توصيفگر ها :
نمودار كنترل، زمان بين وقوع پيشامدها، متوسط طول دنباله، متوسط زمان تا علامت، توزيع نمايي، نمودار كنترل نااريب، سانسور نوع-$II$، نمونه‌گيري دنباله‌اي , نمودار كنترل , زمان بين وقوع پيشامدها , متوسط طول دنباله , متوسط زمان تا علامت , توزيع نمايي , نمودار كنترل نااريب , سانسور نوع-I , نمونه‌گيري دنباله‌اي
چكيده انگليسي :
A study on the control chart for time between events LEILA NAGHSH l naghsh@math iut ac ir July 3 2019 Master of Science Thesis in Farsi Departement of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Maryam Kelkinnama m kelkinnama@cc iut ac irAdvisor Dr Sareh Goli s goli@cc iut ac ir2000 MSC 62P30 62F10Keywords Time between events type II censored average run length average time to signal control chart sequen tial sampling scheme unbiased control chart exponential distributionAbstract This M Sc thesis is based on the following papers Guo B Wang B X and Xie M ARL unbiased control charts for the monitoring of exponentially distributed characteristics based on type II censored samples Journal of Statistical Computation and Simulation 84 12 2014 2734 2747 Yang J Yu H Cheng Y and Xie M Design of exponential control charts based on average time to signal using a sequential sampling scheme International Journal of Production Research 53 7 2015 2131 2145 Huang S Yang J and Xie M A A study of control chart for monitoring exponentially distributed charac teristics based on type II censored samples Quality and Reliability Engineering International 33 7 2017 1513 1526 One important tool of statistical process control SPC is control chart The occurrence of non conforming itemsor defects in a manufacturing process has been widely monitored by the time between events T BE control chartwhich is based on the inter arrival times of non conforming items It is often assumed that the occurrence of defectsis modelled by a homogeneous Poisson process and then the TBEs follow independent and identically distributed i i d exponential variables The average run length ARL is widely used to evaluate the performance of control charts The ARL is de ned asthe average number of samples to be collected until the control chart issues an out of control signal A control chart issaid to be ARL unbiased if its ARL curve attainss its maximum when the process is in control The ARL biasedcontrol chart is undesirable practically since it needs more time on average to show the out of control signal than thein control process One more suitable performance measure for T BE control charts is the average time to signal AT S where itis de ned as the average length of time that a control chart produce an out of control signal It involves both thenumber and the time of samples inspected until a signal occurs therefore the AT S gives much information aboutthe process Similarly the AT S unbiased control chart can be defined as a control chart that achieves its maximumfor the in control situation When the parameters of underlying distribution are unknown they should be estimated from a set of data which iscalled phase I data In this case the estimation precision of unknown parameters should be considered into the designof control charts For the design of T BE control charts it is often assumed that we have complete observations Inmany practical applications such as reliability however observations are often censored because of the cost or timelimitations One important form of censoring is Type II censoring which happens when testing is terminated at thetime of the r th desired event In this thesis the T BE control chart based on exponential distribution is investigated In chapter 2 an ARL unbiased control scheme is developed first for the known parameter and the monitoring statistics is made based ontype II censored sample Second for the case of unknown parameter we provide new control charts based on theadjusted control limits
