## The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time

Question

The mean time between failures (MTBF) is a common metric used to measure the performance of manufacturing systems. MTBF is the elapsed time between failures of a system during normal operations. The failures could be caused by broken machines or computer errors, among other failures. Suppose that the MTBF for a new automated manufacturing system follows an exponential distribution with a mean of 12.2 hours. (a) What is the probability that the automated manufacturing system runs for more than 18 hours without a failure

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3 weeks 2021-08-30T16:28:26+00:00 1 Answers 0 views 0

0.2287

Step-by-step explanation:

The computation of the probability that the automated manufacturing system runs for more than 18 hours without a failure is shown below:

P(X > 17) = 1 – P(X < 17)

= 1 – [1 – e^-18 ÷ 12.2]]

= 1 – [1 -0.228684984
]

= 0.2287