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1. In a life test of 4 batteries, failures were observed after 10, 30, and 40 hours. The 4th battery was tested 75 hours without failure, at which time the test was terminated. What are the estimated Mean-Time-To-Failure (θ) and failure rate (λ) ?
A. Estimated θ = .019; λ = 52
B. Estimated θ = 27; λ = .038
C. Estimated θ = 52; λ = .019
D. Estimated θ = 14; λ = .017


2. The distribution used to describe the time between failures which occur independently and at a constant rate, is the:
A. Log normal.
B. Weibull.
C. Gamma.
D. Exponential.


3. The hazard rate function h(t) for a device is given by the following relationship, where t is time in hours.

What is the reliability of this device at t = 2 hours ?
A. 0.638
B. 0.368
C. 0.486
D. 0.238


4. Pascal’s triangle presents a simple means of determining which of the various terms of the binomial expansion?
A. Exponents.
B. Coefficients.
C. Combinations.
D. Permutations.



5. Using the data to the right, determine if Design A is significantly different than design B.


6. Produce a probability plot that best explains the failure data:
TTFs: 150,250,360,485,650,855,1130,1540

7. Given mean-time-to-failure of 200 hours for each of two components, what is the probability of failure if both components operate in series for one hour ?
A. P = 0.990
B. P = 0.001
C. P = 0.002
D. P = 0.010

8. If a test shows three failures in 50 hours of operation, how many failures will it show in 1000 hours of operation if the failure rate is constant ?
A. 150
B. 20
C. 333
D. 60

9. The failure rate for an IC chip is 0.0023 per hour of operation. Calculate the MTBF given that the failure rate is constant.
A. 37.6 hrs
B. 43 hrs
C. 434.78 hrs
D. 486 hrs

10. The function below has a density distribution where X is a continuous random variable. What is the probability that X = 4.0 ?
1 ≤ X ≤ 5
A. 0.00
B. 0.20
C. 0.30
D. 0.40

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1. The type of stress‐strength analysis when you have 3 or more variables in design for reliability is an example of:A. Deterministic design B. Probabilistic design C. Data mining design D. Design for maintainability   2. A bolted joint has shear strength which is normally distributed with mean, 40 klb/in2, and standard deviation, 4 k‐lb/in2.

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