Lecture 7 - Variable Control Charts Updated

1. Total process variation is made up of:

A. Mean variation + range variation
B. Common cause variation + special cause variation
C. Sample variation + population variation
D. Upper variation + lower variation

B. Common cause variation + special cause variation

2. Which of the following best describes common cause variation?

A. Abnormal variation caused by a specific problem
B. Variation that always means the process is defective
C. Naturally occurring and expected variation
D. Variation caused only by employees

C. Naturally occurring and expected variation

3. Which of the following best describes special cause variation?

A. Normal variation inherent in the process
B. Abnormal or unexpected variation with an assignable cause
C. Variation that must always be ignored
D. Variation caused only by raw materials

B. Abnormal or unexpected variation with an assignable cause

4. Which of the following is listed as a possible source of process variation?

A. People
B. Machines
C. Environment
D. All of the above

The slides list people, machines, materials, methods, measurement, and environment as sources of variation.

D. All of the above

5. What is the main purpose of Statistical Process Control (SPC)?

A. Eliminate all variation from a process
B. Monitor a process and identify special causes of variation
C. Calculate only the process mean
D. Replace quality inspections completely

SPC is defined as a methodology for monitoring a process, identifying special causes, and signaling when corrective action may be needed.

B. Monitor a process and identify special causes of variation

SPC primarily relies on:

A. Histograms
B. Pareto charts
C. Control charts
D. Fishbone diagrams

C. Control charts

Which of the following is NOT listed as an application of control charts?

A. Establish a state of statistical control
B. Monitor when a process goes out of control
C. Determine process capability
D. Eliminate the need to collect process data

D. Eliminate the need to collect process data

The Upper Control Limit (UCL) is generally located:

A. 1 standard deviation above the process average
B. 2 standard deviations above the process average
C. 3 standard deviations above the process average
D. 6 standard deviations above the process average

C. 3 standard deviations above the process average

The Lower Control Limit (LCL) is generally calculated as:

A. Process Average + 3σ3\sigma
B. Process Average − 3σ3\sigma
C. Process Average ÷ 3σ3\sigma
D. Process Average × 3σ3\sigma

The basic control-chart limits are UCL=Process Average+3σUCL=\text{Process Average}+3\sigma and LCL=Process Average−3σLCL=\text{Process Average}-3\sigma.

B. Process Average − 3σ3\sigma

A process has a mean of 50 and a standard deviation of 2. What is the UCL?

A. 52
B. 54
C. 56
D. 44

Calculation: UCL=50+3(2)=56

C. 56

11. Using the same process with a mean of 50 and standard deviation of 2, what is the LCL?

A. 44
B. 46
C. 48
D. 56

Calculation: LCL=50−3(2)=44

A. 44

12. What is a major difference between a histogram and a control chart?

A. Histograms show changes over time better than control charts
B. Histograms do not take changes over time into account
C. Control charts cannot identify process changes
D. Control charts are used only for attribute data

The slides specifically note that histograms do not account for changes over time, while control charts can indicate when a process changes.

B. Histograms do not take changes over time into account

13. An X-bar chart is used to monitor the:

A. Number of defects
B. Average measurement of a process
C. Proportion defective
D. Number of customers

B. Average measurement of a process

14. Which control chart is used for “proportion defectives”?

A. R-chart
B. X-bar chart
C. p-chart
D. c-chart

C. p-chart

15. Which control chart is used for the “number of defects per item”?

A. c-chart
B. p-chart
C. X-bar chart
D. R-chart

The lecture identifies p-charts for proportion defectives and c-charts for number of defects per item.

A. c-chart

16. What does an R-chart primarily measure?

A. Location of the process
B. Average of the process
C. Variability of the process
D. Proportion defective

The X-bar chart shows the location/average of the process, while the R-chart shows process variability.

C. Variability of the process

17. According to the slides, when initially developing X-bar and R-charts, you should begin with at least:

A. 5 subgroups
B. 10 subgroups
C. 15 subgroups
D. 20 subgroups

The slides recommend starting with at least 20 subgroups, usually containing 3–7 observations each.

D. 20 subgroups

18. In the X-bar control-limit formulas below, what does A2A_2 represent?

UCL=Xˉˉ+A2RˉUCL=\bar{\bar X}+A_2\bar RLCL=Xˉˉ−A2RˉLCL=\bar{\bar X}-A_2\bar R

A. The subgroup mean
B. The number of samples
C. A Shewhart factor based on subgroup size
D. The sample range

The slides explain that A2A_2 is a Shewhart factor that depends on subgroup size nn.

C. A Shewhart factor based on subgroup size

19. Which formulas are used to calculate the control limits for an R-chart?

A. UCL=Xˉ+3σUCL=\bar X+3\sigma and LCL=Xˉ−3σLCL=\bar X-3\sigma
B. UCL=D4RˉUCL=D_4\bar R and LCL=D3RˉLCL=D_3\bar R
C. UCL=A2RˉUCL=A_2\bar R and LCL=−A2RˉLCL=-A_2\bar R
D. UCL=Rˉ+3UCL=\bar R+3 and LCL=Rˉ−3LCL=\bar R-3

The R-chart uses D4D_4 and D3D_3, which are selected from the Shewhart table based on subgroup size.

