Estimation Error in Statistical Process Control
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This thesis examines estimation errors which occur in control charts with estimated parameters, the effect that these errors have on the charts and the current methods which aim to account for the errors. There is a particular focus on how these errors affect the average run length of the chart and how to improve the average run length using current methods. The best methods to account for estimation error in Shewhart control charts, from the methods discussed, are the bootstrap method and the reduction of exceedance probability method. Both aim to reduce the probability that the run length of a chart is less than a specified value by adjusting the chart's control limits. However the bootstrap method has the advantage that it can be adapted to other types of control charts including risk-adjusted versions. The bootstrap method is used to analyse the Helping Babies Breath (HBB) training program data to see if there is a clinically relevant change in the probability that an infant survives 24 hours at Haydom Lutheran Hospital, Tanzania. The use of risk-adjusted cumulative sum (CUSUM) charts, with adjusted limits to account for estimation error, shows a decrease in the probability of infants not surviving 24 hours, demonstrating the positive impact of the HBB training program.
Master's thesis in Mathematics and Physics