In this paper we explain a necessary and sufficent condition for independence between any arbitrary statistics with sufficient statistics which is also maximum likelihood estimator in a general‎
‎exponential family with location and scale parameter namely generalized normal distribution‎. ‎At the end‎, ‎it is shown that the converse is true except in the asymptotic cases‎.

In this paper, first, the generalized lambda distribution and the characteristics of this distribution are introduced. The concept of resistance stress is fully explained and the reliability of a system from the perspective of resistance stress is examined. Also, the mathematical form of the resistance stress parameter in the generalized lambda distribution has been calculated. The estimation of the parameters has been investigated by the moments method‎‎ and ‎for different parameters values the graph of generalized lambda distribution is drawn ‎‎and resistance stress parameter calculated. With a real example the application of the results is illustrated.‎‎