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Sampling by Variables for Proportion Nonconforming
Published in Edward G. Schilling, Dean V. Neubauer, Acceptance Sampling in Quality Control, 2017
Edward G. Schilling, Dean V. Neubauer
When population parameters are unknown, 100% confidence can rarely be achieved short of 100% inspection. Even then we cannot often be 100% confident of the inspection procedure. Estimates must be substituted for population parameters, a set of confidence levels, and more sophisticated procedures, often based on the noncentral t-distribution, employed. When parameters are unknown, a typical one-sided variables tolerance interval is of the form X¯+ks for an upper tolerance limit, or X¯−ks for a lower tolerance limit. A two-sided interval may be expressed as X¯±ks It will be recalled that the acceptance criteria for the k method in the variables procedure were precisely X¯+ks<U or X¯−ks>L for one-sided plans, with corresponding criteria for the two-sided case.
Projections of Definitive Screening Designs by Dropping Columns: Selection and Evaluation
Published in Technometrics, 2020
Alan R. Vazquez, Peter Goos, Eric D. Schoen
All noncentrality parameters λ listed in Table 2 are increasing functions of k. As a result, the powers for the four significance tests increase with k and with the number of runs. The powers for the four significance tests can all be calculated as where is a random variable following a noncentral t-distribution with ν degrees of freedom and noncentrality parameter λ, and and are the critical values based on a central t-distribution with ν degrees of freedom for a significance level equal to α. The noncentrality parameters and the resulting powers are independent of the sets of k columns dropped from an -factor sDSD, and from the values of i and j in the effects tested (i.e., βi, βii, and βij); see supplementary Section B for details.
Improved high-dimensional regression models with matrix approximations applied to the comparative case studies with support vector machines
Published in Optimization Methods and Software, 2022
Mahdi Roozbeh, Saman Babaie-Kafaki, Zohre Aminifard
To achieve different degrees of collinearity, following Refs. [10,13], the predictor variables were generated for (high-dimensional) from the following model: where 's are independent standard normal pseudo-random numbers and γ is specified so that the correlation between any two explanatory variables is given by and 0.90. These variables are then standardized so that and are in correlation forms. The observations for the dependent variable are determined by where , are generated from normal distribution with and , and , are generated from standard normal distribution with and for the sparsity purpose. Also, we considered where where is the non-central t-distribution with m degrees of freedom and non-centrality parameter δ. The main reason of choosing this scheme for generating the error terms is to corrupt the data and examine the robustness of the proposed methods. Indeed, we set the first h errors as independent normal random variables and the last n−h errors as independent non-central t-distributed random variables.