Approximation of continuous random variables for the evaluation of the reliability parameter of complex stress–strength models

Abstract In many management science or economic applications, it is common to represent the key uncertain inputs as continuous random variables. However, when analytic techniques fail provide a closed-form solution problem one needs reduce computational load, often necessary resort some problem-specific approximation technique approximate each given probability distribution by discrete distribution. Many discretization methods have been proposed so far; in this work, we revise most popular techniques, highlighting their strengths and weaknesses, empirically investigate performance through comparative study applied well-known engineering problem, formulated stress–strength model, with aim of weighting up feasibility accuracy recovering value reliability parameter, also reference number points. The results overall reward recently introduced method best performer, which derives numerical constrained non-linear optimization, preserving first two moments original This provides more accurate than an ad-hoc first-order technique. computationally demanding well computation time can get even larger that required Monte Carlo if points exceeds certain threshold.