B. UCL=D4RˉUCL=D_4\bar R and LCL=D3RˉLCL=D_3\bar R

20. Approximately what percentage of normally distributed data should fall within ±3 standard deviations of the mean?

A. 68%
B. 90%
C. 95%
D. 99.7%

The slides state that about 99.7% of observations should fall within ±3σ, while approximately 0.27% fall outside. This 0.0027 probability is associated with a Type I error, or false alarm, in this setting.

D. 99.7%

21. A machine normally produces slight differences in part diameter because of small differences in material and temperature. This is an example of:

A. Special cause variation
B. Common cause variation
C. Attribute variation
D. Measurement failure

B. Common cause variation

22. A machine suddenly begins producing oversized parts because a cutting tool breaks. This would most likely be classified as:

A. Common cause variation
B. Expected variation
C. Special cause variation
D. Sampling variation

C. Special cause variation

23. Which equation correctly describes total process variation?

A. Total variation = Common cause − Special cause
B. Total variation = Mean + Standard deviation
C. Total variation = Range + Mean
D. Total variation = Common cause + Special cause

D. Total variation = Common cause + Special cause

24. A process containing only common cause variation would generally be considered:

A. More predictable
B. Completely defect-free
C. Unmeasurable
D. Automatically capable

A. More predictable

25. What should SPC help a manager determine?

A. Whether all variation can be eliminated
B. Whether special causes of variation are present
C. Whether every product is identical
D. Whether the mean is always zero

B. Whether special causes of variation are present

26. A point appearing far above the Upper Control Limit would most likely indicate:

A. Normal/common cause variation
B. The process average is automatically correct
C. Possible special cause variation
D. The control limits should be removed

C. Possible special cause variation

27. If a process average is 80 and the standard deviation is 4, what is the UCL?

A. 84
B. 88
C. 92
D. 76

UCL=80+3(4)=92

C. 92

28. If the same process has a mean of 80 and standard deviation of 4, what is the LCL?

A. 68
B. 72
C. 76
D. 92

LCL=80−3(4)=68LCL=80-3(4)=68

A. 68

29. Which chart would be most appropriate for monitoring the average diameter of manufactured shafts?

A. p-chart
B. c-chart
C. X-bar chart
D. Pareto chart

C. X-bar chart

30. Which chart is paired with an X-bar chart to monitor process variability using ranges?

A. R-chart
B. p-chart
C. c-chart
D. Histogram

X-bar charts monitor process location/average, while R-charts monitor variability.

A. R-chart

31. If you wanted to monitor individual measurements rather than subgroup averages, the slides list which option?

A. c-chart
B. Individual x-chart
C. p-chart
D. R-chart only

B. Individual x-chart

32. Compared with an R-chart, an s-chart is described in the slides as:

A. Less accurate and requiring less data
B. More accurate but requiring more data
C. Used only for attribute data
D. Used only when the sample size equals one

The slides state that the s-chart is more accurate than the R-chart but requires more data.

B. More accurate but requiring more data

33. Control charts plot a ______ rather than a population distribution.

A. Pareto distribution
B. Sampling distribution
C. Frequency table
D. Uniform distribution

34. According to the central limit theorem discussed in the slides, when sample means are plotted, the sampling distribution tends to approximate a:

A. Normal distribution
B. Rectangular distribution
C. Left-skewed distribution
D. Pareto distribution

A. Normal distribution

35. In the hypothesis-testing interpretation of a control chart, the null hypothesis assumes that:

A. The process has special cause variation
B. Every observation equals the mean
C. The process is operating without special or assignable cause variation
D. The process is incapable

C. The process is operating without special or assignable cause variation

36. If Xˉˉ=25\bar{\bar X}=25, Rˉ=4\bar R=4, and A2=0.50A_2=0.50, what is the UCL for the X-bar chart?

A. 23
B. 25
C. 27
D. 29

UCL=Xˉˉ+A2RˉUCL=\bar{\bar X}+A_2\bar R=25+(0.50)(4)=27

C. 27

37. Using the same information, what is the LCL?

A. 21
B. 23
C. 25
D. 27

LCL=25−(0.50)(4)=23LCL=25-(0.50)(4)=23

The X-bar chart limits use Xˉˉ\bar{\bar X}, A2A_2, and Rˉ\bar R.

B. 23

38. Suppose Rˉ=5\bar R=5 and D4=2.2D_4=2.2. What is the UCL for the R-chart?

A. 7.2
B. 10
C. 11
D. 2.2

UCL=D4RˉUCL=D_4\bar R=2.2(5)=11=2.2(5)=11

C. 11

39. Suppose Rˉ=5\bar R=5 and D3=0D_3=0. What is the LCL for the R-chart?

A. 0
B. 5
C. 2.5
D. 10

LCL=D3RˉLCL=D_3\bar R=0(5)=0=0(5)=0

The R-chart formulas are UCL=D4RˉUCL=D_4\bar R and LCL=D3RˉLCL=D_3\bar R.

A. 0

40. With ±3σ control limits, the approximate probability of a Type I error, or false alarm, is:

A. 0.05
B. 0.027
C. 0.0027
D. 0.997

C. 0.0027