In this paper, based on the Weibull Inverse Power Law, we present a methodology to determine the following: (1) the failure percentiles, referred to as the P–S–N field, of an S–N curve for a 42CrMo4 steel material exhibiting bilinear ($s_1 \mathrm{and} s_2)$ behavior (e.g., a competence failure mode); (2) the Weibull family that characterizes the entire bilinear behavior; and (3) the zero-vibration test plan that meets the required vibration reliability index of $R\left(t\right)=0.97$ with a reliability confidence level of $CL=0.75$. From the application, based on the formulated normal–Weibull relationship, we determine the failure percentiles for the normal (one, two, and three) sigma levels, as well as those failure percentiles corresponding to the capability ($Cp$) and ability ($Cpk$) indices. Finally, we present the formulation to determine the $R\left(t\right)$ index and the $CL$ level associated with each normal percentile, along with their numerical values.

In this paper, the method to determine the percentiles of the P-S-N field when it presents bilinear (s1 and s2) behavior (e.g competence failure mode) is given. The percentiles are determined around the Weibull scale (η) parameter in Cycles that corresponds to the median applied stress of the whole bilinear behavior. The reliability (R(t)) index that corresponds to each P-S-N percentile are also determined. As well as the confidence reliability percentile (CL) that corresponds to each P-S-N percentile. The formulation to relate CL with its corresponding normal P-S-N percentile is also given. Numerically, the percentiles of the normal (one, two, and three) sigma levels, as well as those that correspond to the capability Cp and Cpk indices are related with their CL values, and R(t) indices. To validate the Weibull cycle bilinear family, a test plan is designed and numerically performed. In the numerical application we use the 42CrMo4 steel material.