Deck 24: Quality Control

Question 1

By design, a required dimension of a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm. The specification limits for this part are

A) 0.554 to 0.596 cm
B) 0.567 to 0.583 cm
C) 0.576 to 0.598 cm
D) 0.572 to 0.584 cm
E) 0.575 to 0.578 cm

Answer 1

B

Question 2

In order to achieve higher levels of customer satisfaction, a company initiates monitoring the complaint resolution process of its customer service representatives. As a first step, the company decides to collect data on the number of unanswered calls out of the first 250 incoming to its call centre made each day. At the end of monitoring 25 days, it was found that a total of 500 incoming calls went unanswered.
a. What type of control chart should be used by the company in monitoring customer satisfaction at the call centre?
b. Calculate the centreline for this control chart.
c. Calculate the control limits for this control chart.

Answer 2

a. p-chart
b. Centreline = 0.08
c. LCL = 0.029 and UCL = 0.131

Question 3

An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments. Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken.
a. What type of control chart should be used by the importer in monitoring the proportion of scrap tiles?
b. Calculate the centreline for this control chart.
c. Calculate the control limits for this control chart.

Answer 3

a. p-chart
b. Centreline = 0.167
c. LCL = 0.009 and UCL = 0.325

Question 4

A producer of specialty products uses a variety of natural and man-made materials to make unique countertops for kitchens and baths. One product line mixes concrete and natural river stone to make countertops that are polished to a high shine revealing unique patterns. Occasionally coarse sand will result in undesirable pitting and rough spots on surfaces. Consequently, as part of its quality control efforts, 8 by 4 foot polished slabs are checked periodically for imperfections. For each slab inspected the number of imperfections (pits, rough spots, etc.) is recorded.
a. What type of control chart should be used for these data?
b. If the average number of imperfections per 8 by 4 foot polished slab is 2.6, calculate the centreline and control limits for the appropriate control chart.

Question 5

An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments. Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken. The centreline on the p chart for these data is

A) 0.250
B) 1.83
C) 2.5
D) 0.167
E) 6.1

Question 6

A paper products manufacturer coats paper with a thin film of wax. To initiate control charting, data are collected on the thickness of the coating (measured in mm) by taking twenty-five samples each of size five. The appropriate control chart for these data is the

A) c chart
B) p chart
C) Cp index
D) x-bar and R chart
E) ARL chart

Question 7

Which of the following statements is false regarding control charts?

A) If we view using a control chart as a graphical hypothesis test, the null hypothesis is that the process has not changed.
B) A type I error in control charting results in an unnecessary adjustment to the process.
C) A type II error in control charting results in an unnecessary adjustment to the process.
D) A process within which special cause variation is present is said to be out of control.
E) A process which exhibits only common cause variation is said to be in control.

Question 8

A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The lower and upper control limits for the R chart are

A) 0.2992 and 4.1008 mg
B) 0 and 4.4088 mg
C) 0.136 and 1.864 mg
D) 2.1999 and 30.152 mg
E) 0.2493 and 3.4167 mg

Question 9

A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 metre coils. Suppose they sample a total of 40 coils to initiate control charting. The average number of defects per coil is 2.5. The appropriate control chart for these data is the

A) R chart
B) c chart
C) x-bar and R chart
D) p chart
E) ARL chart

Question 10

An automatic filling process is used to dispense hand sanitizer into small purse size bottles. The target weight is 75 ml. The company has initiated control charting to stabilize and improve the automatic filling process. For each of twenty-five samples consisting of four bottles, the contents were measured and the mean weight and range were determined. The average of the means across all samples was found to be 72.5 ml. and the average range was 2.75 ml.
a. Estimate the process standard deviation.
b. Calculate the centreline and control limits for the R chart.
c. Calculate the centreline and control limits for the x-bar chart.

Question 11

A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 foot coils. Suppose they sample a total of 40 coils to initiate control charting. The average number of defects per coil is 2.5. The lower and upper control limits for the appropriate control chart for these data are

A) 0 and 7.24
B) 0 and 5.66
C) 2.24 and 7.24
D) 2.24 and 4.08
E) indeterminate

Question 12

An importer of decorative ceramic tile samples 50 tiles each day from incoming shipments. Some tiles are cracked or broken before or during transit, rendering them useless scrap. Sampling from incoming shipments for 30 days reveals that a total of 250 tiles are cracked or broken. The lower and upper control limits on the p chart for these data are

A) 0.067 and 0.299
B) 0.157 and 0.177
C) 0 and 0.299
D) 1.314 and 10.886
E) 0.009 and 0.325

Question 13

A manufacturer of a particular grade of copper tubing collects data on the number of flaws occurring in 500 metre coils. Suppose they sample a total of 40 coils to initiate control charting. The average number of defects per coil is 2.5.
a. What type of control chart should be used for these data?
b. If the average number of defects per coil is 2.5, calculate the centreline and control limits for the appropriate control chart.

Question 14

A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg.
a. Estimate the process standard deviation.
b. Calculate the centreline and control limits for the R chart.
c. Calculate the centreline and control limits for the x-bar chart.

