OPERATIONS MANAGEMENT – PROBLEMS IN – Statistical Quality Control

Chapter 6. Statistical Quality Control

Question 1

A quality control manager at a manufacturing facility has taken four samples with four observations each of the diameter of a part.

Samples of Part Diameter in Inches

1		2		3		4
6.2		5.8		5.7		5.8
6.2		6.3		6.1		6.1
6.0		5.9		6.2		6.1
5.9		5.7		5.9		6.2

(a) Compute the mean of each sample.  (Round answers to 3 decimal places, e.g. 15.250.)

Mean of sample 1
Mean of sample 2
Mean of sample 3
Mean of sample 4

(b) Compute an estimate of the mean and standard deviation of the sampling distribution.  (Round answers to 4 decimal places, e.g. 15.2500.)

Mean
Standard deviation

(c) Develop control limits for 3 standard deviations of the product diameter.  (Round   answers to 2 decimal places,   e.g. 15.25.)

CL
UCL
LCL

 

 

Question 2 The Awake Coffee Company produces gourmet instant coffee. The company wants to be sure that the average fill of coffee containers is 12.0 ounces. To make sure the process is in control, a worker periodically selects at random a box of six containers of coffee and measures their weight. When the process is in control, the range of the weight of coffee samples averages 0.6 ounces. a) Develop an R-chart and an  -chart for this process and answer the questions. b) The measurements of weight from the last five samples taken of the six containers follow:

 

 

 

Control limits for x-bar chart.  (Round answers to 2 decimal places, e.g. 15.25.) CL   UCL   LCL   Control limits for R-chart.  (Round answers to 2 decimal places, e.g. 15.25.) CL   UCL   LCL

 

 

 

 

Is the process in control?     The process is in control.       The process is not in control.

 

 

 

Question 3

A production manager at a Contour Manufacturing plant has inspected the number of defective plastic molds in five random samples of 35 observations each. Following are the number of defective molds found in each sample:

Sample		Number of Defects		Number of Observations in Sample
1		3		35
2		2		35
3		0		35
4		1		35
5		0		35
Total		6		175

Construct a 3-sigma control chart (z = 3) with this information.  (If the lower control limit is negative, round the LCL to zero and all other answers to 2 decimal places, e.g. 15.25.)

CL
UCL
LCL

 

 

Question 4

U-learn University uses a c-chart to monitor student complaints per week. Complaints have been recorded over the past ten weeks. Develop 3-sigma control limits using the following data:

Week		Number of Complaints
1		0
2		2
3		1
4		2
5		2
6		3
7		3
8		0
9		3
10		3

(If the lower control limit is negative, round the LCL to zero and all other   answers to 2 decimal places, e.g. 15.25.)

CL
UCL
LCL

 

 

Question 5 University Hospital has been concerned with the number of errors found in its billing statements to patients. An audit of 100 bills per week over the past 12 weeks revealed the following number of errors: Week   Number of Errors 1   4   2   5   3   6   4   6   5   3   6   2   7   6   8   7   9   3   10   4   11   3   12   4

 

 

 

What type of chart should be used?     R-chart       p-chart       x-bar chart       c-chart

 

 

 

 

Develop control charts with z = 3: (a) CL, (b) UCL, (c) LCL.  (If the lower control limit is negative, round the LCL to zero and all other   answers to 2 decimal places, e.g. 15.25.) CL   UCL   LCL

 

 

 

 

Is the process in control?     The process is not in control       The process is in control

 

 

 

Question 6

Compute the (a) Cpk and (b) Cp measures of process capability for the following machine.  (Round answers to 2 decimal places, e.g. 15.25.)

Machine data:	USL = 100
	LSL = 70
	Process σ = 5
	Process μ = 80

 

Cpk
Cp

 

 

 

Question 7 Breeze Toothpaste Company makes tubes of toothpaste. The product is produced and then pumped into tubes and capped. The production manager is concerned whether the filling process for the tubes of toothpaste is in statistical control. The process should be centered on 6 ounces per tube. Six samples of five tubes were taken and each tube was weighed. The weights are: Ouches of Toothpaste per Tube Sample   1   2   3   4   5 1   5.78   6.34   6.24   5.23   6.12 2   5.89   5.87   6.12   6.21   5.99 3   6.22   5.78   5.76   6.02   6.10 4   6.02   5.56   6.21   6.23   6.00 5   5.77   5.76   5.87   5.78   6.03 6   6.00   5.89   6.02   5.98   5.78

 

 

 

Develop a control chart for the mean and range for the available toothpaste data.  (Round answers to 3 decimal places, e.g. 15.250.) x-bar chart : CL   UCL   LCL   R-chart : CL   UCL   LCL

 

 

 

 

Choose the appropriate control chart based on your observations.

 

 

 

Question 8 Breeze Toothpaste Company has been having a problem with some of the tubes of toothpaste leaking. The tubes are packed in containers with 100 tubes each. Ten containers of toothpaste have been sampled. The following number of toothpaste tubes were found to have leaks: Sample   Number of  Leaky Tubes   Sample   Number of  Leaky Tubes   1   4   6   6 2   8   7   10 3   12   8   9 4   11   9   5 5   12   10   8           Total   85

 

 

 

Develop a p-chart with 3-sigma control limits: (a) CL, (b) UCL, (c) LCL.  (If the lower control limit is negative, round the LCL to zero and round all other answer to 3 decimal places, e.g. 15.250.) CL   UCL   LCL

 

 

 

 

Is the process in control?     The process is not in control       The process is in control

 

 

 

Question 9

The Crunchy Potato Chip Company packages potato chips in a process designed for 8.0 ounces of chips with an upper specification limit of 8.5 ounces and a lower specification limit of 7.5 ounces. The packaging process results in bags with an average net weight of 7.86 ounces and a standard deviation of 0.1 ounces. The company wants to determine if the process is capable of meeting design specifications.  (Round answers to 3 decimal places, e.g. 15.250.)

Cp
Cpk

The process is .

 

 

Question 1

Discuss the key differences between common and assignable causes of variation. Give examples.

 

 

 

Question 2

 

The standard deviation of the distribution of sample means is computed by

z*σ

 

σ/z

 

 

σ/x

 

 

σ/√n

 

 

 

Question 3

 

For the standard normal distribution, how much confidence is provided within 2 standard deviations above and below the mean?

97.22%

 

95.44%

 

 

99.74%

 

 

99.87%

 

 

90.00%

 

 

 

Question 4

Six-Sigma quality implies how many average defects per million?

3.4

 

6

 

 

2600

 

 

3σ

 

 

6σ

 

 

Question 5

 

A control chart for ______________ is used to monitor characteristics that can be measured.

data

 

attributes

 

 

variables

 

 

limits

 

 

deviations

 

 

 

Question 6

 

A control chart for ______________ is used to monitor characteristics that have discrete values and can be counted.

data

 

attributes

 

 

variables

 

 

deviations

 

 

limits