Question 1. A worker is unable to calibrate a machine properly because of insufficient training, resulting in a number of non-conforming tasks. This is an example of an assignable cause of variation.
a. True
b. False
Question 2. A distribution with a small standard deviation:
a. has a high spread
b. is less likely to be leptokurtic
c. is more likely to be leptokurtic
d. has a high degree of skewness
Question 3. The specifications for a tape component require production of a unit of width of 5mm+/-0.1mm. A sample of the production process is given below.
5.20 5.04 4.86 5.10
5.06 5.04 4.96 5.13
5.05 4.89 4.92 4.91
5.16 5.07 4.95 5.10
The number of cells for a cell interval of 0.07 is:
a. 3
b. 6
c. 8
d. 13
The cell with the highest frequency has which of the following cell boundaries?
a. 4.895 - 4.965
b. 4.965 - 5.035
c. 5.035 - 5.105
d. 5.105 - 5.175
Question 4. A manager wishes to determine the length of time it takes an operator to realign a machine's settings for an alternate production run. Measurements (in minutes), taken at hourly intervals over two shifts, are as follows:
18 18 15 15 11 20 20
12 15 11 17 05 16 13
The mean and median for the data are, respectfully:
a. 13.07; 15.5
b. 14; 15
c. 15; 15
d. 15.07; 15.5
The standard deviation for the data set is:
a. 2.73
b. 3.81
c. 3.96
d. 4.02
The coefficient of skewness for the data is:
a. -0.48
b. -0.68
c. 1.14
d. 1.42
e. 5.64
Question 5. A population has a mean of 40, and a standard deviation of 6. The area under the normal curve between the mean value and a sample value of 49 is:
a. 0.0596
b. 0.4332
c. 0.4441
d. 1.5
Question 6. The life of a battery is normally distributed with a mean of 1000 hours and a standard deviation 0f 50 hours. The amount of production that will have a life of between 930 and 1080 hours is:
a. 44.52%
b. 52.60%
c. 86.44%
d. 94.52%
Question 7. A firm produces a gear for use in assembly machines that has a mean diameter of 12 cm and a standard deviation of 0.75 cm. If production is normally distributed, what percentage of the goods will be produced within the specification limit of 12.2 cm +/- 0.8 cm?
a. 30.36%
b. 62.01%
c. 69.63%
d. 88.54%
8. Control charts for x-bar and R are under development for a dimension of a manufactured part (measured in mm). A subgroup size of 6 was selected and the following data was gathered:
Subgroup x-bar R Subgroup x-bar R Subgroup x-bar R
1 30 4 6 30 6 11 26 5
2 34 4 7 28 4 12 32 4
3 32 3 8 34 5 13 30 4
4 34 5 9 32 3 14 34 6
5 36 4 10 38 4 15 36 5
LCL(x-bar) and UCL(x-bar) are, respectively:
a. 29.86 and 0.00
b. 29.86 and 34.94
c. 30.27 and 34.53
d. 32.59 and 36.86
UCL(R) and LCL(R) are, respectively:
a. 8.02 and 0.00
b. 8.82 and -2.28
c. 8.82 and 0.00
d. 9.3 and 0.00
The process indicates a lack of control.
a. True
b. False
Question 9. Seven consecutive points above the centerline of a control chart:
a. indicates an assignable cause of variation
b. indicates chance variation
c. indicates an assignable cause of variation only if they exhibit an upward or downward trend
d. cannot be determined to indicate assignable variation without further information
Question 10. A analyst checking process capability develops x-bar and R charts with the following values: UCL(x-bar) = 74.8; LCL(x-bar) = 72.37; x-doublebar = 73.58; R-bar = 1.66; 25 samples of n = 4 have been taken. The product specification limits are 80 +/- 10.
Cp is approximately:
a. 0.0108
b. 0.555
c. 1.67
d. 4.14
e. 5.55
Which of the following statements is most accurate?
a. The process is centered and capable
b. The process is centered but is not capable
c. The process is capable but is not centered
d. The process is neither centered nor capable
Question 11. The probability of obtaining a one or a two on a single throw of a fair six-sided die is:
a. 0.028
b. 0.167
c. 0.333
d. 0.50
Question 12. A metal rod used in connecting two subassemblies for a machine part must measure 10 cm in length. Any deviation causes a change in torsion ratios that materially affects the performance of the part. It costs the manufacturer $20 to adjust the rod (under warranty) when a complaint is received. Based on past experience, the average customer has returned the subassembly if the rod measurement is off by at least 0.5 cm. The firm can adjust the rod for only $5.00 at the factory.
The Taguchi loss function for the rod is:
a. L(y) = 20(y-10)²
b. L(y) = 20(y-0.50)²
c. L(y) = 80(y-0.50)²
d. L(y) = 80(y-10)² CO 11
What should the tolerance specification be, before a factory adjustment is made?
a. 10 ± 0.50
b. 0.50 ± 0.25
c. 10 ± 0.25 CO 11
d. 20 ± 5
Question 13. If P[A and B] = 0.24, and P[B] = 0.48, P[A / B] =
a. 0.1152
b. 0.5
c. 2.00
Question 14. A continuous process produces an assembly component. Typically, 5% of the items produced are nonconforming. The probability that less than 2 of 4 randomly selected items are nonconforming is:
a. 0.02
b. 0.64
c. 0.81
d. 0.98
Question 15. A 100-hour test of 20 items result in 3 failures, with the failures occurring after 40, 72, and 88 hours. Then mean life of the product is approximately:
a. 567 hours
b. 633 hours
c. 667 hours
d. 800 hours
Question 16. A system has three parallel components, A, B, and C, with reliability measures of 0.84, 0.92, and 0.94 followed by component D, connected in series, with a reliability measure of 0.98. The reliability of the system is:
a. 0.686
b. 0.92
c. 0.979
d. 0.994
Question 17. A p chart with variable sample sizes yield the following statistics:
Process average = 0.80; UCL = 1.20; average sample size is 100, for an observation of value 1.30 drawn from a sample of 110:
a. the point is under control for the average limit so it will definitely be under control for the individual limit.
b. The individual control limit must be calculated to determine if the point exhibits a lack of control.
c. The point is out of control for the n (ave) limits, and will also be out of control for the n (ind) limits.
Question 18. Inspection results of consecutive batches of 300 units for process Y resulted in the following data:
DAY NUMBER OF DEFECTS DAY NUMBER OF DEFECTS
1 4 6 5
2 7 7 10
3 4 8 3
4 7 9 2
5 13 10 5
Which of the following statements is true:
a. UCL(p)= 0.048; LCL(p)= -0.004
b. UCL(p)= 0.24; LCL(p)= -0.16
c. UCL(p)= 0.044; LCL(p)= 0.00
d. The process is in control.