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Control Charts with Missing Observations
Wilson, Sara R.
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Traditional control charts for process monitoring are based on taking samples from the process at regular time intervals. However, it is often possible in practice for observations, and even entire samples, to be missing. This dissertation investigates missing observations in Exponentially Weighted Moving Average (EWMA) and Multivariate EWMA (MEWMA) control charts. The standardized sample mean is used since this adjusts the sample mean for the fact that part of the sample may be missing. It also allows for constant control limits even though the sample size varies randomly. When complete samples are missing, the weights between samples should also be adjusted. In the univariate case, three approaches for adjusting the weights of the EWMA control statistic are investigated: (1) ignoring missing samples; (2) adding the weights from previous consecutive missing samples to the current sample; and (3) increasing the weights of non-missing samples in proportion, so that the weights sum to one. Integral equation and Markov chain methods are developed to find and compare the statistical properties of these charts. The EI chart, which adjusts the weights by ignoring the missing samples, has the best overall performance. The multivariate case in which information on some of the variables is missing is also examined using MEWMA charts. Two methods for adjusting the weights of the MEWMA control statistic are investigated and compared using simulation: (1) ignoring all the data at a sampling point if the data for at least one variable is missing; and (2) using the previous EWMA value for any variable for which all the data are missing. Both of these methods are examined when the in-control covariance matrix is adjusted at each sampling point to account for missing observations, and when it is not adjusted. The MS control chart, which uses the previous value of the EWMA statistic for a variable if all of the data for that variable is missing at a sampling point, provides the best overall performance. The in-control covariance matrix needs to be adjusted at each sampling point, unless the variables are independent or only weakly correlated.
- Doctoral Dissertations