On the hazard rate process for imperfectly monitored multi-unit systems

International audienceThe aim of this paper is to present a stochastic model to characterize the failure distribution of multi-unit systems when the current units state is imperfectly monitored. The definition of the hazard rate process existing with perfect monitoring is extended to the realistic case where the units failure time are not always detected (non-detection events). The so defined observed hazard rate process gives a better representation of the system behavior than the classical failure rate calculated without any information on the units state and than the hazard rate process based on perfect monitoring information. The quality of this representation is, however, conditioned by the monotony property of the process. This problem is mainly discussed and illustrated on a practical example (two parallel units). The results obtained motivate the use of the observed hazard rate process to characterize the stochastic behavior of the multi-unit systems and to optimize for example preventive maintenance policies

Maintenance policies to guarantee optimal performance of stochastically deteriorating multi-component systems

Guaranteeing a prescribed level of reliability for a complex multi-component system is the problem considered in this thesis. For this, optimal maintenance and inspection policies are derived, taking into account the different deteriorations the components in the system are subject to. These degradations are described with the use of continuous stochastic processes in time and are assumed not to be directly observable. Maintenance decisions are based on a performance measure defined by a functional acting on the system state process. The transient property of the performance measure enables a modified control limit rule, based on last exit times, to be considered. For this a critical level is defined and the probability of never returning below it is used in the decision making approach. A condition based maintenance policy is investigated with the use of a bijective function of the performance measure’s value, that determines the required amount of repair. Both periodic and non-periodic inspections are studied. The nonperiodic approach is handled with the use of an inspection scheduling function which assigns the amount of time between two consecutive inspections to the value of the performance measure at inspection. Two main types of models are proposed. The first type considers one threshold and focuses in guaranteeing a prescribed level of reliability for systems where crossing of a critical boundary does not cause immediate failure but will require action later. Examples include physical infrastructures such as roads. Models of the second type take failure of the system into account with the incorporation of a second threshold. Examples include aeroplanes where safety regulations imply regular inspections and repairs. Occurrence of infrequent catastrophic failures must however be considered