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Models for CM OnlyLet , be the failure times of the system or equivalently the CM times. Let , be the inter-failure times, and be the number of failures up to time . is a point process with the following failure intensity:
where is the history of the failure process at time . Before the first maintenance, the failure intensity is the hazard rate of a new system. It is denoted and is called initial intensity. In the following, we assume that the first failure time has a Weibull distribution, i.e. the initial intensity is:
where and are two positive parameters. The position of with respect to 1 indicates if the system is wearing or not. The CM models implemented in MARS are the ABAO, AGAN, ARA and ARA models [Doyen and GaudoinDoyen and Gaudoin2004]. In the next version, the Brown-Proschan model [Brown and ProschanBrown and Proschan1983] will also be available. The ARA models are virtual age models. These models consider that, after maintenance, the system is equivalent to a new one having survived without failure until an age , with . The virtual age at time is . For instance, the ARA model assumes that maintenance reduces the virtual age of the system of a quantity proportional to the virtual age just before the maintenance. This quantity is denoted and characterizes maintenance efficiency. Thus, the failure intensity of the system is:
Basic models are particular cases of the ARA model, according to the values of :
Stephane Despreaux 2009-06-10 |