Some optimization problems in reliability and maintenance need to iteratively evaluate the renewal function (RF) of a lifetime distribution and/or its integral. For such problems, an accurate RF approximation with a closed-form expression is preferred to a numerical evaluation method. A number of RF approximations have been developed in the literature but few can simultaneously meet the requirements of simplicity, accuracy and integrability. This article aims to fill this gap by proposing such a RF approximation for the Weibull distribution. The proposed approximation is particularly useful for practitioners to solve the optimization problems that involve the RF and/or its integral.

可靠性和维护方面的一些优化问题需要迭代地评估寿命分布和/或其积分的更新函数（RF）。对于此类问题，使用精确的RF近似值和闭式表达式比数字评估方法更可取。文献中已经开发了许多RF近似值，但很少能同时满足简单性，准确性和可集成性的要求。本文旨在通过针对Weibull分布提出这样的RF近似值来填补这一空白。所提出的近似值对于从业者解决涉及RF和/或其积分的优化问题特别有用。