1. Use the exponential distribution with MTTF=50,000 hrs.. What is the time to 10% failure?
A, 5000 hrs
B. 5268 hrs
C. 5450 hrs
D. 5333 hrs
2. Three assembly plants produce the same type of parts. Plant A produces 25% of the volume, and has a defect rate of 1%, Plant B produces 30% of the volume and has a defect rate of 1.2%. Plant C makes the remainder and ships 0.6% defectives. If a component is picked at random from the warehouse stocked by the and is defective, what is the probability it was manufactured by Plant A, Plant B, Plant C?
A. 0.25,0.30,.45
B. 0.36, 0.43, 0.21
C. 0.28, 0.41, 0.31
D. 0.333, 0.333, 0.333
Plant  % Prod  %Defect  Prod x Defect  Prob 
A  25  1  0.0025  0.28 
B  30  1.2  0.0036  0.41 
C  45  0.6  0.0027  0.31 

 Sum=  0.0088 

3. You are asked to construct a Zero failure test for a redesigned ball bearing
( β=2.5) that the design folks believe should have an η=1000hrs. Program Mgmnt wants you to use only 5 tests. How long should you test these five samples to be 90% confident that the ball bearing design is better than 1000hrs?
A. 733hrs,
B. 851hrs
C. 975hrs
D. 1500.hrs
115  1188  1489  1599 
120  1300  1487  1650 
205  1380  1505  1670 
840  1405  1550  1675 
848  1415  1575  1680 
890  1437  1585  1700 
1160  1449  1590  1710 
4. The Reliability analysis of a Submarine firecontrol system involved the lifetest of 500 fuses put on test at 85% of rated current. After 1800 hr, 28 fuses had blown and the test was stopped. A Weibull plot of data
A. (4, 3721 hrs)
B. (3.8, 3865 hrs)
C. (2.0, 7272 hrs)
D. (5.6, 3130 hrs)
5. Referring to the Weibull plot in 4. above, How many Failure modes are there in the fuse reliability test data:
A. 2
B. 3
C. 1
D. 4
6. A bearing manufacturer has a bearing with Weibull β=2 and η=600 hrs. The design team made a small change in the design and a change of material. They now hope they have doubled the characteristic life at 95% confidence. They tested 10 of the new design bearings for 1800 hrs and Had 5 failures : 700, 900, 1000, 1100, and 1300 hrs. Did the new bearing design have 2X the characteristic life With 95% confidence?
A. YES
B. NO
WHY?
7. For a certain 3engine airplane, at least two out of its three engines must function. The engine reliability at time t is 0.995. Find the probability that the airplane flies successfully for T hours, assuming identical and independent engines.
A.0.9998
B. 0.985
C. 0.99945
D. 0.999925
8. A fleet of 100 engines is subjected to a known Weibull failure mode. The Weibull has a slope of 3 and a characteristic life of 1000 hours. The current engine times are as follows:
Calculate the expected number of failures now. Calculate the additional engines
that will be expected to fail in 6 months if the utilization rate is 25 hours/month.
What is the total number of engines expected to fail? Assume that failed units
are not fixed.
A. 6.7
B. 1.9
C 4.9
D. 8.6
No engines  T=now  T+150  F(Nowtime)  F(t+135)  (F(t+150)F(t))/(1F(t))  Exp Now  Exp6mos  Exp(Cum6mos) 
20  150  300  0.003369311  0.026638758  0.023348114  0.067386222  0.466962289  0.53277517 
20  200  350  0.007968085  0.041968864  0.034273876  0.159361703  0.68547751  0.839377271 
20  250  400  0.015503563  0.061995  0.047223571  0.31007126  0.944471422  1.239900009 
20  300  450  0.026638758  0.087096409  0.062112244  0.53277517  1.242244875  1.741928184 
20  350  500  0.041968864  0.117503097  0.078843193  0.839377271  1.576863862  2.350061948 




 Sum =  1.908971625  4.916019958  6.704042581 
9. A system consisting of 4 subsystems in series is required to have a reliability of 0.99 for a mission time of 50 hours. Allocate the reliability requirements to each of the subsystems given the following estimates for present subsystem failure rates;
λ1=0.004 Failures/hour, λ2=0.007 Failures/hour, λ3=0.008 Failures/hour, λ4=0.005 Failures/hour
Hint: Calculate the weighting factors 1st, then solve R=0.99=eλ* 50 for λ*
λ*1λ*4: all x 104
A. (0.235,0.486,0.569,0.418),
B. (0.135,0.486,0.569,0.418),
C. (0.135,0.386,0.469,0.418)
D. (0.335,0.586,0.669,0.418)
10. A parallel system contains four identical and independent active units. Each unit may fail due to Hardware or a human error. The unit constant hardware Failure rate =λ1=0.004 failure/hour, The human error rate is λh= 0.0005 error/hr.
Determine the parallelsystem MTTF.
Hint: