Title
Inference from Grouped Data in Three-Parameter Weibull Models With Applications to Breakdown Voltage Experiments
Authors
H. Hirose, T.L. Lai
Source
Technometrics, Vol.39, No.2, pp.199-210 (1997.5)
Abstract
An important objective of breakdown-voltage experiments is to estimate either the threshold below which no breakdown occurs or other voltage levels' below which breakdown occurs with a small probability. A commonly used statistical technique in these studies is to fit a three-parameter Weibull distribution to the experimental data. Difficulties in applying the method of maximum likelihood to three-parameter Weibull models due to nonregularity have led to a variety of alternative approaches in the literature. In practice, however, voltage breakdown and other failure-time data are usually discretized or rounded off. For grouped data from the Weibull model, there are still difficulties in applying likelihood methods when the sample size is moderate because of the so-called ''embedded-model problem'' After a brief review of this problem and related likelihood theory, we show how the difficulties can be resolved and how likelihood-based confidence intervals for the Weibull parameters and quantiles can be constructed from grouped data, under positivity constraints and for moderately sized samples that commonly occur in practice, by using reparameterization and enlarging the parameter space.
Key Words
Bartlett corrections, embedded-model problem, generalized extreme-value distributions, grouped data, likelihood ratio confidence intervals, three-parameter Weiball distribution, voltage endurance tests, MAXIMUM-LIKELIHOOD ESTIMATION, NONSTANDARD CONDITIONS, SHAPE PARAMETER, TESTS, DISTRIBUTIONS
Citation

　

Times Cited in Web of Science: 12

Times Cited in Scopus: 3

Times Cited in Google Scholar: 19

Inspec: 1

Mathematical Review: 1

Technometrics Impact Factor (SCI)........13.90
Technometrics Journal Performance Indicators ..... #10 in probability and statistics journals

Cited in Books: Horst Rinne, The Weibull Distribution: A Handbook, Chapman and Hall/CRC 2008.; Wallace R. Blischke, D.N. Prabhakar Murthy, Reliability: Modeling, Prediction, and Optimization, Wiley (2000); William Q. Meeker, Luis A. Escobar,
Statistical Methods for Reliability Data, Wiley (1998)； D.N.P. Murthy, M. Xie, R. Jiang, Weibull Models, Wiley (2004)

WoS: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 巻: 44 号: 2 ページ: 295-318 発行: 2015; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 巻: 18 号: 6 ページ: 2095-2102 DOI: 10.1109/TDEI.2011.6118649 発行: DEC 2011; PAKISTAN JOURNAL OF STATISTICS 巻: 27 号: 2 ページ: 111-131 発行: APR 2011; AMERICAN STATISTICIAN 巻: 65 号: 1 ページ: 44-54 発行: FEB 2011; IEEE TRANSACTIONS ON DEVICE AND MATERIALS RELIABILITY 巻: 10 号: 2 ページ: 263-270 発行: JUN 2010 ; JOURNAL OF APPLIED STATISTICS 巻: 37 号: 4 ページ: 617-627 発行: 2010; JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION Volume: 79 Issue: 3 Pages: 215-225 Published: 2009; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION Volume: 16 Issue: 1 Pages: 281-288 Published: FEB 2009; ECOLOGICAL MODELLING 197 (3-4): 478-489 AUG 25 2006; IEEE TRANSACTIONS ON DIELECTRICS AND ELECTRICAL INSULATION 9 (4): 524-536 AUG 2002; MATHEMATICS AND COMPUTERS IN SIMULATION 54 (13): 81-97 NOV 30 2000

Others: Journal of the Japanese Society of Computational Statistics, Vol.22, No.1, pp.79-91 2009.12;