Two approximations of renewal function for any arbitrary lifetime distribution

The renewal functions (RFs) of most distribution functions do not have closed-form expressions while such expressions are desired for the optimization problems involved RF. Many efforts have been made to develop approximations of RF. However, it seems that no RF approximation is accurate enough in t...

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Vydané v:Annals of operations research Ročník 311; číslo 1; s. 151 - 165
Hlavný autor: Jiang, R.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.04.2022
Springer
Springer Nature B.V
Predmet:
Accuracy
Approximation
Approximation theory
Business and Management
Combinatorics
Distribution functions
Inventory control
Mathematical optimization
Methods
Operations research
Operations Research/Decision Theory
Optimization
Reliability (Engineering)
S.I. : Reliability Modeling with Applications Based on Big Data
Theory of Computation
China
Limiting relation
Approximation
Renewal function
Weibull distribution
Lognormal distribution
ISSN:0254-5330, 1572-9338
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Shrnutí:The renewal functions (RFs) of most distribution functions do not have closed-form expressions while such expressions are desired for the optimization problems involved RF. Many efforts have been made to develop approximations of RF. However, it seems that no RF approximation is accurate enough in the entire time range. In this paper, we propose two RF approximations. The first approximation is obtained through smoothly connecting two limiting relations and fairly accurate in the entire time range. The second approximation has the same function form as the first part of the first approximation but the model parameter is determined in a different way so as to achieve higher accuracy for small to moderate time range. The expressions of the proposed approximations are simple and applicable for any arbitrary lifetime distribution. Their accuracy is analyzed and, the appropriateness and usefulness are illustrated by a numerical example.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-019-03356-2