Renewal theory

About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.

Availability for repairable components and series systems

Abstract: The failure pattern of repairable components is often modelled by an alternating renewal process which implies that a failed component is perfectly repaired. In practice, repair is often imperfect. This paper proposes a generalized availability model for repairable components and series systems. The lifetime of a repaired component has a general distribution which can be different from that of a new component. Availability and some asymptotic quantities in these models are derived. An example illustrates the application of these models. >

Mr/gi/1 queues with positively correlated arrival stream

Abstract: The effects of dependencies (such as association) in the arrival process to a single server queue on mean queue lengths and mean waiting times are studied. Markov renewal arrival processes with a particular transition matrix for the underlying Markov chain are used which allow us to change dependency properties without at the same time changing distributional conditions. It turns out that correlations do not seem to be pure effects, and three main factors are studied: (a) differences in the mean interarrival times in the underlying Markov renewal process, (b) intensity in the Markov renewal jump process, (c) variability in the point processes underlying the Markov renewal process. It is shown that the mean queue length can be made arbitrarily large in the class of queues with the same interarrival distributions and the same service time distributions (with fixed smaller than one traffic intensity), by making (a) large enough and (b) small enough. The existence of the moments of interest is confirmed and some stochastic comparison results for actual waiting times

Characterization of distributions by relationships between failure rate and mean residual life

Abstract: The characterizations described use relations between the failure rate function and conditional expectation. The theorems proved here extend the results of some authors and can be used in the context of the renewal process. The utility of these results is demonstrated by using them to characterize some common distributions. >

A Discrete-Time Model for Common Lifetime Inventory Systems

Abstract: We consider a discrete-time (s, S) inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventory-level process. We obtain a closed-form expected cost function. Numerical results demonstrate some properties of optimal ordering policies and cost functions. When compared with the results for the constant lifetime model, the variance of the lifetime significantly affects the system behavior. Thus, the formalism that we create here adds a new dimension to the research in perishable inventory control under uncertainty in lifetime.