Question 1

Given that 20 samples are taken in a control chart initiative, the probability that 5 consecutive samples are below the center line in an R- or x-bar chart is _____.

Accepted Answer

A)  0.02500 
B)  0.03125 
C)  0.06250 
D)  0.25000 
A)  0.02500 
B)  0.03125 
C)  0.06250 
D)  0.25000 B

Question 2

Which of the following statements is TRUE about common cause variations?

Accepted Answer

A)  They can be controlled and described in a non-statistical method. 
B)  They appear at random, and individual sources cannot be identified or explained. 
C)  They account for about 10 to 15 percent of the observed variation in a process. 
D)  They arise from external sources that are not inherent in the process. 
A)  They can be controlled and described in a non-statistical method. 
B)  They appear at random, and individual sources cannot be identified or explained. 
C)  They account for about 10 to 15 percent of the observed variation in a process. 
D)  They arise from external sources that are not inherent in the process. B

Question 3

Alico Steel manufactures steel tubes that are used in gas grills for residential customers. The tube's overall length is crucial to assure a proper fit, and this dimension has been targeted as an important dimension to be stabilized for the steel tube manufacturing process. Gas grill performance and customer safety are key objectives and highlight the importance of producing high quality steel tubes. Tubes are cut from rolls of steel tubing using a punch press. The tubes are measured using an operationally defined method, and Table 1 below summarizes the results. Appendix B with all factors for control charts will be given as a separate class handout.Table 1 Tube Length (in centimeters)
Sample Observations 1 to 6
$\text { Number Average x-bar Average range (R) }$
$\begin{array}{lll}
\hline 1 & 12.90 & 0.35 \
2 & 13.30 & 0.50 \
3 & 12.87 & 0.32 \
4 & 10.93 & 0.44 \
5 & 11.43 & 0.91 \
6 & 11.93 & 0.42 \
7 & 12.90 & 0.29 \
8 & 13.03 & 0.58 \
9 & 13.70 & 0.21 \
10 & 13.70 & 0.11 \
\hline
\end{array}$
Total 126.69 4.13
(a) 	The center line for the trial R-chart is _____.
The center line for the trial X-chart is _____.
The trial UCL for the R-chart is _____.
The trial LCL for the R-chart is _____.

(b)	Assuming that special causes for out-of-control situations in (a) are investigated and corrected using the seven tools of quality management, find the "final set of revised control limits" (i.e., take out any special cause sample(s) from your trial charts and recompute the following). (6 points)

The center line for the final revised R-chart is _____. 
The center line for the final revised X-chart is _____.
The final revised UCL for the R-chart is _____.
The final revised LCL for the R-chart is _____.
The final revised UCL for the x-bar chart is _____. 
The final revised LCL for the x-bar chart is _____.
(c)Plot the X-chart below and make sure you label the chart correctly. 
 
(d) Is the process in statistical process control (SPC)? Justify and explain using facts. What action would you take given your "management by fact" data analysis?

Accepted Answer

a)UCL range = 0.828, LCL range = 0; X-bar = 12.67, R-bar = 0.413
b)revised R-bar = 0.35, revised X-bar = 12.81, UCL range = 0.717, LCL range = 0, UCL x-bar = 12.98, LCL x-bar = 12.64)
c)Plot is totally out of statistical process control (SPC) upper and lower control limits.
d)The process is not in statistical process control (SPC); STOP the process immediately; use the Seven Quality Control (QC) tools; setup a quality team to investigate and work 24/7 (kaizen blitz); and maybe change design specifications, since current process is not capable.

Question 4

Which of the following statements is NOT TRUE about special cause variations?

Accepted Answer

A)  They disrupt the random patterns of common cause variations. 
B)  They arise from internal sources only. 
C)  They appear sporadically. 
D)  They are easily detectable using statistical methods. 
A)  They disrupt the random patterns of common cause variations. 
B)  They arise from internal sources only. 
C)  They appear sporadically. 
D)  They are easily detectable using statistical methods.

