A Bivariate Distribution for the Reliability Analysis of Failure Data in Presence of a Forewarning or Primer Event

Abstract

This article presents a bivariate distribution for analyzing the failure data of mechanical and electrical components in presence of a forewarning or primer event whose occurrence denotes the inception of the failure mechanism that will cause the component failure after an additional random time. The characteristics of the proposed distribution are discussed and several point estimators of parameters are illustrated and compared, in case of complete sampling, via a large Monte Carlo simulation study. Confidence intervals based on asymptotic results are derived, as well as procedures are given for testing the independence between the occurrence time of the forewarning event and the additional time to failure. Numerical applications based on failure data of cable insulation specimens and of two-component parallel systems are illustrated.

Keywords:

• Bivariate distribution
• Forewarning event
• Independence testing
• Maximum likelihood estimation
• Moments method estimation
• Reliability

Mathematics Subject Classification:

• Primary 62N05
• Secondary 60E05, 62F10

Acknowledgment

The author wishes to thank the Associate Editor for some useful comments.

Notes

RB values greater than 1 are favorable to the ML estimators.

RRMSE values greater than 1 are favorable to the ML estimators.