چكيده فارسي :
در اﯾﻦ ﭘﺎﯾﺎن ﻧﺎﻣﻪ دو ﻣﺪل ﺷﻮك،ﮐﻪ ﺑﺮ اﺳﺎس ﻓﺮاﯾﻨﺪ ﺗﺠﺪﯾﺪ ﻣﺎرﮐﻮف ﺑﺎ ﻣﮑﺎﻧﯿﺰم ﺷﮑﺴﺖ ﻣﺘﻌﺪد
ﻣﺪلﺑﻨﺪي ﻣﯽﺷﻮﻧﺪ. ﮐﻪ ﺑﺮ اﯾﻦ اﺳﺎس اﻧﺪازه ﺷﻮك و واﺑﺴﺘﮕﯽ زﻣﺎن ﺑﯿﻦ ورود ﺷﻮكﻫﺎ را ﺑﺮرﺳﯽ ﻣﯽﮐﻨﯿﻢ. اﻧﺪازه و زﻣﺎن ﺑﯿﻦ ورود ﺷﻮكﻫﺎ، ﺗﻮﺳﻂ ﯾﮏ زﻧﺠﯿﺮه ﻣﺎرﮐﻮف ﺟﺎذب )زﻧﺠﯿﺮه ي ﻣﺎرﮐﻮف ﺟﺎذب رده اي از زﻧﺠﯿﺮه ي ﻣﺎرﮐﻮف ﻧﺎارﮔﻮدﯾﮏ ﻫﺴﺘﻨﺪ ﮐﻪ ﺣﺎﻟﺖ ﺟﺎذب دارﻧﺪ( ﺑﺎ ﻓﻀﺎي ﺣﺎﻟﺖ ﻣﺘﻨﺎﻫﯽ ﮐﻨﺘﺮل ﻣﯽﺷﻮﻧﺪ. در ﻣﺪل ﺷﻮك ﺷﺪﯾﺪ رﯾﺴﮏ رﻗﺎﺑﺘﯽ ﺳﯿﺴﺘﻢ زﻣﺎﻧﯽ ﮐﻪ ﯾﮏ ﺷﻮك ﺗﻨﻬﺎ، ﺑﺎ اﻧﺪازه ﺑﺰرگ اﺗﻔﺎق ﻣﯽاﻓﺘﺪ ﯾﺎ زﻣﺎﻧﯽ ﮐﻪ وارد ﺣﺎﻟﺖ ﺟﺎذب ﻣﯽﺷﻮد، ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﯾﻨﮑﻪ ﻫﺮ ﮐﺪام اول اﺗﻔﺎق ﺑﯿﻔﺘﺪ ﻣﻨﺠﺮ ﺑﻪ ﺷﮑﺴﺖ ﺳﯿﺴﺘﻢ ﻣﯽﺷﻮد. ﺗﺤﺖ ﻣﺪل ﺷﻮك ﺗﺠﻤﻌﯽ، رﯾﺴﮏ رﻗﺎﺑﺘﯽ ﺳﯿﺴﺘﻢ ﻫﻨﮕﺎﻣﯽ ﮐﻪ ﺑﻪ ﺣﺎﻟﺖ ﺟﺎذب ﻣﻨﺘﻘﻞ ﻣﯽﺷﻮد ﯾﺎ زﻣﺎﻧﯽ ﮐﻪ ﻣﻘﺪار ﺗﺠﻤﻌﯽ ﻧﺎﺷﯽ از ﺷﻮكﻫﺎ از ﯾﮏ آﺳﺘﺎﻧﻪي ﻓﺮاﺗﺮ رود، ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﯾﻨﮑﻪ ﮐﺪام ﯾﮏ اول اﺗﻔﺎق ﺑﯿﺎﻓﺘﺪ ﻣﻨﺠﺮ ﺑﻪ ﺷﮑﺴﺖ ﺳﯿﺴﺘﻢ ﻣﯽﺷﻮد. ﻣﺪل رﯾﺴﮏ رﻗﺎﺑﺘﯽ، ﻣﺮﺑﻮط ﺑﻪ ﺷﺮاﯾﻄﯽ اﺳﺖ ﮐﻪ ﻣﮑﺎﻧﯿﺰمﻫﺎي ﺷﮑﺴﺖ ﭼﻨﺪﮔﺎﻧﻪ ﻣﯽﺗﻮاﻧﺪ ﻣﻨﺠﺮ ﺑﻪ ﺷﮑﺴﺖ ﺳﯿﺴﺘﻢ ﺷﻮد؛ اﻣﺎ ﻣﮑﺎﻧﯿﺰم ﺷﮑﺴﺖ ﮐﻪ اﺑﺘﺪا رخ ﻣﯽدﻫﺪ ﺷﮑﺴﺖ ﻧﻬﺎﯾﯽ ﺳﯿﺴﺘﻢ را ﻣﻨﺠﺮ ﺧﻮاﻫﺪ ﺷﺪ. ﻣﺪل ﻫﺎ ﺑﻪ دو دﺳﺘﻪ ﻃﺒﻘﻪ ﺑﻨﺪي ﻣﯽﺷﻮﻧﺪ: دﺳﺘﻪي اول، اﻧﺪازه ي ﺷﻮك ﻣﺴﺘﻘﻞ از زﻣﺎن ورود آن اﺳﺖ و ﻣﻌﻤﻮﻻ ﺗﻮزﯾﻊ ﯾﮑﺴﺎﻧﯽ ﻫﻢ دارﻧﺪ؛ و دﺳﺘﻪي دوم، اﻧﺪازه ي ﺷﻮك ﻣﺴﺘﻘﻞ از زﻣﺎن ورود آن ﻧﯿﺴﺖ و از اﯾﻦ رو ﻫﻤﺒﺴﺘﮕﯽ دارﻧﺪ و ﻟﺰوﻣﺎ ﺗﻮزﯾﻊ آﻧﻬﺎ ﯾﮑﺴﺎن ﻧﯿﺴﺖ. در اﯾﻦ ﭘﺎﯾﺎن ﻧﺎﻣﻪ ﯾﮏ ﺣﺎﻟﺖ ﺧﺎص ﮐﻪ ﻓﺮاﯾﻨﺪ ورود ﺷﻮك، ﻣﺴﺘﻘﻞ از زﻣﺎن ورود آن اﺳﺖ ﺑﺮرﺳﯽ ﻣﯽﺷﻮد و رﻓﺘﺎر ﺣﺪي ﺳﯿﺴﺘﻢ و ﻣﯿﺎﻧﮕﯿﻦ زﻣﺎن ﺗﺎ ﺧﺮاﺑﯽ ﺳﯿﺴﺘﻢ ﺗﺤﺖ دو ﻣﺪل ﻓﻮق ﺑﺮرﺳﯽ
ﻣﯽﺷﻮد.
چكيده انگليسي :
Shock models have received much attention in the past decades due to their wide application in many fields such as reliability, operational research. Shocks can be produced in many forms including temperature, voltage, mechanical stress which can destroy or fail the operating system depending on their size. In general, there are five common categories of random shock models: extreme shock, cumulative shock model, δ shock model, mixed shock model, executive shock model that we in this article, we examined two models of severe and cumulative shock. In this article, two Markov renewal shock models with multiple failure mechanisms are presented. Based on this, we examine the shock size and the dependence of the time between the arrival of shocks. The size and time between the arrival of shocks are controlled by an absorbing Markov chain with a finite state space. In the extreme shock model, the competitive risk of the system is when a shock occurs only with a large size or when it enters the absorption state, the system fails, depending on which one happens first, leading to the failure of the system. Under the cumulative shock model, the competitive risk of the system leads to system failure when it moves into absorption mode or when the cumulative amount of damage caused by a shock exceeds a threshold, whichever occurs first. The competitive risk model is related to the situation where multiple failure mechanisms can lead to system failure, but the failure mechanism that occurs first will lead to the final failure of the system .The models are classified into two categories, the first category is the size of the shock independent of the time of its arrival and usually have the same distribution, and the second category is the size of the shock is not independent of the time of its arrival and they are correlated and their distribution is not necessarily the same. In particular, they consider that the shock arrival process is independent of its arrival time and examine the system limit behavior and the average time until system failure under the two models that were mentioned
