The (α, β)-Precise Estimates of MTBF and MTTR: Definition, Calculation, and Observation Time

Abstract

The mean time between failures (MTBF) and mean time to repair (MTTR) of manufacturing equipment (e.g., machines) are used in every quantitative method for production systems performance analysis, continuous improvement, and design. Unfortunately, the literature offers no methods for evaluating the smallest number of up- and downtime measurements necessary and sufficient to calculate reliable estimates of these equipment characteristics. This article is intended to provide such a method. The approach is based on introducing the notion of $(\alpha, \beta)$ -precise estimates, where $\alpha $ characterizes the estimate’s accuracy and $\beta $ its probability. Using this notion, this article evaluates the critical number, $n^{*} (\alpha,\beta)$ , of up- and downtime measurements necessary and sufficient to calculate $(\alpha, \beta)$ -precise estimates of MTBF and MTTR. In addition, this article derives a probabilistic upper bound of the observation time required to collect $n^{*} (\alpha,\beta)$ measurements. Note to Practitioners —To evaluate and predict production systems behavior, managers of manufacturing operations need to know equipment reliability characteristics. Quantifying the equipment status by MTBF and MTTR, this article provides answers to the following questions: Q1: How many measurements of machines up- and downtime are required to obtain reliable estimates of MTBF and MTTR? Q2: How long the observation period must be to collect the desired number of measurements? The answer to Q1 is provided by a rule (formula), which is based on the desired estimate accuracy (characterized by $\alpha $ ) and its likelihood (quantified by $\beta $ ). The answer to Q2 consists of selecting a small number of initial measurements, which can be used to calculate an upper bound of the total observation time.