Goodness-of-fit tests for the power-law process

Author

Park, Won J. ; Kim, Yoon G.

Author_Institution

Dept. of Math. & Stat. Wright State Univ., Dayton, OH, USA

Volume

41

Issue

1

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

107

Lastpage

111

Abstract

The power-law process is often used as a model for reliability growth of complex systems or reliability of repairable systems. Often goodness-of-fit tests are required to check the hypothesis that failure data came from a power-law process model. Three statistics, Kolmogorov-Smirnov, Cramer-von Mises, and Anderson-Darling, are considered for a goodness-of-fit test of a power-law process in the case of failure-truncated data. Tables of critical values for the three statistics are presented and the results of a power study are given under the alternative hypothesis that failure data came from a nonhomogeneous Poisson process with log-linear intensity function. This power comparison is a new result, which can guide in selecting a test statistic and sample size. The power study shows that the tests have acceptable power for some parameter values and the Cramer-von Mises statistic has the highest power for a sample-size ⩾20

Keywords

failure analysis; reliability theory; statistical analysis; Anderson-Darling statistic; Cramer-von Mises statistic; Kolmogorov-Smirnov statistic; complex systems; failure-truncated data; goodness-of-fit tests; log-linear intensity function; nonhomogeneous Poisson process; power-law process; reliability growth; repairable systems; test statistic; Art; Maximum likelihood estimation; Monte Carlo methods; Power system modeling; Power system reliability; Reliability theory; Statistical analysis; Statistical distributions; Statistics; System testing;

fLanguage

English

Journal_Title

Reliability, IEEE Transactions on

Publisher

ieee

ISSN

0018-9529

Type

jour

DOI

10.1109/24.126680

Filename

126680