Let X, X 2 ..... X, are independent and identically distributed random variables with distribution function given by F (x; 0 ) = 1- exp (- (x- 0 )), x > 0, 0 > 0. We observe only the order statistics X(k+,,-m) (..+) ..+2) , x?-m)). The smallest k and the largest m values are censored. This report analyzes the problem of estimating of the function R(x- 0 ) = exp (- (x- 0 )), x > 0 for given value x based on the failure time data x? +'"-m) . In addition we consider the estimation of the reliability parameter from a random censored samples
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