Question 5

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of six was used.
 $\begin{array} { c c c } 
\text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
2 & 16.10 & 0.38 \
3 & 16.02 & 0.08 \
4 & 15.95 & 0.15 \
5 & 16.12 & 0.42 \
6 & 16.18 & 0.23 \
7 & 15.87 & 0.36 \
8 & 16.20 & 0.40
\end{array}$ Worksheet (this will not be graded but will help you answer exam questions)
    
-For the Proctor and Gamble detergent box problem, based on the control charts it can be said that _____.

Accepted Answer

A)  both the R- and X-bar charts are not in statistical control 
B)  the R-chart is not in statistical control, but the X-bar chart is in statistical control 
C)  the R-chart is not in statistical control, but the X-bar chart is in statistical control, and therefore, the process should be stopped and sources of error investigated 
D)  the R-chart is in statistical control, but the X-bar chart is not in statistical control, and therefore, the process should be stopped and sources of error investigated 
A)  both the R- and X-bar charts are not in statistical control 
B)  the R-chart is not in statistical control, but the X-bar chart is in statistical control 
C)  the R-chart is not in statistical control, but the X-bar chart is in statistical control, and therefore, the process should be stopped and sources of error investigated 
D)  the R-chart is in statistical control, but the X-bar chart is not in statistical control, and therefore, the process should be stopped and sources of error investigated

Question 6

When the range of process variation does not conform to the design specifications, the process capability index will be less than 1.

Accepted Answer

A) True 
 B)False

Question 7

Honda wants to monitor the number of blemishes (scratches, blisters, etc.) on the fenders of its cars using a statistical process control chart. The most appropriate type of statistical process control (SPC) chart that can be used in this scenario is a(n) _____.

Accepted Answer

A)  x-bar chart 
B)  R-chart 
C)  Cpk chart 
D)  c-chart 
A)  x-bar chart 
B)  R-chart 
C)  Cpk chart 
D)  c-chart

Question 8

In manufacturing, quality control is generally applied at the receiving stage from suppliers, during various production processes, and at the finished-goods stage.

Accepted Answer

A) True 
 B)False

Question 9

Flaws are counted on a standard steel plate (sheet). Each sheet has the exact same dimensions. Ten sheets are selected at random and the number of flaws per sheet is as follows:
 $$\begin{array} { | c | c | } 
\hline \text { Sheet } & \text { Number of Flaws } \
\hline 1 & 3 \
\hline 2 & 1 \
\hline 3 & 3 \
\hline 4 & 0 \
\hline 5 & 2 \
\hline 6 & 2 \
\hline 7 & 0 \
\hline 8 & 1 \
\hline 9 & 1 \
\hline 10 & 2 \
\hline
\end{array}$$ Determine the lower and upper control limits for a c-chart.

Accepted Answer

Calculate c-bar = 15/10 = 1.5.

Question 10

A bottling machine fills soft drink bottles with an average of 12.000 ounces with a standard deviation of 0.002 ounces. Determine the process capability index, Cp, if the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

Accepted Answer

LSL = 11.985; USL =

Question 11

A manufacturing company has a production process that has a target percentage of nonconformance as 4 percent which was developed based on numerous samples of 200 observations each. They want to develop control charts using 3 standard deviation limits.
a.What is the center line for the p-chart?
b.What is the upper control limit for a p-chart?
c.What is the lower control limit for a p-chart?

Accepted Answer

a.Center line = observed overall proport

Question 12

Which of the following is most closely related to a discrete metric?

Accepted Answer

A)  R-charts 
B)  x-bar charts 
C)  c-charts 
D)  Process capability indices 
A)  R-charts 
B)  x-bar charts 
C)  c-charts 
D)  Process capability indices

Question 13

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times
 $\begin{array} { | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Sample } \
\text { Number }
\end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \
\hline & 1 & 2 & 3 \
\hline 1 & 9.6 & 10.2 & 9.8 \
\hline 2 & 9.4 & 10.0 & 10.4 \
\hline 3 & 9.9 & 9.6 & 9.0 \
\hline 4 & 9.3 & 10.5 & 9.9 \
\hline 5 & 9.7 & 9.2 & 9.7 \
\hline
\end{array}$
-Given the previous results and analysis for the R-chart regarding service waiting times, one would:

