameters is at hand.

A fuzzy software reliability model is proposed where the time intervals between the software failures are taken as the fuzzy variables governed by a membership function. The model takes into account the following assumptions: new faults may be introduced into the software during debugging processes, the number of faults removed after a failure may be greater than one, and there is a growth of human experience during debugging. The model can be considered as an extension of the model developed by Cai, Wen and Zhang. An efficient algorithm is presented for estimating parameters of the model. The numerical examples validate the proposed model.

A circular consecutive 2-out-of-(m, n): F system is considered. A recursive method for calculating the reliability of the system is presented. The method depends on the one-to-one correspondence relation of the systems and the class of 0–1 matrices having no two consecutive 1's at any row or column.

Reliability evaluation of a large and complex system is quite an involved and time-consuming process and its state-of-art is far from being called as satisfactory. This is mainly due to the fact that unionizing path sets results in large number of terms in the reliability expression. Thereafter, the process of computing numerical value of system reliability from its expression is a task not free from the build up of round-off errors. The entire process also restricts the use of a low-end PC for computing system reliability of such systems.

In this paper, we propose an efficient methodology to evaluate reliability of large and complex systems based on minimal path sets; the path sets enumeration procedure used in this paper generates path sets in lexicographic and increasing order of cardinality — a condition, which is helpful in obtaining sum of disjoint products (SDP) of the system reliability expression in a compact form. Although we make use of the system connection matrix but no complicated matrix operations are performed to obtain the results.

The paper further presents an improved multi-variable inversion (MVI) algorithm to evaluate system reliability in a compact form. Our approach offers an extensive reduction in the number of mutually disjoint terms and provides a minimized and compact system reliability expression. The procedure not only results in substantial saving of CPU time but also can be run on a low-end PC. To demonstrate this capability, we solve several problems of varied complexities on a low-end PC and also provide a comparison of our approach with earlier techniques available for the purpose.

In this paper a process targeting model for three class screening problem is developed. The model developed, extends the work in the literature by incorporating product uniformity. The product uniformity is introduced via a Taguchi type quadratic loss function. Two cases for the process Targeting are considered. In addition, an illustrative example is presented. Sensitivity analysis is also conducted to study the effect of model parameters on expected profit and optimal process mean.

For discrete distribution with reliability function R(k), k = 1, 2,…,[R(k - 1) - R(k)]/R(k - 1) has been used as the definition of the failure rate function in the literature. However, this is different from that of the continuous case. This discrete version has the interpretation of a probability while it is known that a failure rate is not a probability in the continuous case. This discrete failure rate is bounded, and hence cannot be convex, e.g., it cannot grow linearly. It is not additive for series system while the additivity for series system is a common understanding in practice. In the paper, another definition of discrete failure rate function as In[R(k - 1)/R(k)] is introduced, and the above-mentioned problems are resolved. On the other hand, it is shown that the two failure rate definitions have the same monotonicity property. That is, if one is increasing/decreasing, the other is also increasing/decreasing. For other aging concepts, the new failure rate definition is more appropriate. The failure rate functions according to this definition are given for a number of useful discrete reliability functions.