Open book, open notes; blank All graphs made should note the question they pertain to. All work must be shown for full credit. Clarity, neatness and accuracy are all important indications of the quality of your work.
1. (10) A product has a characteristic life of 150,000 hours.
The slope of the Weibull failure characteristic is 2.5.
a. If the warranty period is to be 100,000 hours, what percentage
of the products can be expected to fail during the warranty period?
b. If the cost to the manufacturer is $300 per unit failing during warranty, what is the amount of sales revenues that should be allocated to "Warranty Charges" if 5000 units are to be sold?
2. (5) A Weibull distribution with a b of 1 indicates which
type of failure rate:
a. reducing
b. increasing
c. constant
d. not enough information to decide
3. (5) A Weibull distribution with a b less than 1 is typical of which portion of the "bath-tub" curve.
4. (5) A Weibull distribution wherein b is in the 3 to 4 range
is typical of a
____________________ distribution.
5. (20) When a mold ($100,000) for a plastic injection molding machine fails during a production run it causes excessive down time. It is desired to set up a preventative maintenance program to be done between runs. Data from the running of this mold shows the following failures (values are in millions of cycles); determine the underlying distribution by plotting on Weibull paper:
0.9, 1.7, 2.5, 3.1, 3.2, 4.3, 4.6
Plot this data and determine the Characteristic Life (q) and slope
(b).
Comment as necessary about the graphical results.
6. (20) A wire cutting machine has been redesigned & 15
units were put on test. The failure rate is assumed constant
(Exponential distribution). The following is the time of the
first 6 unit failures. The engineer needs an estimate of the
life characteristics at this point since she must know if more
redesign effort may need to be planned.
10, 11, 13, 16, 17, 20
All values are in millions of feet of #16 AWG copper wire.
Based upon this limited data estimate:
a. MTTFb. Failure Rate
c. Reliability at 30 x 106 ft.
d. What percentage of the machines are expected to fail between 20 and 30 million feet.
7. (15) An industrial truck tire has been tested under simulated
real world operating conditions. The test results were: mean life
of 1000 hours and a std. dev. of 125 hours.
The designer now needs an estimate of the reliability. They have a large customer who needs 750 hours with a reliability of 95%. (assume a Normal failure distribution). What do you tell the designer? (Give him the facts)
8. (20) A small labeling machine has been redesigned &
8 units were tested to failure.The failure rate is assumed constant.
The following is the time to which each unit failed.
43, 19, 53, 16, 28, 34, 28, 19
a. Estimate the characteristic life and the limits for a 90% 2-sided confidence interval.
b. At what time is it expected that 10% will have failed?