If the individual reliabilities are denoted by p₁, p₂, . . ., p_n, which of the following best represents the system reliability R_p of an n-component parallel system? A) Rp = 1 - (1 + p₁) (1 + p₂) (1 + p₃) . . . (1 + p_n) B) Rp = 1 - (1 - p₁) (1 - p₂) (1 - p₃) . . . (1 - p_n) C) Rp = (p₁) (p₂) (p₃) . . . (p_n) D) Rp = (p₁) + (p₂) + (p₃) + . . . (p_n)

Question

Quizplus · Accepted Answer

In a parallel system, if one component fails, the entire system still works. Therefore, the system is considered operational if at least one component is operational. Thus, the system reliability can be found by taking the complement of the probability that all components fail. This can be expressed as Rp = 1 - [(1-p₁) x (1-p₂) x... x (1-p_n)]. Therefore, choice B is the correct answer.

If the Individual Reliabilities Are Denoted by P1, P2

If the Individual Reliabilities Are Denoted by P₁, P₂