Assume that 100 components are placed on test for 1000 h. From previous testing,

Question

Assume that 100 components are placed on test for 1000 h. From previous testing, we believe that the hazard rate is constant, and the MTTF = 500 h. Estimate the number of components that will fail in the time interval of 100 - 200 h. How many components will fail if it is known that 15 components failed in T < 100 h?

Assume that 100 components are placed on test for 1000 h. From previous testing, we believe that the hazard rate is constant, and the MTTF = 500 h. Estimate the number of components that will fail in the time interval of 100 - 200 h. How many components will fail if it is known that 15 components failed in T

Explanation / Answer

Ignore my first answer.

lambda = 1/MTTF = 1/500

Thus, the number that are expected to fail between 100 and 200, as there are 100, equals

100 * [F(200) - F(100)]

F(t) = 1 - e^-lambda t

Thus, F(200) = 1 - e^-1/500*200 = 1-e^-2/5

F(100) = 1-e^-1/500*100 = 1-e^-1/5

Then, 100 * [F(200) - F(100)] = 100 * ((1-e^-2/5) - (1-e^-1/5)) = 100 * (e^-1/5 - e^-2/5) =

100e^-1/5 - 100e^-2/5 =

14.8410707042342

If 15 fail in 0-100, there are 85 left at time 100. Then, as this is a memoryless process with a constant hazard rate, the number that are expected to fail in the next 100 hours is

85*(F(200-100) - F(100-100)) = 85*(F(100)-F(0)) = 85 * ((1-e^-1/5) - 0) = 85 - 85e^-1/5 =

15.4078859883715

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