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: In this article, a renewal theory-based life cycle analysis (RTLCA) is proposed to obtain important life-cycle variables such as the expected time lost in repairs, the reliability of the system and the cost of operation and failure.
63 citations
62 citations
TL;DR: It is shown for two cases that a practical indicator of service received by the renewal customers is the coefficient of variation of their interarrival time distribution, and if the coefficient is less than unity, then the renewalcustomers receive better service than the Poissonian customers.
Abstract: In a queueing system with two independent input streams, as exists, for example, when first-routed and overflow traffic streams are offered to a common sender-group, the state of the system encountered by the two different types of customers upon their arrival will generally be different. Consequently, in a system where delayed customers wait for service, the service rendered to the individual streams may also be different. The delay distribution in a single-server queue for each type of customer is derived under the assumption that one stream is Poissonian and the other is described by a renewal process. The difference in service received by the two streams is examined with the aid of numerical examples for two interarrival time distributions of the renewal stream. We show for two cases that a practical indicator of service received by the renewal customers is the coefficient of variation of their interarrival time distribution. If the coefficient is less than unity, then the renewal customers receive better service than the Poissonian customers. The converse is true when the coefficient exceeds unity. The stationary distribution of the number of busy servers in an infinite-server system as seen by the two types of customers is also derived.
62 citations
TL;DR: In this paper, the authors proposed a new method to determine lifetime distributions for concrete bridges and to compute the expected cost of maintaining and replacing a bridge stock, where the uncertainty in the lifetime of a bridge is represented with a Weibull distribution.
62 citations
TL;DR: In this article, the first two moments of a compound renewal present value risk (CRPVR) process were derived under regularity conditions, using renewal theory arguments, and some examples, extensions and limiting results are also given.
Abstract: Delbaen and Haezendonck [Ins. Math. Econ. 6 (1987) 85] and Willmot [Scand. Actuarial J. 1 (1989) 1] give an analytical expression for the net premium density of a compound Poisson present value risk (CPPVR) process. Their calculation is based, essentially, on the independence of the increments of the CPPVR process. In this paper, under regularity conditions, we derive the first two moments of a compound renewal present value risk (CRPVR) process using renewal theory arguments. Some examples, extensions and limiting results are also given.
62 citations