  Under adaptive progressive Type-II censoring schemes, order restricted
inference based on competing risks data is discussed in this article. The
latent failure lifetimes for the competing causes are assumed to follow Weibull
distributions, with an order restriction on the scale parameters of the
distributions. The practical implication of this order restriction is that one
of the risk factors is dominant, as often observed in competing risks
scenarios. In this setting, likelihood estimation for the model parameters,
along with bootstrap based techniques for constructing asymptotic confidence
intervals are presented. Bayesian inferential methods for obtaining point
estimates and credible intervals for the model parameters are also discussed.
Through a detailed Monte Carlo simulation study, the performance of order
restricted inferential methods are assessed. In addition, the results are also
compared with the case when no order restriction is imposed on the estimation
approach. The simulation study shows that order restricted inference is more
efficient between the two, when this additional information is taken into
consideration. A numerical example is provided for illustrative purpose.

Methodology;Applications