Abbreviation	Description
VHCF	Very high cycle fatigue
${\sigma }_{\mathrm{LLF}}$	Long-life fatigue strength
$B,a$	Material dependent coefficients of the Kuguel approach
$V_{95}$	95% highly-stressed volume
$V_{90}$	90% highly-stressed volume
$\kappa$	Weibull coefficient
$V_{\kappa \infty }$	Threshold volume
$\mathsf{\Delta }{\sigma }_0$	Fatigue strength range of the defect free material
$\mathsf{\Delta }{K}_{th,lc}$	Long crack threshold
Y	Geometry factor
a	Crack length
KTD	Kitagawa–Takahashi diagram
$\mathsf{\Delta }{K}_{th,eff}$	Effective crack threshold
$\mathsf{\Delta }a$	Crack extension
$\mathsf{\Delta }K$	Stress intensity factor range
$K_{max}$	Maximum stress intensity factor
$K_{min}$	Minimum stress intensity factor
$\mathsf{\Delta }{K}_{eff}$	Effective stress intensity factor range
$K_{op}$	Opening stress intensity factor
$\mathsf{\Delta }{K}_{th,\mathsf{\Delta }a}$	Crack threshold range in respect of the crack extension
${\nu }_i$	Weighting factor for crack closure effects
$l_i$	Necessary crack elongation for complete build-up of crack closure
$\sqrt{area}$	Defect size parameter
LN	Lognormal distribution
EV	Extreme Value distribution type one
GEV	Generalized Extreme Value distribution
$P\left(\sqrt{area}\right)$	Cumulative distribution function
$\mu$	Location parameter of the GEV
$\delta$	Scale parameter of the GEV
$\xi$	Shape parameter of the GEV
$P_{Occ}$	Probability of occurrence
$V_0$	Reference volume
$EVIR$	Extreme value inclusion rating
$V_{\alpha }$	Control volume
T	Return period
$F_j$	Cumulative probability
j	Index variable
n	Maximum index variable
$y_j$	Reduced variate
HV	Vickers hardness
$C_1,C_2$	Coefficients of Murakami’s $\sqrt{area}$ concept
HIP	Hot isostatic pressing
DAS	Dendrite arm spacing
$l_{const}$	Length of constant specimen diameter
HCF	High cycle fatigue
$k_1$	Slope of S/N-curve in finite life region
$k_2$	Slope of S/N-curve in long-life region
$N_T$	Number of load cycles for transition point
$T_S$	Scatter band in the long-life region
${\kappa }_{exp}$	Experimentally evaluated Weibull factor
$P_S$	Probability of survival
$\alpha$	Return period of reference volume
$p_{ks}$	p-Value of Kolmogorov-Smirnov test
$\sqrt{area}{P}_{Occ=0.5}$	Defect size with a probability of occurrence of 50%
${\mu }_0$	Reference defect distribution location parameter
$\mathsf{\Delta }$	Deviation of model to experiment