Question 1

Five samples of size 3 were collected for a variable measurement.All sample data were greater than or equal to 4.0.The sample means and sample ranges are provided in the following table.

The values of which sample are identical?
A)sample 1
B)sample 2
C)sample 3
D)sample 4

Accepted Answer

The answer of Five samples of size 3 were collected...

Question 2

A p-chart is also called a:
A)pre-control chart.
B)probability chart.
C)fraction defective chart.
D)process capability chart.

Accepted Answer

A p-chart is also known as a fraction defective chart, as it is used to monitor the proportion of defective units in a sample. A pre-control chart is a simpler variation of the control chart and is used to monitor small changes in the process, whereas a probability chart is not a commonly used term in quality control. A process capability chart is another type of control chart that measures the ability of the process to produce within specification limits.

Question 3

Which of the following is NOT an indication of an out-of-control process?
A)Five consecutive points fall on one side of the center line.
B)Four of five consecutive points fall within the outer two-thirds region between the center line and one of the control limits.
C)Two of three consecutive points fall in the outer one-third region between the center line and one of the control limits.
D)A single point falls above the upper control limit.

Accepted Answer

The answer of Which of the following is NOT an...

Question 4

A delivery company defines a "defect" as a package delivered later than the promised delivery time.Management wants to monitor the proportion of packages per week delivered beyond their promised delivery time.Management plans to sample 150 packages per week.The appropriate control chart is a(n):
A)  -chart.
B) R-chart.
C) p-chart.
D) np-chart.

Accepted Answer

Since the company wants to monitor the proportion(defectives) of packages per week and the sample size is constant(150 packages per week), the appropriate control chart is a p-chart. The p-chart is used to monitor the proportion of defectives in a sample.

Question 5

A manager at a canning company wants to monitor the number of orange juice cans it produces each day that are beyond the upper specification limit for can diameter.Each day an employee will randomly select 150 cans and then determine and plot the number of cans that are beyond the upper specification limit for can diameter.The appropriate control chart is a(n):
A)  -chart.
B) R-chart.
C) p-chart.
D) np-chart.

Accepted Answer

The answer of A manager at a canning company wants...

Question 6

The s-chart is recommended when:
A)the sample size equals one.
B)tight control of variability is required.
C)loose control of variability is acceptable.
D)the sample size needs to be reduced.

Accepted Answer

The s-chart is a control chart that monitors the variability or dispersion of a process. It is recommended when tight control of variability is required, as it provides a visual representation of any changes or shifts in process variability over time. Other control charts, such as the X-bar chart, may be more appropriate when monitoring the process mean. Having a sample size of one does not necessarily impact the use of an s-chart. Similarly, the s-chart is not recommended when loose control of variability is acceptable or when the sample size needs to be reduced.

Question 7

If the process mean and variance do not change over time,the process is considered to be:
A)in control.
B)symmetric.
C)stable.
D)capable.

Accepted Answer

The answer of If the process mean and variance do...

Question 8

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are $ 37.50 \pm 0.25 \mathrm{~cm} $. The company has established an $ \bar{x} $-chart and an $ R $-chart using samples of size five. The centerlines for the $ \bar{x} $ chart and $ R $-chart are set at $ 37.65 \mathrm{~cm} $ and $ 1.03 \mathrm{~cm} $, respectively. What is the value of $ C_{p k} $ for this process?

A) 0.08
B) 0.28
C) 0.75
D) 0.03

Accepted Answer

The answer of A precision parts manufacturer produces bolts for...

Question 9

Which of the following is a likely cause of the control chart pattern known as a "trend?"
A)Aging equipment
B)Change in setup method
C)New operator
D)A mixture of two materials

Accepted Answer

A trend in a control chart indicates a gradual shift or change in the process mean over time. Aging equipment can lead to gradual wear and tear, contributing to a gradual shift in the mean. Change in setup method, new operator, and a mixture of two materials may cause sudden shifts or variations in the process, but not a gradual trend.

Question 10

Determine the sample standard deviation for the following sample data: 7,9,2,0,1,and 5.
A)3.347
B)3.266
C)2.993
D)3.578

Accepted Answer

The answer of Determine the sample standard deviation for the...

Question 11

A precision parts manufacturer produces bolts for use in military aircraft. The specifications for bolt length are $ 37.50 \pm 0.25 \mathrm{~cm} $. The company has established an $ \bar{x} $-chart and an $ R $-chart using samples of size five. The centerlines for the $ \bar{x} $ chart and $ R $-chart are set at $ 37.65 \mathrm{~cm} $ and $ 1.03 \mathrm{~cm} $, respectively. What is the value of $ C_{p} $ for this process?

A) 0.188
B) 1.333
C) 0.301
D) 0.166

Accepted Answer

The value of $ C_{p} $ is calculated as:$$C_{p} = \frac{USL - LSL}{6\sigma}$$where $ USL $ is the upper specification limit, $ LSL $ is the lower specification limit, and $ \sigma $ is the standard deviation of the process.In this case, $ USL = 37.75 \mathrm{~cm} $, $ LSL = 37.25 \mathrm{~cm} $, and $ \sigma = R/d_{2} = 1.03 \mathrm{~cm} / 2.326 = 0.443 \mathrm{~cm} $. Therefore,$$C_{p} = \frac{37.75 - 37.25}{6(0.443)} = 0.188$$

Question 12

Six samples of size 10 were collected.The data are provided in the following table.