Question 15

A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The lower and upper control limits for the x-bar chart are

A) 52.67 and 57.33 mg
B) 51.15 and 58.85 mg
C) 54.18 and 55.82 mg
D) 48.89 and 57.61 mg
E) 37.84 and 72.16 mg

Question 16

A major airline is interested in monitoring customer satisfaction with its baggage handling process. To do so, each day the airline randomly selects 100 customers and surveys them to determine if they are satisfied or not with the service provided. After 20 samples, a total of 260 unsatisfied customers were counted. The lower and upper control limits for the appropriate control chart for these data are

A) 0.0292 and 0.2308
B) 0 and 0.2308
C) 0.0964 and 0.1363
D) 0 and 0.4236
E) indeterminate

Question 17

Machine oil is used by clothing manufacturers to lubricate and protect sewing machines. A company that produces machine oil must ensure that the viscosity of its product meets customer requirements. Consequently, the viscosity of every batch of oil produced is measured. Suppose that the process mean is 101 cP and the process standard deviation is 1.50 cP.
a. What type of chart should be used to ensure the process remains in control?
b. Determine the centreline and control limits for this chart.
c. Suppose that customer specifications require viscosity of the machine oil to be 100 cP ± 4.5 cP (i.e., the LSL = 95.5 cP and the USL = 104.5 cP). Calculate both the Cp and Cpk indices and interpret.

Question 18

By design, a required dimension on a part is 0.575 cm plus or minus 0.008 cm. Assume that the process producing this part is stable with a mean of 0.579 cm and standard deviation of 0.002 cm.
a. What are the specification limits on this part?
b. Compute the Cp index.
c. Compute the Cpk index.
d. Which index is a better measure of the process capability in this instance? Explain.

Question 19

A company that manufactures health food snacks produces low sodium rice chips. To monitor the process for sodium levels, chips are selected periodically and the amount of sodium (mg) measured. For each of thirty samples consisting of 8 chips, the mean and range in sodium content is determined. The average of the means across all samples is 55 mg and the average range is 2.2 mg. The estimated process standard deviation ( ) is

A) 0.773 mg
B) 2.683 mg
C) 0.073 mg
D) 16.176 mg
E) 1.833 mg

Question 20

A major airline is interested in monitoring customer satisfaction with its baggage handling process. To do so, each day the airline randomly selects 100 customers and surveys them to determine if they are satisfied or not with the service provided. After 20 samples, a total of 260 unsatisfied customers were counted. The appropriate control chart for these data is the

A) p chart
B) x-bar chart
C) R chart or s-bar chart
D) c chart
E) R chart

Question 21

Consider the following to answer the question(s) below:
A company that fills 12 ounce soft drink bottles wishes to monitor the quality of their process. To do this, the company has taken a series of samples of 4 bottles. The overall average fill is 12.03 ounces. The average range for the samples has been 0.06 ounces.
What is the correct estimate of σ?

A) 0.029
B) 0.01
C) 0.02
D) 2.059
E) 3.99

Question 22

A powerful tool in establishing and out-of-control action plan is

A) a fishbone diagram
B) an x-bar chart
C) an R chart
D) a p chart
E) a c chart.

Question 23

The main cross-town transit route in a large Ontario town makes 120 trips per day. The transit authority will tolerate an average of no more than 5 late running trips per day. They wish to use a control chart to monitor the timeliness of the route. The following data were collected for 8 days. Based on this information, the values of the appropriate lower and upper control limits are

A) 0 and 10.2
B) -1.97 to 10.2
C) 0 and 19.5
D) -9.75 and 19.5
E) none of the above

Question 24

Consider the following to answer the question(s) below:
A company that fills 12 ounce soft drink bottles wishes to monitor the quality of their process. To do this, the company has taken a series of samples of 4 bottles. The overall average fill is 12.03 ounces. The average range for the samples has been 0.06 ounces.
Based on this information, what is the value of the upper control limit for the R chart?

A) 0.137
B) 2.282
C) 0
D) 0.026
E) 0.88

Question 25

Suppose, after developing the control chart, a subgroup of size 4 yields a sample mean of 12.09 ounces and a range of 0.08. Which of the following statements is true?

A) The process is out of control on the x-bar chart but in control on the R chart.
B) The process is in control on the x-bar chart and in control on the R chart.
C) The process is out of control on the x-bar chart and out of control on the R chart.
D) The process is in control on the x-bar chart but out of control on the R chart.
E) The process is out of control on the R chart.

Question 26

Consider the following to answer the question(s) below:
A company that fills 12 ounce soft drink bottles wishes to monitor the quality of their process. To do this, the company has taken a series of samples of 4 bottles. The overall average fill is 12.03 ounces. The average range for the samples has been 0.06 ounces.
Based on this information, what is the value of the upper control limit for the x-bar chart?

A) 12.074
B) 12.059
C) 0.0437
D) 12.09
E) 0.729

Question 27

The control limits in a control chart can

A) describe the range of virtually all common cause variation
B) describe the range of virtually all special cause variation
C) describe any value falling within the limits as a product of high quality
D) describe any value falling outside the limits as a product that should be rejected
E) indicate that the data is normally distributed

Question 28

Recently a shipping company took 30 samples of the delivery times of packages that it was responsible for. Each sample was of 100 packages. Out of the 3,000 total packages, 300 were delivered late. In setting up a process control chart, what would be the correct upper control limit for the appropriate control chart for these data?

A) 0.19
B) 0.03
C) 0.07
D) 0.13
E) none of the above