Optimal replacement policy for a periodically inspected system subject to the competing soft and sudden failures

Abstract

Optimal replacement pOlicy fOr a periOdically inspected system subject tO the cOmpeting sOft and sudden failures Optymalna pOlityka wymiany dO zastOsOwania w systemach pOddawanych przeglądOm OkresOwymnarażOnych na kOnkurujące uszkOdzenia parametryczne i nagłe demonstrated that the optimal replacement policy was a multi-level control-limit policy with monotonically increasing control limits. However, considering only the soft failure seems to be inadequate for the degrading systems that are also subject to the sudden failures. In many practical situations, sudden failures are very likely to interrupt the graceful degradation and then result in more serious consequences. Therefore, in this paper, we consider a competing risk maintenance situation. The system is regarded as failed when the degradation process reaches a critical threshold or when the sudden failure occurs although the degradation process has not reached the threshold. Most of the present papers that deal with such failure scenario assume that the degradation process and the sudden failure are independent with each other. Nevertheless, even if independence is demonstrated to be appropriate for certain types of competing risks, e.g. [2,8,20,21], in many situations the dependent structure between the two failure modes is of importance and should not be neglected. We consider the dependence is described by the failure rate of the sudden failure, which is influenced by both the age and the degradation state of the system. Similar assumptions were also found in Huynh et al. [9], Liu et al. [15], Castro et al. [3] and Huynh et al.[10] to deal with competing risk maintenance situation. A preventive threshold in terms of the degradation state was optimized in Huynh et al. [9] and Liu et al. [15] with different monitoring strategies. The former focused on periodically inspected systems and the latter dealt with continuously monitored ones. Castro et al. [13] also considered a degradation state -based control limit as the alarm of preventive maintenance, but multiple degradation processes were involved in the failure mechanism. In Huynh et al. [10], a novel CBM strategy was proposed using the mean residual life as the control limit. The effectiveness and potential of condition indices that are not strictly limited to failure mechanism in CBM decision-making problems was firstly investigated.In this paper, we will focus on analyzing the optimal replacement policy for a periodically inspected system subject to the competing soft and sudden failures. This policy performs the preventive replacement only at inspection instants, and correctively replaces the system at the time of failure. We describe the degrading system using a gamma degradation process, which implies that the soft failure of the system results from a gradual and irreversible accumulation of deterioration. The failure rate corresponding to the sudden failure is described by a proportional hazards model, which means that it is influenced by both the age of the system and the state degradation of ...

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