Gustavo L. Gilardoni

ARA and ARI imperfect repair models: Estimation, goodness-of-fit and reliability prediction

An appropriate maintenance policy is essential to reduce expenses and risks related to equipment failures. A fundamental aspect to be considered when specifying such policies is to be able to predict the reliability of the systems under study, based on a well fitted model. In this paper, the classes of models Arithmetic Reduction of Age and Arithmetic Reduction of Intensity are explored. Likelihood functions for such models are derived, and a graphical method is proposed for model selection. A real data set involving failures in trucks used by a Brazilian mining is analyzed considering models with different memories. Parameters, namely, shape and scale for Power Law Process, and the efficiency of repair were estimated for the best fitted model. Estimation of model parameters allowed us to derive reliability estimators to predict the behavior of the failure process. These results are a valuable information for the mining company and can be used to support decision making regarding preventive maintenance policy.

Nonparametric estimation and bootstrap confidence intervals for the optimal maintenance time of a repairable system

Consider a repairable system operating under a maintenance strategy that calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, the failures are assumed to follow a nonhomogeneous Poisson process with an increasing intensity function. This paper departs from the usual power-law-process parametric approach by using the constrained nonparametric maximum likelihood estimate of the intensity function to estimate the optimum preventive maintenance policy. Several strategies to bootstrap the failure times and construct confidence intervals for the optimal maintenance periodicity are presented and discussed. The methodology is applied to a real data set concerning the failure histories of a set of power transformers.

Power Law Selection Model for Repairable Systems

A repairable system, under minimal repair, is usually modeled according to a Non-Homogeneous Poisson Process (NHPP) assuming a Power Law intensity function. A traditional approach considers iid NHPPs in order to conduct a statistical analysis based on a sample of systems. However, systems might be heterogeneous due to unmeasured variables such as age, suppliers, and so on. In order to verify this assumption a frequentist approach is proposed in this article. Some possible model scenarios considering different systems heterogeneity are compared using likelihood ratio tests and information criteria. Real data sets illustrate the proposed methodology.

Optimal Maintenance Time for Repairable Systems Under Two Types of Failures

Determination of preventive maintenance is an important issue for systems under degradation. A typical maintenance policy calls for complete preventive repair actions at pre-scheduled times and minimal repair actions whenever a failure occurs. Under minimal repair, failures are modeled according to a non homogeneous Poisson process. A perfect preventive maintenance restores the system to the as good as new condition. The motivation for this article was a maintenance data set related to power switch disconnectors. Two different types of failures could be observed for these systems according to their causes. The major difference between these types of failures is their costs. Assuming that the system will be in operation for an infinite time, we find the expected cost per unit of time for each preventive maintenance policy and hence obtain the optimal strategy as a function of the processes intensities. Assuming a parametrical form for the intensity function, large sample estimates for the optimal maintenance check points are obtained and discussed.

Optimal periodic maintenance policy under imperfect repair: A case study on the engines of off-road vehicles

ABSTRACT In the repairable systems literature one can find a great number of papers that propose maintenance policies under the assumption of minimal repair after each failure (such a repair leaves the system in the same condition as it was just before the failure—as bad as old). This article derives a statistical procedure to estimate the optimal Preventive Maintenance (PM) periodic policy, under the following two assumptions: (i) perfect repair at each PM action (i.e., the system returns to the as-good-as-new state) and (ii) imperfect system repair after each failure (the system returns to an intermediate state between as bad as old and as good as new). Models for imperfect repair have already been presented in the literature. However, an inference procedure for the quantities of interest has not yet been fully studied. In the present article, statistical methods, including the likelihood function, Monte Carlo simulation, and bootstrap resampling methods, are used in order to (i) estimate the degree of efficiency of a repair and (ii) obtain the optimal PM check points that minimize the expected total cost. This study was motivated by a real situation involving the maintenance of engines in off-road vehicles.

Dynamics of an optimal maintenance policy for imperfect repair models

A preventive maintenance policy that considers information provided by observing the failure history of a repairable system is proposed. For a system that is to be operated for a long time, it is shown that the proposed policy will have a lower expected cost than a periodical one which does not take into account the failure history. Statistical inference using both maximum likelihood point estimates and bootstrap confidence intervals is discussed. The proposed policy is applied to a real situation involving maintenance of off-road engines owned by a Brazilian mining company. A simulation study compares the performance between the maintenance policy proposed and the periodical one.