Recently, Kambo and his co-researchers (2012) proposed a method of approximation for evaluating the one-dimensional renewal function based on the first three moments. Their method is simple and elegant, which gives exact values for well-known distributions. In this article, we propose an analogous method for the evaluation of bivariate renewal function based on the first two moments of the variables and their joint moment. The proposed method yields exact results for certain widely used bivariate distributions like bivariate exponential distribution, bivariate Weibull distributions, and bivariate Pareto distributions. An illustrative example in the form of a two-dimensional warranty problem is considered and comparisons of our method are made with the results of other models.
Availability function which forms an important part of reliability analysis is expressed in terms of an integral equation. The analytical solution of such an equation is possible only in very simple cases and hence approximations are the only tools available; very few such approximations are available in the literature. This paper proposes three useful approximations, two of which are based only on the first few moments of the underlying distributions and do not require their functional forms. The third approximation uses the Riemannian sum to approximate the integral equation. Numerical illustrations based on test cases are provided to show the efficacy of the approximations. As an application, the problem of an opportunistic channel access scheme in a communication network is used to test the approximations.
The main objective of this research is to find a simple and precise methodology for the stochastic generation of flow series having statistical behaviour similar to the registered or reconstituted historical series. The common statistical parameters are the mean, the variance, the auto- and cross-correlations, and, under particular conditions, the skewness coefficient. A procedure to disaggregate annual series to lower levels (monthly or seasonal) is also presented. Finally, the article describes the general computer model utilized for the synthetic generation. Key words: synthetic generation, flow series, disaggregation, computer model.
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