TY - JOUR

T1 - Inference for Reliability and Stress-Strength for a Scaled Burr Type X Distribution

AU - Surles, J. G.

AU - Padgett, W. J.

N1 - Funding Information:
We would like to thank the referees for their insightful and helpful comments and suggestions. This research was partially supported by the National Science Foundation under grant numbers DMS-9503104 and DMS-9877107 to the University of South Carolina.

PY - 2001

Y1 - 2001

N2 - Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are developed. A bootstrap method to estimate variance for the maximum likelihood estimators is also discussed. To illustrate these techniques, an example using carbon fiber strength data is given. Simulations to assess the effectiveness of these techniques, as well as other concerns, are presented.

AB - Inference for R = P(Y < X) is considered when X and Y are independently distributed as scaled Burr type X random variables. Under this model, exact inference procedures for R cannot be found. Hence, based on the expected Fisher information matrix which is derived here, asymptotic inference procedures for R and other general functions of the parameters are developed. A bootstrap method to estimate variance for the maximum likelihood estimators is also discussed. To illustrate these techniques, an example using carbon fiber strength data is given. Simulations to assess the effectiveness of these techniques, as well as other concerns, are presented.

KW - Burr distributions

KW - Carbon composite materials

KW - Fisher information

KW - Maximum likelihood

KW - Stress-strength model

UR - http://www.scopus.com/inward/record.url?scp=0035377893&partnerID=8YFLogxK

U2 - 10.1023/A:1011352923990

DO - 10.1023/A:1011352923990

M3 - Article

C2 - 11458657

AN - SCOPUS:0035377893

SN - 1380-7870

VL - 7

SP - 187

EP - 200

JO - Lifetime Data Analysis

JF - Lifetime Data Analysis

IS - 2

ER -