Repairable System Analysis Using the Discrete Weibull Distribution

In many practical circumstances, a repair can be performed when a system fails to restore to a condition before a failure. This type of repair is known as minimal repair and one of the most used models is the power law process (PLP). It is common to consider equipment failure time as a continuous variable in this model, assuming a high degree of accuracy in the measurement tool. However, in practical situations, failures are usually observed and recorded as integer numbers of time units, such as the number of days and hours, indicating a discrete process. In this study, we used a discrete Weibull distribution instead of a continuous Weibull distribution. Since both Weibull models have similar complexities, some benefits are observed in the usage of the discrete model, such as a lower standard deviation of the parameter related to the system deterioration and also a lower Akaike's information criterion. For illustrative purposes, the use of a discrete Weibull distribution was applied to a dataset related to the failures of concrete mixer trucks. Moreover, an approach using a Markov chain with discrete states to obtain the average number of failures and the respective optimum maintenance policy was included. Additionally, six cases (found in the literature) fitted by the PLP model were reanalyzed and compared under the discrete model perspective.