Outliers identification and robust estimation method in analysis of crossed gage repeatability and reproducibility, random effect model

Measurement system analysis (MSA) is a rigorous assessment of measurement systems that is crucial in a manufacturing process. Under MSA, measurement accuracy and precision are observed. Measurement accuracy comprises of biasness and linearity of a gage while measurement precision focus on two types of variations which are part to part variation and gage variation. Part variation is the variability due to different items or units being measured while gage variation is due to measurement systems that consists of repeatability and reproducibility (R&R). This thesis will focus on crossed Gage R&R, random effect model. Repeatability is the variation in the measurement system which is due to measurement device while reproducibility is the variation in the measurement system which is caused by differences between operators who record the measurements. The Gage R&R study employs Analysis of Variance (ANOVA) technique to analyse the variation associated with each component, subsequently further analysis is done to determine whether or not measurement system precision can be acceptable. Nonetheless, many are not aware that outliers have an adverse effect on the measurement system accuracy and precision. Hence, the effect of outliers on the measurement system analysis, crossed Gage R&R random effect model is analysed. The results clearly show that the measurement system accuracy and precision are badly affected by outliers which provide misleading results to the Gage R&R analysis and estimation. Therefore, the existence of outliers must be identified and rectified to provide an accurate analysis of Gage R&R. The classical standardized residual (CSR) is the widely used method to identify outliers in the analysis of variance model. However, this method is not very successful in detecting outliers since the CSR is based on sample mean in its computation of residuals and mean squares errors. Hence, robust standardized residual (RSR) is formulated by incorporating median in the calculation of residuals and mean squares errors. The findings show that the RSR is very successful in identifying outliers with no masking effect and smaller rate of swamping. This thesis also addresses the problems of parameters estimation in the crossed Gage R&R, random effect model when outliers are present in a data set. The classical analysis of variance (ANOVA) method is the commonly used method to estimate the parameters of the model. The shortcoming of using the classical ANOVA is that the computation of each source of variation is based on sample mean which is easily affected by outliers. In order to give an accurate and efficient estimation, the effect of outliers should be reduced. Thus, an improvised ANOVA is developed by incorporating a weighting scheme such that outlying observations will be assigned a weight less than 1 while good observations are set a value equal to 1. The results of the study signify that the improvised ANOVA is more efficient than the classical ANOVA.

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