Finite sample behaviour of the Hollander-Proschan goodness of fit with reliability and maintenance data
In maintenance and reliability everyday practices the data samples which are often made available are multiply censored, i.e. the times to failure are randomly mixed with incomplete lifetimes. This fact adds complexity when sound decisions are required to be made in identifying failure mechanisms, evaluating maintenance practices and/or manufacturing methods. Hollander & Proschan have derided a Goodness of Fit (GOF) test statistic which has a number of advantages, i.e. can accommodate multiply censored data, can be employed irrespective of the failure and censoring distributions, and finally is indeed an omnibus and straightforward method to compute. Although the test statistic has received attention in the literature of reliability and maintenance applications over the last two decades, only a limited investigation has been carried out in terms of its finite sample behavior. This paper investigates the usefulness of this particular GOF method within the reliability and maintenance context and provides a literature review of alternative approaches. Furthermore, the finite sample properties are investigated through extensive Monte Carlo Simulations, with the Weibull distribution when parameters are estimated from the data and a wide range of censoring percentages.
KeywordsWeibull Distribution Incomplete Observation Scale Alternative Censor Survival Data Weibull Shape Parameter
Unable to display preview. Download preview PDF.
- 5.Efron B. (1967) The Two Sample Problem with Censored Data, Conference Proceedings. 5th Berkley Symposium on Mathematical Statistics and Probability edited by J. Newman, 4, 831-853, Berkley: University of California Press.Google Scholar
- 6.Lee E.T. (1992) Statistical Methods for Survival Data Analysis, John Wiley and Sons, New York.Google Scholar
- 7.Dodson B. (1994) Weibull Analysis, ASQC, Quality Press.Google Scholar
- 37.Nelson W. (1969) Hazard Plotting Methods for Incomplete Failure Data, Journal of Quality Technology, 1(1), 27-52.Google Scholar
- 46.Kostagiolas, P. A. (2000) The Goodness of Fit Problem with Industrial Reliability Data, Ph.D thesis, Univ. of Birmingham.Google Scholar