Question 1

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.

Accepted Answer

The appropriate control chart for monitoring customer satisfaction with a process that produces a binary outcome (satisfied or unsatisfied) is the p chart. The p chart tracks the proportion of samples that are defective (unsatisfied) over time. In this case, the airline is randomly selecting 100 customers each day and counting the number of unsatisfied customers. After 20 samples, a total of 260 unsatisfied customers were counted, which corresponds to a proportion of 0.26 (260/1000). The p chart would plot this proportion over time to monitor the stability of the baggage handling process and determine if any improvements are necessary.

Question 2

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.

Accepted Answer

The x-bar and R chart is the best choice for monitoring the thickness of the wax coating as it allows for the monitoring of the central tendency (x-bar) and variability (R) of the data. The c chart and p chart are used for count data, while the Cp index and ARL chart are used for process capability analysis and monitoring the average run length, respectively.

Question 3

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.

Accepted Answer

A type II error in control charting actually results in a failure to detect a special cause when it is present, which means that an adjustment to the process may not be made when it is necessary. Therefore, statement C is false.

Question 4

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.

Accepted Answer

The answer of A manufacturer of a particular grade of...

Question 5

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.

Accepted Answer

The answer of In order to achieve higher levels of...

Question 6

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.

Accepted Answer

The answer of An importer of decorative ceramic tile samples...

Question 7

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.

Accepted Answer

The c chart is used for counting defects when the number of opportunities for defects is constant, as is the case with a fixed length of copper tubing (500 metre coils).

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) 0.299 and 4.101 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.

Accepted Answer

The correct choice is A) 0.299 and 4.101 mg. This is because control limits for an R chart are calculated using the average range (R-bar) and factors from a statistical table based on sample size. For a sample size of 8, the appropriate factors (D3 and D4) are used to calculate the lower and upper control limits as follows: LCL = D3(R-bar) and UCL = D4(R-bar). Given the average range of 2.2 mg, and knowing the factors for a sample size of 8 (D3 and D4 values), the calculated limits match those in option A.

Question 9

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.

Accepted Answer

The answer of By design, a required dimension on a...

Question 10

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.

Accepted Answer

The answer of A company that manufactures health food snacks...

Question 11

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.

Accepted Answer

The centerline of a p-chart is calculated as the average proportion of defective items. Here, 250 tiles are defective out of 1500 sampled (50 tiles/day * 30 days), so the centerline is 250/1500 = 0.167.

Question 12

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.

Accepted Answer

The answer of An automatic filling process is used to...

Question 13

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.

Accepted Answer

The answer of A producer of specialty products uses a...

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. 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.

Accepted Answer

The answer of A company that manufactures health food snacks...

Question 15

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.

Accepted Answer

The answer of An importer of decorative ceramic tile samples...

Question 16

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.

Accepted Answer

The answer of A company that manufactures health food snacks...

Question 17

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) 0.029 and 0.231.
B) 0 and 0.145.
C) 0.0964 and 0.1363.
D) 0 and 0.4236.
E) 0 and 0.356.

Accepted Answer

The correct answer is A because the lower and upper control limits for the appropriate control chart for these data are 0.029 and 0.231, respectively. This is calculated using the formula:UCL = p + 3 * sqrt(p * (1 - p) / n)LCL = p - 3 * sqrt(p * (1 - p) / n)where p is the sample proportion and n is the sample size. In this case, p = 260 / 2000 = 0.13 and n = 100. Plugging these values into the formula, we get:UCL = 0.13 + 3 * sqrt(0.13 * (1 - 0.13) / 100) = 0.231LCL = 0.13 - 3 * sqrt(0.13 * (1 - 0.13) / 100) = 0.029

Question 18

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 and interpret both the Cp and Cpk indices.

Accepted Answer

The answer of Machine oil is used by clothing manufacturers...

Question 19

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.

Accepted Answer

The upper specification limit (USL) can be calculated by adding the upper limit of the required dimension tolerance (+0.008 cm) to the mean of the process (0.579 cm). 
USL = 0.579 + 0.008 = 0.587 cm. 
Similarly, the lower specification limit (LSL) can be calculated by subtracting the lower limit of the required dimension tolerance (-0.008 cm) from the mean of the process (0.579 cm). 
LSL = 0.579 - 0.008 = 0.571 cm. 
Therefore, the specification limits for this part are 0.567 cm to 0.583 cm, which is choice B.

Question 20

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 8.70.
D) 2.24 and 4.08.
E) 0.80 and 8.70.

Accepted Answer

The appropriate control chart for defect data (count data) is a c-chart, which is used for the number of defects per unit. The control limits for a c-chart are calculated using the formula: LCL = c - 3√c and UCL = c + 3√c, where c is the average number of defects per unit. Here, c = 2.5, so LCL = 2.5 - 3√2.5 ≈ -0.24 (but since the number of defects cannot be negative, we set LCL = 0), and UCL = 2.5 + 3√2.5 ≈ 7.24.

Quiz 24: Quality Control

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

Which of the following statements is false regarding control charts?

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

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