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