“…Based on the operating conditions of the VSV mechanism in engineering practice (Zhang et al ., 2022a), the dimensional parameters (crank 1 length L 1 , crankshaft height L 2 , crank 2 upper length L 3 and second crank 2 lower length L 4 ), physical random parameters (material density ρ , rotating friction coefficient u R , ball-hinged friction coefficient u s and pneumatic moment τ ), temperature parameters (thermal conductivity λ , expansion coefficient α and gas temperature T ) and life parameters ( γ , β , S 0 ) are regarded as random variables (Li et al ., 2022e; Nie et al ., 2021), whose distribution traits are shown in Table 5. Note that all random variables are assumed to be independent of each other.…”