In the field of reliability, a lot has been written on the analysis of phenomena that are
related. Estimation of the difference of two population means have been mostly
formulated under the no-correlation assumption. However, in many situations, there
is a correlation involved. This paper addresses this issue. A sequential estimation
method for linearly related lifetime distributions is presented. Estimations
for the scale parameters of the exponential distribution are given under
square error loss using a sequential prediction method. Optimal stopping rules
are discussed using concepts of mean criteria, and numerical results are
presented.