System CDF for exponential parallel systems

Computes \(F_{sys}(t) = \prod_j (1 - e^{-\lambda_j t})\) using the inclusion-exclusion expansion.

Usage

F_sys_exp(t, par)

Arguments

t

Scalar time point (non-negative numeric).

par

Numeric vector of rates (length m).

Value

Scalar CDF value \(P(T_{sys} \le t)\).

See also

S_sys_exp() for the survival function.

Examples

F_sys_exp(1, c(1, 2))  # P(T_sys <= 1) for 2-component parallel
#> [1] 0.5465723