ABCDEFGHIJKLMNOPQRSTUVWXYZ
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Exponential Distribution
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A service machine always has a stand by unit for immediate replacement upon failure. The time
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to failure of the machine (or its standby unit) is exponential and occurs every 5 hours, on the
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average. The machine operator claims that the machine is “in the habit” of breaking down every
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night around 8:30 p.m. Analyze the operator’s claim.
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The average failure rate of the machine is 𝜆 = 1/5 =
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failure per hour. Thus, the exponential
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distribution of the time to failure is
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HourTime
Probability
HourTime𝜆𝑡-𝜆𝑡
Probability
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20:300,000,00%20:300,000,00000,00000,00%
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20:200,173,28%20:200,170,0333-0,03333,28%
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20:100,336,45%20:100,330,0667-0,06676,45%
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20:000,509,52%20:000,500,1000-0,10009,52%
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13:007,5077,69%13:008,001,6000-1,600079,81%
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