Finding solutions to the Bellman equation often relies on restrictive boundedness assumptions. In this paper we develop a method of proof that allows to dispense with the assumption that returns are bounded from above. In applications our assumptions only imply that long run average (expected)...

In this paper, we survey a portion of the literature in the analysis of warranty costs. In order to compare the price of different warranty policies, we review a framework which leads to expressing the expected costs in terms of complex functions arising in renewal theory. These functions and...

The paper considers a renewal risk process in which a given inter-arrival time possibly has an impact on the size of the resulting claim. Under a fairly general dependency structure which contains various well-known examples in the literature as special cases, recursive formulas for the moments...

A simple but effective approximation is proposed to compute the renewal function, M(t), and its integral. The asymptotic approximation of the renewal function and its integral, which are widely used in decision makings involving a renewal process, may not perform well when t is not large enough....

It is hard to find explicit expressions for the renewal function U(x)=∑n=0∞F∗n(x). Many researchers have made attempts to find suitable approximations for U(x). In this paper we present simple approximations and show that they cover many of the known results.

We consider a positive recurrent Markov chain on R+ with asymptotically zero drift which behaves like −c1/x at infinity; this model was first considered by Lamperti. We are interested in tail asymptotics for the stationary measure. Our analysis is based on construction of a harmonic function...

Abstract Frequent wastage or exit of personnel are common in many administrative and production oriented organizations. Once the accumulated number of exits from the organization reaches a certain threshold level, it could be viewed as a “breakdown point”. The time to attain breakdown point...

Abstract In this article, an exponential model with only one shape parameter, which can be used in modeling survival data, reliability problems and fatigue life studies, is studied. We derive explicit expressions for some of its statistical and mathematical quantities including the ordinary...

Abstract In this article, a new family of distributions is introduced by using transmutation maps. The proposed family of distributions is expected to be useful in modeling real data sets. The genesis of the proposed family, including several statistical and reliability properties, is presented....

Abstract This paper deals with a new method of deriving the Process Capability Index (PCI) when the quality characteristic X follows a positively skewed distribution. The focus of the paper is to derive a new estimate of PCI by taking into account the {100(1-{\alpha})}   Confidence Intervals...