طراحی نمودار کنترل برای پایش پایایی سیستم های در معرض شوک های تجمعی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری، دانشکده مهندسی صنایع، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران

2 استاد، دانشکده مهندسی صنایع، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران

چکیده

در مدل‌های شوک، سیستم به‌محض این‌که میزان خسارات ناشی از شوک‌ها، از آستانه تحمل آن عبور نماید، دچار خرابی می‌شود. در این پژوهش، به طراحی نمودار کنترل برای پایش پایایی سیستم‌های با آستانه تحمل تصادفی در معرض شوک‌های تصادفی تجمعی پرداخته می‌شود. در مدل شوک تجمعی، سیستم زمانی از کار می‌افتد که میزان تجمعی خسارات ناشی از شوک‌ها از آستانه تحمل سیستم بیش تر شود. برای حل تحلیلی مدل‌ مرتبط با نمودار کنترل، چالش‌هایی نظیر نامشخص بودن توزیع‌ها، به‌دست آوردن پیچش توزیع‌ها و محاسبات انتگرال وجود دارند. برای غلبه کردن بر این چالش‌ها، از توزیع نوع مرحله‌ای برای مدل‌سازی مسئله استفاده می‌شود. با ارائه مثال عددی، نتایج حاصل از مدل تحلیلی ارائه شده با روش شبیه‌سازی مونت‌کارلو ارزیابی و مقایسه شده است. هم‌چنین، عملکرد نمودار کنترل پیشنهادی نیز با استفاده از معیارهای متوسط طول دنباله و متوسط زمان تا رسیدن به هشدار خارج از کنترل مورد ارزیابی قرار گرفته است.

کلیدواژه‌ها


عنوان مقاله [English]

Design of control chart for reliability monitoring of systems subjected to cumulative shocks

نویسندگان [English]

  • Yousof Shamstabar 1
  • Hamid Shahriari 2
1 Ph.D candidate, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran
2 Professor, Department of Industrial Engineering, K. N. Toosi University of Technology, Tehran, Iran
چکیده [English]

In shock models, the system will fail as soon as the amount of damages caused by shocks exceeds its failure threshold. In this research, the design of control chart for reliability monitoring of systems with random failure threshold subjected to cumulative random shocks is discussed. In the cumulative shock model, the system fails when the cumulative amount of damage caused by the shocks exceeds the failure threshold of the system. For the analytical solution of the model related to the control chart, there are some complexities such as the existence of unknown distributions, obtaining the convolutions of the distributions and integral calculations. To overcome these problems, phase-type distribution is used for modeling. By presenting a numerical example, the results of the presented analytical model are evaluated and compared with the Monte Carlo simulation method. Also, the performance of the proposed control chart using the average run length and average time to out of control signal criteria is evaluated.

کلیدواژه‌ها [English]

  • System failure
  • Shock models
  • Cumulative shock
  • Reliability
  • Control chart
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