A Comparison of Estimators of an Arithmetic Process Using Simulation

Abstract

The arithmetic process (AP) approach can be used to resolve system maintenance problems. The approach is realistic and direct in modelling the characteristics of a deteriorating system such as an engine, as a decreasing AP can model an engine's successive operating times and an increasing AP can model the corresponding consecutive repair times. Fitting a model to failure and/or repair data is preliminary to utilizing an optimization model from which an optimal maintenance policy based on minimizing cost or downtime may be found. Some simulation studies were performed to evaluate various estimators and to compare the estimates, obtained from various estimators, of the parameters. The authors make some suggestions, based on the results of the simulation studies, for selecting the best estimators when d∈[0,μA1n−1],d<0or d = 0. Having obtained the estimates d∧,μ∧A1, and σ∧2A1 using the relevant estimators suggested by the simulation studies, of the parameters d,μA1 and σ2A1of a single system, we can compute the averages of the respective estimates for a collection of homogeneous systems and then use these averages to estimate d∧,μ∧A1 and σ∧2A1. The parameters d, μA1 and σ2A1 and σ2A1 for n = 1, 2, . , N represent the common difference, means, and variances, respectively, of an AP, which are determined by a sequence of random variables A1,A2........AN. The methods used to derive the estimators are nonparametric, so we can apply the methods and estimators to any AP including a renewal process. In other words, there is distribution free underpinning a failure process or a repair process.