بهينه‌سازي همزمان قابليت اطمينان و هزينه‌ي طراحي در سيستم‌هاي سري ـ موازي k-out-of-n با در نظرگرفتن نرخ خرابي وابسته به تعداد اجزاي در حال كار

Reliability and cost optimization of a series-parallel system with k-out-of-n Sub-systems with considering dependent components failure rate

در اين نوشتار مدل جديدي براي مسيله‌ي تخصيص افزونگي با ساختار سري ـ موازي و زيرسيستم‌هاي k-out-of-n با در نظر گرفتن «نرخ خرابي وابسته به تعداد اجزاي در حال كار» ارايه شده كه در آن سياست افزونگي آماده به كار سرد يا فعال براي زيرسيستم ها در نظر گرفته مي شود. هدف، تعيين سياست افزونگي، نوع و تعداد اجزا مازاد تخصيص يافته به هر زيرسيستم به‌منظور بيشينه‌سازي قابليت اطمينان و كمينه‌سازي هزينه‌ي كل سيستم تحت محدوديت وزن است. به‌دليل NP-hard بودن مسيله از دو الگوريتم فراابتكاري «الگوريتم ژنتيك مرتب‌سازي نامغلوب 2» (NSGA II) و «الگوريتم ژنتيك رتبه‌بندي نامغلوب» (NRGA) براي حل مدل و از روش سطح پاسخ براي تنظيم پارامترها استفاده شده است. همچنين با استفاده از پنج شاخص عملكردي، عملكرد الگوريتم‌ها مورد بررسي و مقايسه قرار گرفته است. در انتها نيز براي تحليل نتايج و اثبات درستي روند استفاده از اين الگوريتم‌ها از آزمون فرض استفاده شده است.

Nowadays, with technological advances and the need for high reliable systems, extensive research has been done in the field of reliability optimization. Redundancy allocation problem (RAP) is one of the main issues that has been raised in relation to this subject. Many studies have been carried out in this area and many solutions such as redundancy allocations and component failure rate reduction have been brought up to increase the system reliability. In this paper we considered a series-parallel system with k-out-of-n subsystems and developed a RAP with components failure rate that depend on the number of working components. In this type of failure rate, when a component fails, the remained components work with more pressure and failure rate of these components increases. The system redundancy strategies are considered as cold standby or active for the subsystems. This model has two objective functions (1) maximizing system reliability and (2) minimizing the system cost. The goals of this model are to select the redundancy strategy between active and cold standby and to determine component type and number of allocated redundant components to each subsystem. As RAP belongs to NP-hard problems, so it is very difficult to optimally solve such a problem by using traditional optimization tools. Therefore for solving the model, two effective meta-heuristic algorithms named Non-dominated Sorting Genetic Algorithm (NSGAII) and Non-dominated Ranked Genetic Algorithm (NRGA) are presented. We use design of experiment (DOE) for parameter tuning of this algorithms response surface methodology (RSM) is applied for determining the optimum amount of parameters. Then to illustrate the effectiveness of algorithms, a numerical example is presented and algorithms are compared using five different performance metrics. In order to determine whether there is a significant difference between the performance of algorithms, a single factor ANOVA in significant level (?= 0.05) is performed. Finally performance of the algorithms is analyzed and the results are reported.