In this article, we consider nonparametric estimation methods for a periodic replacement problem with minimal repair, where the expected cumulative number of failures (minimal repairs) is unknown. To construct the confidence interval of an estimator of the optimal periodic replacement time which minimizes the long-run average cost per unit time, we apply two kernel-based bootstrap estimation methods and three replication techniques for bootstrap samples, to estimate the optimal periodic replacement time under incomplete knowledge on the failure time distribution. In simulation experiments, we compare those results with the well-known constrained nonparametric maximum likelihood estimate and some parametric models. We also conduct the field data analysis based on an actual minimal repair data and refer to an applicability of our methods.
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