Weibull component reliability prediction with masked data

Under the conditions that the exact component causing the system to failure may be unknown or 'masked', we present an iterative approach to estimate the component lifetime parameters of a system consisting of two Weibull components. The time and cause of system failure are assumed to follow a competing risks model, and the masking probability of minimum random subsets need not to be subjected to the symmetry assumption. On the basis of considering the effect of failure time and components in minimum random subsets, we redefine the computation of masking probability and the likelihood function is derived for the masked data. An iterative procedure to find the maximum likelihood estimates is presented via an iterative computing method. The developed approach is illustrated with a simple numerical example.