The Rick A. Tee Company operates a sky train that takes tourists to the top of M

Question

The Rick A. Tee Company operates a sky train that takes tourists to the top of Mount Weibull where they can enjoy a breathtaking view of Failure Canyon and Lake Redundant. The sky train operates twice a day-once in and Lake the morning and once in the afternoon. The design capacity of the sky train 10,000 pounds. Once a month (every 20 working days), a safety is conducted and all parts showing wear are replaced (as-good-as-new maintenance policy). Data collected over the previous season has determined that the customer load per trip is lognormally distributed with a shape parameter of .3 and a mean of 5000 pounds (a safety margin of 10,000/5,000 = 2). Determine the static reliability that the load will not exceed the design strength of the sky train resulting in a catastrophic failure. Determine the dynamic reliability over a 20-day maintenance interval.

Explanation / Answer

(a) Probability that lognormal(µ, .3) is greater than 10000, where mean is 5000. As mean is exp(µ+0.5^2), we get µ=ln(5000)-0.5*0.3^2=8.472 (correct upto 3 decimal places).

Now, we calculate the probability that LN(8.472,0.09)>10000.

implies that,

N(8.472,0.09)>Ln(10000)=9.21

Thus,

Probability that N(0,1)>(9.21-8.472)/0.3=2.46

Thus the probability is 1-0.99305=0.695%

b.) Dynamic reliability=1-(.99305)^20=13%

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