Optimum two-stage selection procedures for Weibull populations
type: Item
instance of: scholarly article
title: Optimum two-stage selection procedures for Weibull populations
zbMATH Open document ID: 0601.62033
DOI: 10.1016/0378-3758(86)90093-5
author: Shanti S. Gupta
author: Klaus J. Miescke
published in: Journal of Statistical Planning and Inference
publication date: 1987-01-01T00:00:00Z
review text: Let \(\pi_ 1,...,\pi_ k\) be Weibull populations with a common known shape parameter, and with unknown scale parameters. The goal is to find the population with the largest scale parameter. From each population, type II-censored observations are available at two stages, where censoring at stage 1 (2) occurs at the q-th (r-th) failure. Two-stage procedures with screening at the first stage are considered which are optimum permutation invariant in terms of the risk with respect to a large class of loss functions. For the procedure with a fixed subset size at stage 1, the least favorable parameter configuration under the indifference zone approach is of the slippage type, which makes it feasible to control the infimum of the probability of a correct selection. Some extensions of the results are discussed at the end.
Mathematics Subject Classification ID: 62F07
Mathematics Subject Classification ID: 62L99
Mathematics Subject Classification ID: 62N05
zbMATH DE Number: 3969871
zbMATH Keywords: optimum two-stage selection
zbMATH Keywords: selecting the best
zbMATH Keywords: Weibull populations
zbMATH Keywords: known shape parameter
zbMATH Keywords: unknown scale parameters
zbMATH Keywords: type II-censored observations
zbMATH Keywords: screening
zbMATH Keywords: optimum permutation invariant
zbMATH Keywords: risk
zbMATH Keywords: loss functions
zbMATH Keywords: least favorable parameter configuration
zbMATH Keywords: indifference zone approach
zbMATH Keywords: probability of a correct selection
MaRDI profile type: Publication
full work available at URL: 0378-3758(86)90093-5
OpenAlex ID: W2089613419
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description: scientific article; zbMATH DE number 3969871