Abstract
The repair rate is a very important parameter for system maintainability and can be defined as a frequency of successfully performed repair actions on a failed component per unit of time. This paper analyzes the integral characteristics of a stochastic repair rate for corresponding values of availability in a system operating under maintenance contracts. The probability density function (PDF) of the repair rate has been studied extensively and it was concluded that it is not a symmetric function so its mean value does not correspond to its maximum. Based on that, the equation for the envelope line of the PDF maximums of the repair rate has been provided. Namely, instead of repair rate PDF equations, we can use envelope line parameters for certain calculations, which are expressed in a simpler mathematical form. That will reduce time required for calculations and prediction and enhance reactions in failure events. Further, for the analytical and numerical evaluation of a system performance, the annual repair rate PDFs are analyzed, such as particular solutions of corresponding differential equation, while the existence of a singular solution is considered and analyzed under different conditions. Moreover, we derived optimal values of availability for which the PDF maximums have been obtained. Finally, in order to generalize the behavior of the repair process, a partial differential equation, as a function of the repair rate process and availability parameter, has been formed.
Highlights
We have derived the optimal values of availability for which the probability density function (PDF) maximums have been obtained
The analysis of this dependence shows that the increase in parameter A results in smaller values of the PDF maximums reached for higher values of repair rate
By observing the repair rate PDF curve, we have concluded that all the maximums lie along a single curve, and that envelope of maximums is traceable
Summary
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Due to importance of the repair time in MRO, in [17], the authors have recommended a novel stochastic model for determining the annual repair rate for critical aircraft components in order to achieve the desired level of availability Those results can be used for the planning of the required numbers of spare parts and the repair facilities’ overall capacities. Using an expression for the probability density function (PDF) can precisely model the repair rate by generating the exact values of repair rate samples for the related values of availability and the MTBF Such simulations can serve for dynamic forecasting of system’s characteristics, as well as for planning and implementation of new repair stations and increase in any other repair capacities in order to improve efficiency of the maintenance systems.
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