Accepted Answer

A)  conclude that the R-chart is in statistical control and proceed to develop the x-bar chart. 
B)  conclude that the R-chart is not in statistical control and proceed to develop the x-bar chart. 
C)  investigate sample # 3 as it is outside the R-chart control limits and redo the R-chart. 
D)  conclude that the variation is not random and the decreasing trend in the range should be investigated. 
A)  conclude that the R-chart is in statistical control and proceed to develop the x-bar chart. 
B)  conclude that the R-chart is not in statistical control and proceed to develop the x-bar chart. 
C)  investigate sample # 3 as it is outside the R-chart control limits and redo the R-chart. 
D)  conclude that the variation is not random and the decreasing trend in the range should be investigated.

Question 14

Which of the following statements is TRUE?

Accepted Answer

A)  Common cause variation arises from external sources that are not inherent in the process and is where statistical quality control methods are most useful. 
B)  If the metric is discrete, a p- or c-chart is normally used. 
C)  Statistical process control is not used in hospitals due to the high liability costs. 
D)  Statistical process control charts are most efficient when trying to monitor and control 5- and 6-sigma quality levels. 
A)  Common cause variation arises from external sources that are not inherent in the process and is where statistical quality control methods are most useful. 
B)  If the metric is discrete, a p- or c-chart is normally used. 
C)  Statistical process control is not used in hospitals due to the high liability costs. 
D)  Statistical process control charts are most efficient when trying to monitor and control 5- and 6-sigma quality levels.

Question 15

Over several days, 25 samples of 100 items each were tested for electrical resistance. A total of 60 items failed. Determine the control limits for a p-chart.

Accepted Answer

p-bar = 60/(25 x 100) = 0.024

Question 16

A key element of a control system is the ability to measure performance and compare it to a performance standard.

Accepted Answer

A) True 
 B)False

Question 17

Define and give an example of the three components of any control system.

Accepted Answer

The three components of any control syst

Question 18

If process quality approaches six sigma levels, then standard types of control charts are not useful.

Accepted Answer

A) True 
 B)False

Question 19

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times
 $\begin{array} { | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Sample } \
\text { Number }
\end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \
\hline & 1 & 2 & 3 \
\hline 1 & 9.6 & 10.2 & 9.8 \
\hline 2 & 9.4 & 10.0 & 10.4 \
\hline 3 & 9.9 & 9.6 & 9.0 \
\hline 4 & 9.3 & 10.5 & 9.9 \
\hline 5 & 9.7 & 9.2 & 9.7 \
\hline
\end{array}$
-In Table 1, the sample values represent service waiting times in minutes. For the R-chart, what is the value of UCLR?

Accepted Answer

A)  Less than or equal to 1.5 
B)  Greater than 1.5 but less than or equal to 2.0 
C)  Greater than 2.0 but less than or equal to 2.5 
D)  Greater than 2.5 
A)  Less than or equal to 1.5 
B)  Greater than 1.5 but less than or equal to 2.0 
C)  Greater than 2.0 but less than or equal to 2.5 
D)  Greater than 2.5

Question 20

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of six was used.
 $\begin{array} { c c c } 
\text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
2 & 16.10 & 0.38 \
3 & 16.02 & 0.08 \
4 & 15.95 & 0.15 \
5 & 16.12 & 0.42 \
6 & 16.18 & 0.23 \
7 & 15.87 & 0.36 \
8 & 16.20 & 0.40
\end{array}$ Worksheet (this will not be graded but will help you answer exam questions)
    
-For the Proctor and Gamble detergent box problem, the lower control limit for the x-bar chart is _____.

Accepted Answer

A)  less than or equal to 12 
B)  more than 12 but less than or equal to 14 
C)  more than 14 but less than or equal to 16 
D)  more than 16 
A)  less than or equal to 12 
B)  more than 12 but less than or equal to 14 
C)  more than 14 but less than or equal to 16 
D)  more than 16

Given that 20 samples are taken in a control chart initiative, the probability that 5 consecutive samples are below the center line in an R- or x-bar chart is _____.