The upper control limit (UCL)and lower control limit (LCL)for an s-chart are:
A)LCL = 0.2840, UCL = 1.7160
B)LCL = 0.0994, UCL = 0.6006
C)LCL = 4.6256, UCL = 5.3256
D)LCL = 3.6750, UCL = 5.7750

Accepted Answer

To find the upper and lower control limits for an s-chart, we first calculate the average range using the formula:

Average Range = (Range1 + Range2 + ... + Range6) / 6

= (0.32 + 0.38 + 0.28 + 0.44 + 0.36 + 0.40) / 6

= 0.35

Next, we calculate the control limits using the formula:

UCL = Average Range * A2 
LCL = Average Range * D3

A2 and D3 values can be found in statistical tables. For a sample size of 10, A2 = 0.577 and D3 = 0.0.

Plugging in the numbers, we get:

UCL = 0.35 * 0.577 = 0.201 
LCL = 0.35 * 0.0 = 0

Therefore, the upper control limit is 0.201 and the lower control limit is 0. For the given options, only option B has the correct UCL and LCL values.

Question 13

For variables data,the sample means are assumed to be:
A)uniformly distributed.
B)normally distributed.
C)Poisson distributed.
D)binomially distributed.

Accepted Answer

The Central Limit Theorem states that when a sufficiently large sample size is taken from any population with a finite mean and variance, the distribution of sample means will approximate a normal distribution regardless of the shape of the population distribution. Therefore, sample means for variables data are assumed to be normally distributed.

Question 14

A company wishes to monitor the variation in the length of time it takes to process and send a bill to a customer.Five bills will be randomly selected each day and the length of time it takes to process and send the bill to a customer will be recorded for each bill.The appropriate control chart is a(n):
A)  -chart.
B) R-chart.
C) p-chart.
D) u-chart.

Accepted Answer

The appropriate control chart in this case would be the R-chart, which is used to monitor the variation in the process. By tracking the range between the maximum and minimum values of the processing time over time, this chart allows the company to quickly identify any out-of-control points and take corrective action. The other chart options (A, C, D) are not suitable for this scenario.

Question 15

The output of a process is stable and normally distributed.If the process mean equals 23.5,the percentage of output expected to be less than or equal to the mean:
A)is less than 25% .
B)is 50%.
C)is greater than 75%.
D)cannot be determined without knowing the standard deviation value.

Accepted Answer

For a normally distributed process, 50% of the output is expected to be below the mean, and 50% above the mean. Therefore, the percentage of output expected to be less than or equal to the mean (23.5) is 50%.

Question 16

Short repeated patterns in a control chart,with alternating high peaks and low valleys,are known as:
A)trends.
B)cycles.
C)spikes.
D)reciprocals.

Accepted Answer

Short repeated patterns with alternating high and low values are known as cycles. Trends are a long-term pattern in the data, spikes represent a sudden and temporary deviation from the norm, and reciprocals are not commonly used in control charts.

Question 17

Which of the following pairs of charts are used together?
A)  -chart and p-chart
B)R-chart and p-chart
C)R-chart and s-chart
D)  -chart and R-chart

Accepted Answer

The answer of Which of the following pairs of charts...

Question 18

If a process is neither capable nor in control,the appropriate first step is to:
A)remove common causes.
B)redesign the equipment.
C)remove sources of special cause variation.
D)determine the process capability index.

Accepted Answer

If a process is neither capable nor in control, it means that there are sources of both common and special cause variation present in the process. The first step is to remove sources of special cause variation, as these are the most unpredictable and damaging to the process. Once these are eliminated, the next step would be to address any common causes of variation that may still be present. Redesigning the equipment or determining the process capability index would come later, once the process is under control and capable.

Question 19

Each day,a manufacturing company producing circuit boards will randomly sample 60 circuit boards and then determine and plot the number of defects contained in each of these boards.The appropriate control chart is a:
A)  -chart.
B) p-chart.
C) np-chart.
D) c-chart.

Accepted Answer

The answer of Each day,a manufacturing company producing circuit boards...

Question 20

An alternative to using the R-chart is the:
A)np-chart.
B)s-chart.
C)c-chart.
D)p-chart.

Accepted Answer

The s-chart is a good alternative to the R-chart when variable data is being measured, as opposed to attribute data. The s-chart does not require subgrouping like the R-chart does, making it more flexible and easier to use.

Quiz 13: Statistical Process Control

Five samples of size 3 were collected for a variable measurement.All sample data were greater than or equal to 4.0.The sample means and sample ranges are provided in the following table. The values of which sample are identical?

A p-chart is also called a:

Which of the following is NOT an indication of an out-of-control process?

A delivery company defines a "defect" as a package delivered later than the promised delivery time.Management wants to monitor the proportion of packages per week delivered beyond their promised delivery time.Management plans to sample 150 packages per week.The appropriate control chart is a(n) :

The s-chart is recommended when:

If the process mean and variance do not change over time,the process is considered to be:

Which of the following is a likely cause of the control chart pattern known as a "trend?"

Determine the sample standard deviation for the following sample data: 7,9,2,0,1,and 5.

Six samples of size 10 were collected.The data are provided in the following table. The upper control limit (UCL) and lower control limit (LCL) for an s-chart are:

For variables data,the sample means are assumed to be:

The output of a process is stable and normally distributed.If the process mean equals 23.5,the percentage of output expected to be less than or equal to the mean:

Short repeated patterns in a control chart,with alternating high peaks and low valleys,are known as:

Which of the following pairs of charts are used together?

If a process is neither capable nor in control,the appropriate first step is to:

Each day,a manufacturing company producing circuit boards will randomly sample 60 circuit boards and then determine and plot the number of defects contained in each of these boards.The appropriate control chart is a:

An alternative to using the R-chart is the: