Weibull analysis for normal/accelerated and fatigue random vibration test

In this paper, the formula to estimate the sample size n to perform a random vibration test is derived only from the desired reliability ( R ( t )). Then, the addressed n value is used to design the ISO16750‐3 random vibration test IV for both normal and accelerated conditions. For the normal case, the applied random vibration stress ( S ) is modeled by using the Weibull stress distribution [ W ( s )]. Similarly, for the testing time ( t ), the Weibull time distribution [ W ( t )] is used to model its random behavior. For the accelerated case, by using the over‐stress factor fitted from the W ( t ) and W ( s ) distributions, four accelerated scenarios are formulated with their corresponding testing's profiles. Additionally, from the W ( s ) analysis, the stress formulation to perform the fatigue and Mohr stress analysis is given. Since the given Weibull/fatigue formulation is general, then the formulas to determine the W ( s ) parameters, which correspond to any principal stresses values and/or vice versa, are given. Although the application is performed to demonstrate R ( t ) = 0.97 by testing only n 2  = 6 parts, the guidelines to use the values given in columns n , S , and t of the Weibull analysis table to generate several accelerated testing plans are given.