Alagar Rangan and Ehsan MoghimiHadji
The purpose of the paper is to provide useful approximations for the computation of g‐renewal function, since no closed form solution of such a function is available
Abstract
Purpose
The purpose of the paper is to provide useful approximations for the computation of g‐renewal function, since no closed form solution of such a function is available
Design/methodology/approach
One of the methods uses a simple identity to obtain an approximation. The second method uses the Riemann sum to approximate the integrals to obtain a method of successive approximation.
Findings
The two methods provide satisfactory approximations with the relative errors in the computations are well within the acceptable limits. The accuracy of the successive approximation method could be improved with finer partition of the interval integration but at the cost of computational time.
Research limitations/implications
The computational time increases for the evaluation of the renewal function for increasing values of t.
Originality/value
The paper provides easy to evaluate approximations for g‐renewal functions, which do not have closed form analytical solutions.
Details
Keywords
Alagar Rangan, Dimple Thyagarajan and Y Sarada
The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems.
Abstract
Purpose
The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems.
Design/methodology/approach
An N‐policy was adopted by which the system was replaced after the Nth failure.
Findings
The model was found to have practical applications in warranty cost analysis.
Originality/value
By identifying the instance of a shock as the failure of the system and the threshold times as the warranty period offered and changing the definition of lethal shock (system failure in this case) as the occurrence of a shock within a threshold period in our generalized model, one can study the renewing warranty cost analysis.