The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions
DOI:
https://doi.org/10.31764/jtam.v4i1.1831Keywords:
Two-Dimensional Warranty, Renewal Functions, Renewal Integral Equations, Mean Value Theorem for Integrals, Bivariate Weibull Model.Abstract
An important aspect in the provision of a two-dimensional warranty is the expected number of failures of a component during the two-dimensional warranty period. The purpose of this paper is to present a new method to obtain the expected number of failures of a nonrepairable compoÂnent from the two-dimensional renewal functions as the soÂlution of two-dimensional renewal integral equations through the Mean Value Theorem for Integrals (MeVTI) method. The two-dimensional renewal integral equation involves Lu-Bhattacharyya’s bivariate Weibull model as a two-dimensional failure model. It turns out that the estimation of the expected number of failures using the MeVTI method is close to that of the other method, Riemann-Stieljies method. The bivariate data behaviour of the failures of an automobile component is also studied in this paper.
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