بهينه‌سازي حد تعويض پيشگيرانه و برنامه بازرسي‌ها در نگه‌داري و تعمير مبتني بر شرايط، با فرض غيرنزولي بودن هزينه‌ي تعويض به‌دليل خرابي

Optimal Replacement Threshold and Inspection Scheme (Periodic and Non-periodic) for Condition-Based Maintenance with Non-decreasing Failure Cost

در نگه‌داري و تعمير مبتني بر شرايط دستگاه (CBM) هدف اين است كه با انجام بازرسي و كنترل شرايط دستگاه به عمر واقعي تعويض نزديك شود. در اغلب مدل‌هاي ارايه شده تاكنون فرض بر اين بوده است كه هزينه‌ي تعويض به‌دليل خرابي دستگاه در طول مدت بهره‌برداري از آن ثابت و همچنين بازرسي‌ها در فواصل زماني ثابت و بدون هزينه است. در مدل پيشنهادي هزينه‌ي تعويض به‌دليل خرابي، تابعي صعودي از عمر دستگاه و مقادير متغير‌هاي تشخيص خرابي در نظر گرفته شده است. همچنين، علاوه بر هزينه‌هاي تعويض، هزينه‌ي انجام بازرسي‌ها ــ اعم از بازرسي با فواصل زماني ثابت يا غير ثابت ــ در مدل لحاظ ‌مي‌‌شود. هدف تعيينِ حد تعويض پيشگيرانه و برنامه‌ي بازرسي‌ها است به‌گونه‌يي كه متوسط مجموع هزينه‌ها در واحد زمان كمينه ‌شود. براي تشريح بهتر مدل پيشنهادي، مثال عددي نيز آورده شده است.

In condition-based maintenance (CBM), the underlying system (or an item) is preventively replaced if failure risk, which is calculated based on monitoring information, exceeds a pre-determined threshold. It is also replaced if, at any time, failure occurs. In the determination of optimal replacement threshold, it is often assumed that the failure replacement cost is constant. It is also assumed that inspections are performed at equal time intervals with no cost. However, these assumptions are not always true as, in practice; inspections may require labors, specific test devices, and sometimes suspension of operations. Thus, when inspection is considerable, performing inspections in short intervals incur large inspection cost. In contrast, if inspections are carried out in long intervals, the cost of failure replacements may significantly increase. This implies that there must be a trade-off between inspection costs and possible failure costs. Also, failure replacement cost may depend on the item’s degradation state at which failure occurs and/or the time it fails. This is because, in some cases, failure of an item may affect other items and the later its failure occurs the more damages may be observed on the other components and, thus, the failure replacement of the item has to be performed at higher cost as it may require some other repairs on other components. In this paper, the two above-mentioned assumptions in the traditional CBM’s optimization models are relaxed. A non-decreasing failure cost that depends on both the age of the system and the value of the covariates observed at inspections is considered. In addition, inspection cost is taken into account. Two types of inspection scheme, namely, periodic and non-periodic are considered for CBM. For each type of inspection schemes, the system’s expected total cost per unit time is formulated in terms of the inspection scheme and the replacement threshold. Then, for obtaining the optimal periodic inspection scheme, the expected total cost is evaluated for all alternative periodic inspection schemes. For obtaining optimal non-periodic inspection scheme, A* search algorithm is employed to search through alternative inspection schemes to determine the optimal one. Numerical examples are given to illustrate the proposed approach.