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Statistical Process Control for Monitoring Type I Censored Weibull Lifetimes and INAR(1) Processes

  • Author(s): Xu, Shangjie
  • Advisor(s): Jeske, Daniel R.
  • et al.
Abstract

Statistical process control (SPC) methods are widely used in many fields, such as manufacturing, engineering and scientific studies aiming to reduce both financial and time costs through detecting abnormal process changes and making real-time decisions. Hence, the performance of a SPC method is usually measured by its detection time, and we favor the method that can detect a deterioration in the process as early as possible. In this dissertation, we propose SPC methods for monitoring two commonly encountered types of data, namely, Type I censored Weibull lifetime data and autocorrelated count data. Both methods are shown having significantly shorter detection time than existing methods.

In the first half of this dissertation, we first propose a SPC method for monitoring the Weibull scale parameter in the context of Type I censored data, assuming the shape parameter is fixed. The proposed method is a Shewhart-type method based on a likelihood ratio test (LRT) that utilizes an exponentially weighted moving average of the log-likelihood. In previous literature, this type of method is called a weighted exponentially weighted moving average (WEWMA) method. The WEWMA method is compared with a more standard exponentially weighted moving average (EWMA) method and a cumulative sum (CUSUM) method which were studied as alternative solutions to the monitoring problem. Numerical results show that the WEWMA method often performs better than these two alternatives. Sensitivity studies show that the WEWMA method is more robust to variations in batch sizes and censoring times. Moreover, two good properties of the WEWMA method are proved. A rust-resistant example is used to illustrate the proposed WEWMA method. We then extend the WEWMA and the CUSUM methods to the context where the shape parameter also needs to be monitored. Joint charts that simultaneously look for a change in either parameter are proposed.

In the second half of this dissertation, we deal with a problem in monitoring autocorrelated count data. Poisson integer valued autoregressive (INAR) models have been showed as an effective method to model autocorrelated count data without overdispersion and Poisson lognormal (PLN) INAR models extend their use to overdispersed contexts. We propose the use of a repeated sequential probability ratio test (SPRT) procedure to detect a change in first-order INAR and PLN INAR models. We consider a change in the mean, the autocorrelation parameter, and the overdispersion parameter. Simulation results show the repeated SPRT procedure performs favorably relative to previously proposed CUSUM procedures that are based on either the observations themselves or residuals of the observations from predicted values. A data set on invasive insect species is used to illustrate the repeated SPRT procedure.

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