Inverse normal and lognormal distributions for reliability design

In a reliability design problem it is often the case that the design parameters are found after the design reliability, for which cost and availability of resources may be a deciding factor, has been fixed. For an accurate design it is necessary to calculate the design values as precisely as possible. It is often the case that tables do not give the desired accuracy in the inverse problem of parameter search. For the conventional search of parameters, readily available tables suffer from the disadvantage of their inability to provide suitable and accurate values where the inversion is in a very narrow limit. A direct inversion, by using an expression which can facilitate any desired accuracy, is a promise of this paper. The authors have developed inverse normal and lognormal distributions which find an application in a wide variety of problems particularly in designs involving steel and structural alloys.