On the Simultaneous Estimation of Weibull Reliability Functions

Under the homogeneity assumption of k reliability functions from a two-parameter Weibull distribution, we have developed the asymptotic theory for the simultaneous estimation of reliability functions. Improved estimation strategies based on the Graybill Deal, preliminary test and the James-Stein type shrinkage principles are discussed. Using the sequence of local alternatives and squared error loss function, we have derived the asymptotic distributional quadratic bias and risk of the said estimators. A comparison in terms of risk has also been carried out among the listed estimators relative to the benchmark maximum likelihood estimator. To be more specific, we have pointed out the regions where our suggested estimators perform better than other estimators. A comprehensive Monte-Carlo simulation study is presented to validate the behavior of various estimation methods in terms of simulated relative efficiency along with a real-data application.