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چكيده انگليسي :

Improved CUSUM Charts for Controlling Process Mean Mona Saberin Boroujeni m saberin95@gmail com September 22 2020 M S Thesis in Farsi Department of Mathematical Sciences Isfahan University of Technology Isfahan 84156 8311 IranSupervisor Dr Maryam Kelkinnama m kelkinnama@cc iut ac ir2000 MSC 90B25 62K10 62N05 Keywords Control Charts CUSUM Chart Probability Control Limit Ranked Set Sampling Abstract This M S c thesis is based on the following papers Haq A Munir W Improved CUSUM charts for monitoring process mean Journal of Statistical Computation and Simulation 2018 88 9 1684 1701 Huang W Shu L Woodall WH and Tsui K L CUSUM procedures with probability control limits for moni toring processes with variable sample sizes IIE Transactions 2016 48 8 759 771 Quality control charts are well known process monitoring tools in the Statistical Process Control SPC that can beused to help control predict and improve the processes The control charts are divided into two categories namely the memoryless and the memory type charts The memoryless control charts are called the Shewhart type charts which are sensitive against the large process shifts On the other hand the memory type charts are frequently used in the process and service industries to detect smalland moderate shifts in the process parameter s to avoid severe financial penalties that arise from these process shifts Memory type control charts include the cumulative sum CUSUM and the exponentially weighted moving average EWMA charts When monitoring a production process it is essential to detect all kinds of shifts in the process parameter s Tra ditional control charts for process monitoring are often based on constant size samples In practice there are manysituations where the sample size is variable Hence the varying population size must be considered when develop ing an efficient control chart Recently control charts with time varying sample sizes are developed When usinga constant limit under a varying sample size distribution we require the sample size distribution to determine thecontrol limit In this thesis we design a CUSUM chart using probability control limits to control the conditional falsealarm rate under the situation of a time varying sample size The conditional false alarm rate means the probability ofthe current observations triggering a false alarm conditioned that there are no false alarms before the current time point The resulting control limits are dynamic and thus are more general and capable of accommodating more complexsituations in practice than the use of a constant control limit To simplify the CUSUM control chart s design andanalysis with dynamic probability control limits we develop an integral equation approach It is known that the location and scale estimators with ranked set sampling RSS are more precise than those withsimple random sampling SRS Hence in recent years RSS has been used to construct improved quality controlcharts for monitoring the process parameter s Using RSS as an efficient alternative to SRS is conditioned to thecase that it is possible to rank the study variable s values using the ranks of the auxiliary variable which has a highcorrelation with the primary variable In this thesis we propose new CUSUM charts for monitoring the process mean using RSS and ordered RSS ORSS Monte Carlo simulations are used to compute the run length characteristics of the proposed CUSUM charts such asthe average run length ARL It turns out that the proposed CUSUM charts are uniformly better than the existingCUSUM charts when detecting different kinds of shifts in the process mean

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