Analysis of Reliability Experiments with Blocking

Abstract Many reliability life tests contain blocking or subsampling. This is often the case when treatments are directly applied to test stands rather than individual specimen. Or, when specimens come from different production batches. Incorrectly assuming completely randomized design underestimates the standard errors due to overstating the true experimental degrees of freedom. In this paper, a survey of existing approaches to analyzing reliability life tests data under subsampling is conducted. We propose a method that integrates the idea of frailty, which accounts for the subsampling effect, and the technique of multiple imputation for analyzing experimental data. A step-by-step description of the approach is presented, followed by a numerical example based on a popular reliability dataset. Finally, comprehensive comparison studies between the proposed method and existing methods are conducted.

[1]  Ewan Macarthur,et al.  Accelerated Testing: Statistical Models, Test Plans, and Data Analysis , 1990 .

[2]  D. Rubin,et al.  Multiple Imputation for Nonresponse in Surveys , 1989 .

[3]  L. Tierney.  Markov Chains for Exploring Posterior Distributions , 1994 .

[4]  Margaret J. Robertson,et al.  Design and Analysis of Experiments , 2006, Handbook of statistics.

[5]  Simon French,et al.  Statistical Analysis of Reliability Data , 1992 .

[6]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[7]  J. Vaupel,et al.  The impact of heterogeneity in individual frailty on the dynamics of mortality , 1979, Demography.

[8]  Joseph D. Conklin.  Classical Competing Risks , 2002, Technometrics.

[9]  Ramón V. León,et al.  Effect of Not Having Homogeneous Test Units in Accelerated Life Tests , 2009 .

[10]  Thomas A. Louis,et al.  Assessing gamma frailty models for clustered failure time data , 1995, Lifetime data analysis.

[11]  D. Rubin.  Multiple Imputation After 18+ Years , 1996 .

[12]  G. Geoffrey Vining,et al.  Reliability Data Analysis for Life Test Experiments with Subsampling , 2010 .

[13]  Peter Green,et al.  Markov chain Monte Carlo in Practice , 1996 .

[14]  Jian Xu,et al.  A three-parameter Weibull statistical analysis of the strength variation of bulk metallic glasses , 2009 .

[15]  Marvin Zelen,et al.  Factorial Experiments in Life Testing , 1959 .

[16]  Alan H. Feiveson,et al.  Reliability of Space-Shuttle Pressure Vessels With Random Batch Effects , 2000, Technometrics.

[17]  Ramón V. León,et al.  Bayesian Modeling of Accelerated Life Tests with Random Effects , 2007 .

[18]  William Q. Meeker,et al.  A Comparison of Maximum Likelihood and Median-Rank Regression for Weibull Estimation , 2010 .

[19]  Martin Crowder,et al.  Statistical Analysis of Reliability Data , 1991 .

[20]  Gordon Johnston,et al.  Statistical Models and Methods for Lifetime Data , 2003, Technometrics.

[21]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[22]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[23]  Anatoli I. Yashin,et al.  HIDDEN FRAILTY : MYTHS AND REALITY by , 2005 .

[24]  Fp Gerstle,et al.  Prediction of Long-Term Failure in Kevlar 49 Composites , 1983 .

[25]  Jerald F. Lawless,et al.  Statistical Models and Methods for Lifetime Data: Lawless/Statistical , 2002 .

[26]  Xiao Liu,et al.  Planning of Accelerated Life Tests With Dependent Failure Modes Based on a Gamma Frailty Model , 2012, Technometrics.