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Covariance estimation and application to building a new control chart

Fan, Yiying
http://rave.ohiolink.edu/etdc/view?acc_num=case1291406214

Abstract Details

2010, Doctor of Philosophy, Case Western Reserve University, Statistics.
Development of new methods of statistical process control (SPC) is extremely important for modern surveillance applications. Typical challenges in SPC are that the data are correlated and multivariate. In this dissertation we provide a new control chart based on the approximation of the joint tail distribution of P{St/sqrt(var(St))>= x, Mt>= y } where Mt = sup u∈[0,t] Zu and St =int Zudu are supremum and cumulative sum of a continuous time process {Zt}. This new control chart is motivated from combining the merits of the Shewhart and cumulative-sum (CUSUM) control charts for process monitoring. To construct control boundaries for any control chart, the covariance function of an in-control time processes must be known or estimated. We systematically discuss and provide solutions to covariance estimation for both parametric and nonparametric models with or without stationarity when there is either single or multiple realizations of the process. We use continuous Gaussian processes with covariance functions r(s, t) = cos(s-t) for s, t in [0, pi/4 ], r(s, t) = exp[-(s-t)2] for s, t in [0, T] where T > 0 and discrete autoregressive moving average (ARMA) processes to evaluate the new control chart for both in-control and out-of-control performances in comparison to the standard Shewhart, CUSUM and exponentially weighted moving average (EWMA) control charts. It is shown through simulation that the new control chart is efficient and compares well to the standard control charts for both the in and out of control scenarios.
Jiayang Sun (Committee Chair)
Joseph Sedransk (Committee Member)
Patricia P. Williamson (Committee Member)
Robert C. Elston (Committee Member)
Mark D. Schluchter (Committee Member)
Stephen J. Ganocy (Committee Member)
104 p.
Statistics
covariance estimation; control chart; continuous Gaussian processes; stationarity; nonstationarity

Recommended Citations

Citations

  • Fan, Y. (2010). Covariance estimation and application to building a new control chart [Doctoral dissertation, Case Western Reserve University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=case1291406214

    APA Style (7th edition)

  • Fan, Yiying. Covariance estimation and application to building a new control chart. 2010. Case Western Reserve University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=case1291406214.

    MLA Style (8th edition)

  • Fan, Yiying. "Covariance estimation and application to building a new control chart." Doctoral dissertation, Case Western Reserve University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=case1291406214

    Chicago Manual of Style (17th edition)

case1291406214
587
© 2010, all rights reserved.
This open access ETD is published by Case Western Reserve University School of Graduate Studies and OhioLINK.