[version 2 - after correction of the formula, and related details. JD]

@ Omar

Dear Omar, can you please explain what information about the reliability is available for you? Without any knowledge one cannot do anything. Or, just take arbitrary probability distribution, say  F , find the quasi inverse of it  F-1, generate  a sample of  uniform variable  U_1, U2, . . .  U_n, and calculate   T_j :=  F-1(U_j), for  j=1,2,...,n.  The results form a simple sample of random time to the first failure following the pd, determined by  F . Then a simulation  of  the reliability function R=1- F  is a the step function called in the literature empirical reliability function, defined by the formula

Remp(t) = 1/n  ( 1{ T_1 >t }  +  1{ T_2 >t } + ... + 1{T_n >t} )

where  1 is the index function for the inequality in the braces (=1  if the inequality holds, and equal  0  if it does not). For example, if   R(t) = 1 - F(t) = exp( - a t), and  U  has uniform distribution on [0,1], then  the cdf.  of  T= -ln(U)/a   equals  F(t), t >0.  If you don't know anything about the cdf of  T - no suggestion is possible.

Regards, Joachim