بهينه‌سازي حد كنترل در نگه‌داري و تعمير مبتني بر شرايط با فرض ثابت نبودن هزينه‌ي تعويض به‌دليل خرابي

Optimization of Replacement Threshold in Condition-Based Maintenance with Variable 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 شد. در روش حد كنترل، تابع توام نرخ مخاطره دستگاه و تاثير متغيرهاي كنترل شرايط ، با استفاده از مدل تلفيقي نرخ مخاطره (PHM)، و با توجه به سوابق اطلاعاتي دستگاه تخمين زده مي‌شود. سپس، بهترين حد كنترل به‌گونه‌يي تعيين مي‌شود كه متوسط هزينه‌هاي تعويض به‌دليل خرابي و تعويض پيشگيرانه در يك دوره‌ي طولاني كمينه شود. در مدل ارايه‌شده در اين نوشتار، فرض ثابت بودن هزينه‌ي تعويض به‌دليل خرابي حذف و هزينه‌ي اين نوع خرابي، تابعي صعودي از عمر دستگاه و مقادير متغير‌هاي تشخيص خرابي در نظر گرفته شده است. سپس مدلي براي تعيين بهترين حد كنترل ارايه شده است، به‌گونه‌يي كه متوسط هزينه‌هاي تعويض كمينه شود. يك مثال عددي نيز به‌منظور تشريح بهتر مدل، ارايه شده است.

The primary goal of condition-based maintenance (CBM) is to extend system lifetime based on the information collected through periodic inspections. There have been many attempts to include economic considerations in the process of decision making in CBM. A well-known approach is called the control limit policy. In this approach, using historical data of the equipment and the values of condition monitoring covariates, the hazard rate function is first estimated. It is assumed that the inspections are performed at fixed and given intervals of time. The equipment is replaced whenever it fails. Also, after each inspection and based on the inspection results, if the cost-related failure rate reaches or exceeds a pre-determined limit, a preventive replacement is scheduled. The limit is, then, determined such that the expected average maintenance costs per unit time, due to preventive and failure replacements over a long time horizon, is minimized. However, it is assumed that the failure cost is constant, no matter when or at which state the failure occurs. Using the main principals of the control limit policy, this paper extends the approach assuming that the failure cost depends on both the age of the system and the value of the covariates observed. This assumption is more practical, as equipment usually incurs more failure cost as it deteriorates. However, determination of the function that can represent the variable failure cost is often difficult. In this paper, we consider a hypothetical non-decreasing failure cost function. This does not limit the scope of the application of the proposed method, as its relaxation only entails replacing the failure cost function with the one determined in a given application. The derivation of the required mathematical formulation to obtain the optimal control limit is presented in detail. A numerical example is also given to illustrate the proposed approach.