II. Probability and Statistics for Reliability
B. Statistical inference
1. Point estimates of parameters (Evaluate)
Obtain point estimates of model parameters using probability plots, maximum likelihood methods, etc. Analyze the efficiency and bias of the estimators.
Additional References
Quick Quiz
1-17. In a life test of 4 power cells, failures were observed after 12, 22, 30, and 37 hours. A fifth cell was tested for 75 hours without failure, at which time the test was terminated. Calculate the estimated mean time to failure and the failure rate.
(A) MTTF = 35.2; failure rate = 0.0284
(B) MTTF = 44; failure rate = 0.0227
(C) MTTF = 35.2; failure rate = 0.0227
(D) MTTF = 44; failure rate =0.0284
(B) MTTF = 44; failure rate = 0.0227
The formula for MTTF is the total test time divided by the number of failures. In this case add the time to failure times of the four units that failed and the total time for the one unit that did not fail. That is 12 + 22 + 30 + 37 + 75 = 176 hours of total test time. Then divide by the number of failure, 176 / 4 = 44 hours MTTF. The inverse of MTTF is an estimate of the failure rate, 1 / 44 = 0.0227.
The question did not mention the units being replace or quickly repaired after failures, that the test time ends for each unit upon failure. Plus it is looking for the MTTF both of which imply non-repairable units. If you divided by 5 or didn’t check failure rate calculation is correct, there is an answer listed.
1-31. The failure rate for a flash drive is 0.00023 per hour of operation. Calculate the MTBF assuming that the failure rate is constant.
(A) 435 hours
(B) 3125 hours
(C) 4,348 hours
(D) 43,478 hours
(C) 4,348 hours
For the exponential distribution (assuming constant failure rate) the MTBF is the inverse of the failure rate. Thus
$$ \theta =\frac{1}{\lambda }=\frac{1}{0.00023}=4,348\text{ hours}$$
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