The Mean Value Theorem for Integrals Method  for Estimating Two-Dimensional Renewal Functions

Leopoldus Ricky Sasongko; Bambang Susanto

doi:10.31764/jtam.v4i1.1831

The Mean Value Theorem for Integrals Method for Estimating Two-Dimensional Renewal Functions

Leopoldus Ricky Sasongko, Bambang Susanto

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 component from the two-dimensional renewal functions as the solution 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.

Keywords

Two-Dimensional Warranty; Renewal Functions; Renewal Integral Equations; Mean Value Theorem for Integrals; Bivariate Weibull Model.

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DOI: https://doi.org/10.31764/jtam.v4i1.1831