  This paper is speculated to propose a class of shrinkage estimators for shape
parameter beta in failure censored samples from two-parameter Weibull
distribution when some 'apriori' or guessed interval containing the parameter
beta is available in addition to sample information and analyses their
properties. Some estimators are generated from the proposed class and compared
with the minimum mean squared error (MMSE) estimator. Numerical computations in
terms of percent relative efficiency and absolute relative bias indicate that
certain of these estimators substantially improve the MMSE estimator in some
guessed interval of the parameter space of beta, especially for censored
samples with small sizes. Subsequently, a modified class of shrinkage
estimators is proposed with its properties.
