  Quite often, we observe reliability data with two failure modes that may
influence each other, resulting in a setting of dependent failure modes. Here,
we discuss modelling of censored reliability data with two dependent failure
modes by using a bivariate Weibull model with distinct shape parameters which
we construct as an extension of the well-known Marshall-Olkin bivariate
exponential model in reliability. Likelihood inference for modelling censored
reliability data with two dependent failure modes by using the proposed
bivariate Weibull distribution with distinct shape parameters is discussed.
Bayesian analysis for this issue is also discussed. Through a Monte Carlo
simulation study, the proposed methods of inference are observed to provide
satisfactory results. A problem of practical interest for reliability engineers
is to predict field failures of units at a future time. Frequentist and
Bayesian methods for prediction of future failures are developed in this
setting of censored reliability data with two dependent failure modes. An
illustrative example based on a real data on device failure with two failure
modes is presented. The model and methodology presented in this article provide
a complete and comprehensive treatment of modelling censored reliability data
with two dependent failure modes, and address some practical prediction issues.
