Inter-failure Times Research Articles

On the Software Reliability Models of Jelinski-Moranda and Littlewood

This note provides an alternative formulation of the software reliability models of Jelinski-Moranda and Littlewood. The formulation is in terms of failure times rather than interfailure times; the models are then equivalent to observing the first n order statistics (n is random) from a random sample of size N. The models can be generalized by using a decreasing failure rate for the failure times. For the Jelinski-Moranda model, we comment on the maximum likelihood estimate and an improved estimate for the initial number of faults in the software. We discuss how to check the validity of the Jelinski-Moranda model.

Initial Provisioning of a Standby System with Deteriorating and Repairable Spares

A technique is developed for finding the time dependent operating probabilities used by reliability systems designers for provisioning a system with N + k identical units, k of which are called spares and N called operating units, and s repair facilities. System failure occurs when less than N units are operational. Units fail with exponential interfailure times and are repaired with exponential service time. Idle spares fail due to deterioration at a rate possibly different from that of the operating units. Graphs are presented which show the minimum numbers of spares needed to achieve system reliabilities of 0.90 and 0.99 as a function of time. The technique is applicable for finding, numerically, the first passage time distribution for any system modeled by birth and death processes.

Stochastic duels with nonrepairable weapons

This paper examines the effect of limitation, regarding weapons that are likely to fail during the period of deployment, on the final outcome in a stochastic duel model. Inter-firing times as well as inter-failure times have been assumed to be exponentially distributed.

Probabilistic models of decreasing failure rate processes

AbstractThe “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non‐independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.

On the Behaviour of Complex Systems with Regard to Dependability

In Part I, a Complex System consisting of n components having a wide class of inter-failure time distributions and general repair time distributions with probability densities S1(x), S2(x), .., Sn(x) is examined with regard to Dependability. Some particular results are derived at the end of this part. The well-known phase and supplementary-variable techniques are employed for the solution. Part II considers the possibility of the inclusion of waiting time distribution for a failed system while examining its behaviour with regard to dependability. The Laplace transforms of various probabilities that the system is operable, waiting for repair and under repair are obtained. Some particular cases are then discussed in some detail.