An Approximation to Weibull Renewal Function

doi:10.12005/orms.2022.0394

Abstract

Abstract: The renewal function of the Weibull distribution has many applications, such as product warranty policy analysis, maintenance decision optimization and spare part demand forecasting. The Weibull renewal function does not have a closed-form analytic expression. This leads to inconvenience for solving the optimization problems that involve the Weibull renewal function. A common problem of the existing approximations of the Weibull renewal function is that the accuracy decreases as the shape parameter increases. To address this issue, a novel approximation is proposed in this paper. When the shape parameter is larger than 3.65, the maximum relative error of the proposed approximation is considerably smaller than the maximum relative errors of the existing approximations. An example that deals with maintenance policy optimization is included to illustrate the accuracy and usefulness of the proposed approximation.

Key words: Weibull distribution, renewal function, approximation, maintenance policy optimization

摘要： 威布尔分布的更新函数有许多应用,如产品质保政策分析、维修决策优化和备件需求预测。威布尔更新函数没有解析表达式,这给求解各种涉及更新函数的优化问题带来不便。已有的威布尔更新函数近似式有一个共同的问题:其精度随威布尔形状参数的增大而减小。为克服这个问题,本文提出一个新的近似式,对于大的威布尔形状参数(>3.65),其相对误差比已有近似式的相对误差小得多。一个维修政策优化的数例例证其精确性和有用性。

关键词: 威布尔分布, 更新函数, 近似式, 维修政策优化

CLC Number:

O174

JIANG Ren-yan, ZHANG Bi-wen. An Approximation to Weibull Renewal Function[J]. Operations Research and Management Science, 2022, 31(12): 106-110.

蒋仁言, 张碧雯. 威布尔更新函数的一个精确近似式[J]. 运筹与管理, 2022, 31(12): 106-110.

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