Control Charts With Estimated Process Parameters And A Proposed Coefficient Of Variation Chart
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Date
2015-09
Authors
You, Huay Woon
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Abstract
Control charts receive great attention in Statistical Process Control (SPC) as the most useful tool in detecting process shifts so that corrective actions can be taken to identify and eliminate the assignable causes that are present. The main objective of this research is to address the problems of estimation of process parameters for the side sensitive group runs (SSGR) chart and synthetic double sampling (SDS) chart. Most control charts require the assumption that the target values of the in-control process parameters, i.e. the mean and standard deviation are known for the computation of the control charts’ control limits and statistics. Unfortunately, process parameters are usually unknown in real situations, where they are estimated from an in-control Phase-I dataset. In this research, the performances of the SSGR and SDS charts with estimated process parameters are compared with that of their known process parameters counterparts. The findings indicate that the performances of the SSGR and SDS charts differ when process parameters are known and when process parameters are estimated. This is due to the existence of variability in the estimation of process parameters. In view of this, the optimization designs for the estimated process parameters based SSGR and SDS charts are developed to resolve the effects of variability due to estimation of process parameters. Optimal charting parameters can be computed using the newly developed optimization designs so that the estimated process parameters based SSGR and SDS charts perform as favourable as the known process parameters based SSGR and SDS charts. Examples are provided to demonstrate the applications of the optimal estimated process parameters based SSGR and SDS charts. Another objective of this research is to propose the SSGR coefficient of variation (SSGR CV) chart. In many situations, the mean and standard deviation are not constant. Instead, the standard deviation is proportional to the mean. In such scenarios, monitoring the coefficient of variation (CV) is more meaningful. The implementation procedure and optimization design of the SSGR CV chart are presented in this thesis. The performance of the SSGR CV chart is compared with that of all existing CV charts. The results show that the SSGR CV chart outperforms all existing CV charts under comparison for detecting all sizes of CV shifts. However, the EWMA CV chart is superior to the SSGR CV chart for detecting small CV shifts but the latter surpasses the former for detecting moderate and large CV shifts. This shows that the SSGR CV chart provides promising performance yet maintaining the simplicity of implementation. The application of the optimal SSGR CV chart is illustrated with an example.
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Mathematics