Producer's and consumer's risk in measurement system analysis: distributional modeling, process capability and repeated measurement strategies

Measurement System Analysis is a methodology aimed at assessing the reliability of measurement systems, particularly in fields such as manufacturing and engineering. The main objective of measurement system analysis is to isolate the true variation of the process from the variation caused by measurement, thus enabling accurate monitoring of process performance. However, factors such as calibration errors, inconsistencies between operators, equipment wear, or fluctuations in environmental conditions bring the risk of misclassification. Among these risks, the most critical are the probabilities of misclassification known as producer risk and consumer risk. In this thesis, the problem of statistically modeling and estimating the misclassification probabilities arising from measurement errors is addressed. In this context, cases where the part and measurement errors follow Weibull and normal, exponential and Laplace, linear hazard rate and normal, and linear hazard rate and Laplace distributions, respectively, are examined. Then, closed-form expressions of misclassification probabilities are derived for the case where both the part and the measurement error follow normal distributions. The effect of additional repeated observations obtained using a single operator on the estimation of misclassification probabilities is investigated. Additionally, a log-linear regression model is proposed that links the Taguchi process capability index used in measurement system analysis to process covariates. Finally, a maximum likelihood-based method is proposed to explain and quantify the covariate-level factors affecting the producer risk. In this context, the maximum likelihood method is used for point estimation. EM algorithms are derived for estimating the misclassification probabilities in the linear hazard rate–normal and linear hazard rate–Laplace cases. For interval estimation, approximate confidence intervals, non-parametric normal bootstrap, basic bootstrap, percentile bootstrap, bias-corrected and accelerated bootstrap confidence intervals, Bayesian credible intervals, and highest posterior density intervals are used. Comprehensive Monte Carlo simulation studies are conducted to examine the performance of the methods discussed in the study. The findings are supported by numerical examples.