This paper models age replacement and block replacement when there is the possibility of defaulting on the planned maintenance. A default occurs when a planned preventive replacement is not executed, and we discuss how defaults can arise in practice. Our aim is to study the robustness of block replacement and age replacement, bearing in mind that (a) these policies are frequently used in practice, (b) in the standard scenario (no defaulting) age replacement has a lower economic cost rate than block-replacement and (c) block replacement is simple to manage because component age does not have to be monitored. We model defaults as independent Bernoulli trials. We prove that a cost-minimizing critical age for replacement in the age policy with defaulting exists if the time to failure distribution has an increasing failure rate. A numerical study of the policies indicates that: age replacement is effective if maintenance control is good, that is, when there is only a small chance of defaulting; block replacement is relatively robust to defaulting (postponement), but less so to lack of knowledge about component reliability.

中文翻译：

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使用默认值进行预防性替换

当计划的维护可能发生违约时，本文将对年龄替换和块替换进行建模。当不执行计划的预防性更换时，就会发生违约，我们将讨论在实践中如何产生违约。我们的目的是研究区块替换和年龄替换的鲁棒性，同时牢记（a）这些政策在实践中经常使用，（b）在标准情况下（无违约），年龄替换的经济成本率低于区块-replacement和（c）块替换易于管理，因为不必监视组件寿命。我们将默认值建模为独立的伯努利试验。我们证明，如果失效时间分配的失效率不断增加，则存在将费用默认值最小化的可替换年龄策略中的临界年龄。对这些策略的数值研究表明：如果维护控制良好，即只有很少的违约机会，则更换年龄是有效的；块替换对于默认（延迟）相对较健壮，但对于缺少组件可靠性的知识则较差。