Systems with exponential life using components with HNBUE lives

The authors show that if the convolution of n HNBUE distributions is exponential, then n-1 of the distributions are degenerate at zero and the other distribution is exponential. This result is also shown to hold for the wider HNBUE(3) class. The result extends similar results previously published for the IFRA and NBU cases. The authors conjecture that if a monotonic system formed with independent components has exponential life, it must be essentially a series system with exponential components