Topic
Renewal theory
About: Renewal theory is a research topic. Over the lifetime, 2381 publications have been published within this topic receiving 54908 citations.
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TL;DR: The economic and economic-statistical design of a χ 2 chart for a maintenance application is considered, and an additional constraint guaranteeing the occurrence of the true alarm signal on the chart before failure with given probability is considered.
44 citations
15 May 2010
TL;DR: In this paper, a point process describing the occurrence of the claims, a model for the cost of claims, and a premium are discussed, and examples of Cox processes which have been used in risk models are given.
Abstract: An insurance risk model consists of three parts: a point process describing the occurrence of the claims, a model for the cost of the claims, and a premium. Here Poisson processes, renewal processes, and Cox processes are discussed. Examples of Cox processes which have been used in risk models are given. Classes of distributions for the cost of the claims mentioned are exponentially bounded distributions or light-tailed distributions, subexponential distributions or heavy-tailed distributions, and an intermediate case.
Keywords:
poisson process;
renewal process;
cox process;
exponentially bounded distributions;
light tails;
subexponential distributions;
heavy tails
44 citations
TL;DR: In this paper, a multi-objective model for the time-cost trade-off problem in a dynamic PERT network using an interactive approach is developed, where the activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities.
44 citations
TL;DR: In this article, the authors conjecture the limit distributions of the "understandingshoot" and "overshoot" at the passage of a high level by subordinators, and then prove these conjectures by Levy-process methods.
44 citations
01 Jan 2006
TL;DR: A multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach is developed and extended to the generalized Erlang activity durations.
Abstract: We develop a multi-objective model for the time–cost trade-off problem in a dynamic PERT network using an interactive approach. The activity durations are exponentially distributed random variables and the new projects are generated according to a renewal process and share the same facilities. Thus, these projects cannot be analyzed independently. This dynamic PERT network is represented as a network of queues, where the service times represent the durations of the corresponding activities and the arrival stream to each node follows a renewal process. At the first stage, we transform the dynamic PERT network into a proper stochastic network and then compute the project completion time distribution by constructing a continuous-time Markov chain. At the second stage, the time–cost trade-off problem is formulated as a multi-objective optimal control problem that involves four conflicting objective functions. Then, the STEM method is used to solve a discrete-time approximation of the original problem. Finally, the proposed methodology is extended to the generalized Erlang activity durations. 2006 Elsevier B.V. All rights reserved.
44 citations