Resumen
It is well known that, given observable data for a competing risk problem, there is always an independent model consistent with the data. It has been pointed out, however, that this independent model does not necessarily have to be one with proper marginals. One purpose of this paper is to explore the extent to which one might try to use the non-parametric assumption that the marginals are proper in order to test whether or not independence holds. This will lead us naturally to a closely related estimation problem—how we estimate the marginals given that a certain quantile of one variable is reached at the same time as a given quantile of the other variable. The problem will be considered using the copula-based approach of Zheng and Klein. Two different methods are discussed. One is a non-parametric maximum likelihood method. The other is a consistent estimator, called the bilinear adjustment estimator, that can be computed quickly and which thus lends itself more readily to simulation methods such as bootstrapping.

Resumen
Reliability analysis is plagued by a lack of accurate data, leading to suboptimal parameter estimates and inaccurate decisions about replacement intervals and preventive maintenance activities. This paper discusses some of the problems associated with failure and maintenance data extraction from coal-fired power plant maintenance databases. Data from four generating units were observed for over 5 years and a reasonable number of equipment classes reviewed. The coal mills are identified as significant equipment that affects the availability of the generating units. This paper describes the interplay of events which includes failure modes, failure, repair and operating time. We investigate a database showing operation of coal mills, and give an exploratory data analysis in which we investigate engineering hypotheses related to mill operation. A competing risk probability model is proposed which captures some of the observed features of the systems under study.