5003

4708

كارشناسي ارشد

آمار

اصفهان: دانشگاه صنعتي اصفهان، دانشكده علوم رياضي

1388

[نه]، 146ص.

ص.ع. به: فارسي و انگليسي

صفيه محمودي، افشين پرورده

مجيد اسدي

17/11/88

محمد حسين علامت ساز، علي رجالي

رياضي

ID4708

به فارسي و انگليسي: قابل رويت در نسخه ديجيتال

A Discussion in the Analysis R out of N Repairable Systems Hajar Golriz Jirandeh hgolriz@math iut ac ir September 22 2009 Master of Science Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 83111 IranSupervisors Dr Safiyeh Mahmoodi smahmoodi@cc iut ac ir and Dr Afshin Parvardeh aparvardeh@sci ui ac ir2000 MSC Primary 90B25 Secondary 60K10 60k15 Key words availability phase type distribution markov renewal process semi regenerative process Abstract In this thesis we present an expanded account of a discussion in the analysis R out of Nrepairable systems based on the article by Y Barron and E Frostig and B Levikson 2004 These days one of the main discussion in studing systems that has been considered muchby statisticians and engineers is calculating availability of R out of N Repairable Systems An R out of N repairable system consisting of N components is operating if at least Rcomponents are functioning otherwise the system freezes The down time period terminatesat the rst time that the number of working components increases to R Repairable meansthat faild components are repaired and upon repair completion they are as good as new We consider phase type distribution and its properties in this paper We studied twoR out of N repairable systems with one repairman and 1 out of N repairable systems with crepairmen We use regenerative semi regenerative and markov renewal processes are usedfor analyzing these repairable systems Numerical example are given for several life timesand repair times distributions This thesis is organized as follows In chapter one we give a history and a brief introduc tion to what we are going to do Chapter two deals with discussing the necessary de nitionsand concepts Then in chapter three we present the de nition of phase type distributionand its properties We use this distribution for analysis repairable systems In chapter four we studied two systems and assume that life time of the components are exponential and re pair times of the components are generally distributed Also the analysis is done for systemswith either cold or warm standby In chapter ve we assume that life time of componentsare phase type distribution The analysis of repairable systems is done based on regenerativeand semi regenerative model We drive formulas for the expected up time and availability ofthe system using semi regenerative and markov renewal processes 1

صفيه محمودي، افشين پرورده

مجيد اسدي

محمد حسين علامت ساز، علي رجالي