قابلیت اعتماد سیستم‌های ‎k از n‎ وزنی ‌با مؤلفه‌های تصادفی‌‌شده از چندین دسته

نویسندگان
مرضیه صالحی
زهره شیشه بر
سمیه زارع زاده
دانشگاه شیراز
چکیده
سیستم‌های k از n وزنی (به اختصار k/n‎ وزنی)، از مهم‌ترین نوع ساختارهای افزونگی هستند. در این مقاله سیستم ‎k/n وزنی با مؤلفه‌های وابسته در نظر گرفته شده است که در آن مؤلفه‌های سیستم از ‎p دسته متمایز با طول عمرهای مختلف ‌ انتخاب می‌شوند. فرض بر این است که انتخاب مؤلفه‌های سیستم بر اساس یک بردار تصادفی M‎ با بعد p-1 ‎از میان p-1 دسته باشد در حالی که مؤلفه‌های باقی‌مانده نیز از آخرین دسته انتخاب می‌شوند. علاوه بر این فرض شده است که ساختار وابستگی مؤلفه‌ها توسط یک تابع مفصل تبادل‌پذیر مدل‌بندی می‌شود. تابع قابلیت اعتماد پویای سیستم در هر زمان به عنوان آمیخته‌ای از تابع قابلیت اعتماد سیستم‌های k/n ‎وزنی با تعداد ثابتی از مؤلفه‌های p دسته، ضرب ‌در تابع جرم احتمال بردار M بیان می‌شود. برخی از مقایسه‌های تصادفی بین طول عمرهای دو سیستم k/n ‎وزنی صورت گرفته است و نشان داده شده است هرگاه روش تصادفی انتخاب مؤلفه‌ها در دو سیستم از منظر ترتیب تصادفی معمولی مرتب شوند آن‌گاه، تحت شرایطی، طول عمر دو سیستم نیز مرتب می‌شوند.
کلیدواژه‌ها
قابلیت اعتماد
سیستم k/nوزنی
ترتیب تصادفی معمولی
تابع مفصل

عنوان مقاله English

The Reliability of Weighted k-out-of-n Systems with Randomized Components of Several Batches

نویسندگان English

Marziyeh Salehi
Zohreh Shishebor
Somayeh Zarezadeh
Shiraz University
چکیده English

One of the most important types of redundancy structures is weighted k-out-of-n system (which briefly denoted as weighted k/n system)‎. ‎In this paper‎, ‎a weighted k/n system‎ ‎with dependent components is considered and it is assumed that the components of the system are selected from p, p≥3, ‎batches‎. ‎The components in the batches are different in terms of their weights and reliability‎ ‎functions‎. ‎It is supposed that the selection of components from p-1 batches is based on a random‎ ‎vector with dimension p-1‎, ‎and the remaining components are chosen from the last batch‎. ‎The structure of dependency of components is also determined using a copula function‎. ‎Under these circumstances‎, ‎a mixture representation is given for the reliability function of the system based on the reliability functions of weighted k/n systems with a fixed number of the components in the batches‎. ‎Some stochastic orderings are presented‎, ‎under some conditions‎, ‎for comparing two different weighted k/n systems with randomized components‎. ‎The results are illustrated using some examples and graphs‎.

کلیدواژه‌ها English

Reliability‎
‎weighted k-out-of- n system‎
‎usual stochastic ordering‎
‎copulas‎
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