Nonparametric estimation of bivariate survivor function under masked causes of failure

Abstract

Consider a system that consists of k components. Each component is subject to more than one cause of failure. Due to inadequacy in the diagnostic mechanism or reluctance to report any specific cause of failure (disease), the exact cause of failure cannot be identified easily. In such situations, where the cause of failure is masked, test procedures restrict the cause of failure to a set of possible types containing the true failure cause. In this paper, we develop a nonparametric estimator for the bivariate survivor function of competing risk models under masked causes of failure based on the vector hazard rate. Asymptotic properties of the estimator are established. A simulation study is carried out to assess the performance of the estimator. We also illustrate the method with a data set.

Keywords:

• bivariate survivor function
• competing risks
• masked causes of failure
• cause-specific hazard
• vector hazard rate

Acknowledgements

We would like to thank the editor and referees for their valuable suggestions. The first author is thankful to the Council of Scientific and Industrial Research, India, for the financial support. The second author is grateful to U.G.C, India, for the financial support. We also express our sincere gratitude to Dr. T.M. Jacob, Nirmala College, Muvattupuzha, for his help in doing the simulation work.