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The Birnbaum-Saunders distribution is widely used in fields such as survival analysis. In this paper, we use a new method to construct confidence intervals for the shape parameter of the Birnbaum-Saunders distribution and find it superior to some existing methods. Our method can be called the 'joint pivot method' as we obtain the confidence interval by uniting two pivots. Furthermore, we find that the joint pivot method can also be used to solve the Behrens-Fisher problem. Simulation studies show that the joint pivot method is comparable with some commonly practiced ones. Finally, we analyse two real data sets to illustrate the proposed procedure. [ABSTRACT FROM AUTHOR]