Bootstrap-based tolerance intervals for nested two-way random effects models

Variance component, or random effects, models are frequently used by manufacturers to model the variance present in a manufacturing process. By applying tolerance intervals to variance component models, manufacturers are able to set upper and lower limits to monitor the variance within a process. Existing methods for constructing tolerance intervals are constrained by the necessity for data to be normally distributed. Recently, non-parametric bootstrap-based methods were developed by Deyzel (2018) to obtain α-expectation and (α, β) two-sided tolerance intervals for the two-way nested random effects model. Classical and non-parametric methods for obtaining tolerance intervals for the one way random effects model have been assessed in accordance with Rebafka et al. (2007). The present study assesses and compares classical, Bayesian and non-parametric methods for obtaining tolerance intervals for the two-way nested random effects model under different assumptions of the underlying distribution. Results show that the non-parametric methods provided relatively narrow intervals, and generally retain the nominal content and guarantee levels, regardless of the underlying distributionThesis (MSc) -- Faculty of Science, Mathematical Statistics , 202