A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed

Question

A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.
(a) – Read section 1.5.2 in the textbook.
(b) – What is the mean time to failure for component A and for component B

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Thu Thảo 6 months 2021-07-20T21:19:17+00:00 1 Answers 23 views 0

Answers ( )

  1. MichaelMet
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    2021-07-20T21:20:49+00:00
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    Answer:

    E(x) = \frac{1}{2} — Component A

    E(x) = \frac{1}{3} — Component B

    Step-by-step explanation:

    Given

    Distribution = Exponential

    \lambda = 2 — Component A

    \lambda = 3 — Component B

    Solving (a): The mean time of A

    The mean of an exponential distribution is:

    E(x) = \frac{1}{\lambda}

    We have:

    \lambda = 2 — Component A

    E(x) = \frac{1}{2}

    Solving (b): The mean time of B

    The mean of an exponential distribution is:

    E(x) = \frac{1}{\lambda}

    We have:

    \lambda = 3 — Component B

    E(x) = \frac{1}{3}

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Giải phương trình 1 ẩn: x + 2 - 2(x + 1) = -x . Hỏi x = ? ( )