Which of the following statements is TRUE about common cause variations?

Which of the following statements is NOT TRUE about special cause variations?

When the range of process variation does not conform to the design specifications, the process capability index will be less than 1.

Honda wants to monitor the number of blemishes (scratches, blisters, etc.) on the fenders of its cars using a statistical process control chart. The most appropriate type of statistical process control (SPC) chart that can be used in this scenario is a(n) _____.

In manufacturing, quality control is generally applied at the receiving stage from suppliers, during various production processes, and at the finished-goods stage.

Flaws are counted on a standard steel plate (sheet). Each sheet has the exact same dimensions. Ten sheets are selected at random and the number of flaws per sheet is as follows: Sheet Number of Flaws 1 3 2 1 3 3 4 0 5 2 6 2 7 0 8 1 9 1 10 2 Determine the lower and upper control limits for a c-chart.

A bottling machine fills soft drink bottles with an average of 12.000 ounces with a standard deviation of 0.002 ounces. Determine the process capability index, C_p, if the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

Which of the following is most closely related to a discrete metric?

Which of the following statements is TRUE?

Over several days, 25 samples of 100 items each were tested for electrical resistance. A total of 60 items failed. Determine the control limits for a p-chart.

A key element of a control system is the ability to measure performance and compare it to a performance standard.

Define and give an example of the three components of any control system.

If process quality approaches six sigma levels, then standard types of control charts are not useful.

Goods, Services, and Operations Management

Value Chains

Measuring Performance in Operations

Operations Strategy

Technology and Operations Management

Goods and Service Design

Process Selection, Design, and Analysis

Facility and Work Designs

Supply Chain Design

Capacity Management

Forecasting and Demand Planning

Managing Inventories

Resource Management

Operations Scheduling and Sequencing

Quality Management

Appendix: Quality Management

Appendix: Queuing Analysis

Appendix: Modeling Using Linear Programming

Lean Operating Systems

Appendix: Simulation

Project Management

Appendix: Decision Analysis

Filters

Exam 16: Quality Control and Spc

Given that 20 samples are taken in a control chart initiative, the probability that 5 consecutive samples are below the center line in an R- or x-bar chart is _____.

Which of the following statements is TRUE about common cause variations?

Which of the following statements is NOT TRUE about special cause variations?

When the range of process variation does not conform to the design specifications, the process capability index will be less than 1.

Honda wants to monitor the number of blemishes (scratches, blisters, etc.) on the fenders of its cars using a statistical process control chart. The most appropriate type of statistical process control (SPC) chart that can be used in this scenario is a(n) _____.

In manufacturing, quality control is generally applied at the receiving stage from suppliers, during various production processes, and at the finished-goods stage.

A bottling machine fills soft drink bottles with an average of 12.000 ounces with a standard deviation of 0.002 ounces. Determine the process capability index, Cp, if the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.

Which of the following is most closely related to a discrete metric?

Which of the following statements is TRUE?

Over several days, 25 samples of 100 items each were tested for electrical resistance. A total of 60 items failed. Determine the control limits for a p-chart.

A key element of a control system is the ability to measure performance and compare it to a performance standard.

Define and give an example of the three components of any control system.

If process quality approaches six sigma levels, then standard types of control charts are not useful.

Goods, Services, and Operations Management

Value Chains

Measuring Performance in Operations

Operations Strategy

Technology and Operations Management

Goods and Service Design

Process Selection, Design, and Analysis

Facility and Work Designs

Supply Chain Design

Capacity Management

Forecasting and Demand Planning

Managing Inventories

Resource Management

Operations Scheduling and Sequencing

Quality Management

Appendix: Quality Management

Appendix: Queuing Analysis

Appendix: Modeling Using Linear Programming

Lean Operating Systems

Appendix: Simulation

Project Management

Appendix: Decision Analysis

Filters

A bottling machine fills soft drink bottles with an average of 12.000 ounces with a standard deviation of 0.002 ounces. Determine the process capability index, C_p, if the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces.