Metrika

Zhang, Tian-fang; Duan, Yingxing; Zhao, Shengli; Li, Zhiming

2024 Metrika

doi: 10.1007/s00184-024-00972-2

The general minimum lower order confounding (GMC) is a criterion for selecting designs when the experimenter has prior information about the order of the importance of the factors. The paper considers the construction of 3n-m\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3^{n-m}$$\end{document} designs under the GMC criterion. Based on some theoretical results, it proves that some large GMC 3n-m\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$3^{n-m}$$\end{document} designs can be obtained by combining some small resolution IV designs T. All the results for 4≤#{T}≤20\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$4\le \#\{T\} \le 20$$\end{document} are tabulated in the table, where #\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\#$$\end{document} means the cardinality of a set.

Joshi, Neeraj; Bapat, Sudeep R.; Sengupta, Raghu Nandan

2024 Metrika

doi: 10.1007/s00184-024-00973-1

In this research, we present two-stage and purely sequential methodologies for estimating the scale parameter of the Moore and Bilikam family of lifetime distributions (see Moore and Bilikam in IEEE Trans Reliabil 27:64–67, 1978). We propose our methodologies under the minimum risk point estimation setup, whereby we consider the modified LINEX loss function plus non linear sampling cost. We study some interesting exact distributional properties associated with our stopping rules. We also present simulation analyses using Weibull distribution (special case of the Moore and Bilikam family) to check the performance of our two-stage and purely sequential procedures. Finally, we provide a real data set from COVID-19 and analyze it using the Weibull model in support of the practical utility of our proposed two-stage methodology.