Mathematical modelling of dynamic characteristics of repair process for
system operating under maintenance contracts
Abstract
Repair rate is very important parameter in a system maintainability and
it can be defined as frequency of the successfully performed repair
actions on failed component per unit of time. This paper analyses the
integral characteristics of a stochastic repair rate for corresponding
values of availability in the system operating under maintenance
contracts. The equation for the envelope line of the probability density
function (PDF) maximums of the repair rate has been provided. This new
expression can be used for planning of base stock levels and capacities
of repair facilities. Namely, in that way instead of repair rate PDF
equation, for some calculations we can use envelope line parameters,
which are expressed in simpler mathematical form, to reduce the time
required for calculations and prediction and enhance reactions in
failure events. For analytical and numerical evaluation of system
performance, the annual repair rate PDFs are analyzed like particular
solutions of corresponding differential equation, while the existence of
singular solution is considered and analyzed under different conditions.
Moreover, we have derived optimal values of availability for which the
PDF maximums have been obtained. Finally, in order to generalize
behavior of the repair process, a partial differential equation, as a
function of the repair rate process and availability parameter, has been
formed.