Question 1

For a process control chart a process is generally considered to be in control if
A)most points are near the center line
B)approximately an equal number of sample points are above and below the center line
C)there is no discernible pattern to the sample points
D)all of the above

Accepted Answer

A process is generally considered to be in control if most points are near the center line, approximately an equal number of sample points are above and below the center line, and there is no discernible pattern to the sample points. Therefore, all of the above conditions need to be met for a process to be considered in control.

Question 2

In a process where a large number of defects are likely to occur A)C_p < 1.0 B)C_p= 1.0 C)C_p> 1.0 D)C_p = C_pk

Accepted Answer

A process capability index (C_p) less than 1.0 indicates that the process variation is greater than the specification limits, leading to a higher likelihood of defects.

Question 3

In order to determine if the time required for students to take a final exam is excessive,five students were selected at random from each of six classes.If the process average is 123.77 minutes and the average range is 66.83 minutes,the upper and lower control limits of a 3-sigma x-chart are
A)UCL = 187.35,LCL = 109.95
B)UCL = 157.80,LCL = 89.80
C)UCL = 176.66,LCL = 120.33
D)UCL = 162,53,LCL = 89.01

Accepted Answer

D

Question 4

An example of a product or service quality attribute is
A)the weight of a bag of potato chips
B)the time it takes to serve a customer at a store
C)the completeness of an online retail order
D)the temperature of a cup of coffee at a barista

Accepted Answer

The completeness of an online retail order is an attribute of product or service quality that relates to whether all items ordered have been included and whether the order has been packaged and shipped correctly. A and D are physical attributes that relate to the condition of a product or service, while B is a measure of efficiency and not necessarily a measure of quality.

Question 5

If samples of 100 for a process are taken and p is 0.15,the upper and lower control limits for a 3-sigma p-chart are
A)UCL = 0.190 ,LCL = 0.010
B)UCL = 0.257,LCL = 0.043
C)UCL = 0.322,LCL = 0.000
D)UCL = 0.045,LCL = 0.005

Accepted Answer

To calculate the upper and lower control limits for a 3-sigma p-chart, we use the following formulas:
UCL = p + 3sqrt((p(1-p))/n)
LCL = p - 3sqrt((p(1-p))/n)
Substituting n=100 and p=0.15 into these formulas yields:
UCL = 0.15 + 3sqrt((0.15(1-0.15))/100) = 0.257
LCL = 0.15 - 3sqrt((0.15(1-0.15))/100) = 0.043
Therefore, choice B is the correct answer.

Question 6

In order to determine if the time required for students to take a final exam is excessive,five students were selected at random from each of six classes.If the process average is 123.77 minutes and the average range is 66.83 minutes,the upper and lower control limits of a 3-sigma R-chart are
A)UCL = 141,LCL = 0
B)UCL = 133.6,LCL = 0
C)UCL = 96,LCL = 0
D)UCL = 152.3,LCL = 0

Accepted Answer

The upper control limit (UCL) of a 3-sigma R-chart is calculated as UCL = D4 * R, where D4 is a constant that depends on the sample size and R is the average range. For a sample size of 5, D4 = 2.114. Therefore, UCL = 2.114 * 66.83 = 141. The lower control limit (LCL) of a 3-sigma R-chart is always 0.

Question 7

In a "zone" pattern test each zone is how many standard deviations wide? A)1 B)1/3 C)2 D)A₂R

Accepted Answer

In a "zone" pattern test, each zone is 1 standard deviation wide. This is a common method used in statistical analysis and quality control to determine how far data points deviate from the mean.

Question 8

In an Excel spreadsheet for a p-chart,if the total number of defectives for 20 samples of 100 observations each is in cell F26,the Excel formula for p is
A)=F26)/20)*100))
B)=F26)/20)
C)=F26)*100))/20
D)=F26)*20))/100

Accepted Answer

The formula for p is =F26/20, which calculates the proportion of defectives in the sample.

Question 9

One of the general guidelines for identifying a pattern in a control chart is
A)14 points on one side of the center line
B)4 out of 5 consecutive points in zone A on one side of the center line
C)8 consecutive points on one side of the center line
D)8 consecutive points alternating up or down

Accepted Answer

8 consecutive points on one side of the center line is a common rule used in control chart pattern analysis to identify a non-random pattern, suggesting a potential shift in the process level.

Question 10

Wider control limits on a process control chart i.e. ,3 sigma as opposed to 2 sigma limits)makes the chart
A)more sensitive to changes in the process
B)correspond to an overall normal probability of 95%
C)have a higher probability that the sample values will fall outside the control limits
D)harder to show changes in the process that are not random

Accepted Answer

Wider control limits, such as 3 sigma limits, encompass more of the natural variability of the process, making it less sensitive to detecting small shifts or non-random changes. This means it's harder to discern changes that are not part of the process's inherent variability.

Question 11

If the process capability index,C_pk_.is greater than 1.00_,then A)the process is not capable of meeting design specifications B)the process is capable of meeting design specification C)the process corresponds to six sigma quality D)the process will generate defects

Accepted Answer

A process capability index (CPK) greater than 1.00 indicates that the process is capable of meeting design specifications with a high degree of confidence. A CPK of 1.00 indicates that the process is just capable of meeting design specifications, and a CPK less than 1.00 indicates that the process is not capable of meeting design specifications. A CPK of 1.33 corresponds to six sigma quality. Therefore, choice B is the correct answer as it represents the capability of the process to meet design specifications.

Question 12

Statistical process control is a tool primarily for
A)identifying process variability due to natural occurrences
B)accepting or rejecting products
C)identifying process variability due to nonrandom causes
D)training workers for a production process

Accepted Answer

Statistical process control is a tool used to identify process variability due to nonrandom causes. By analyzing data from the production process, it helps to determine whether the process is in control or out of control. The goal of statistical process control is to identify and eliminate the sources of variation in a process, thus improving product quality and reducing waste.

Question 13

A cookie company makes chocolate chip cookies and it wants them to average 8 chocolate chips apiece.To control the quality of the production process the company should use a
A)p-chart
B)x-chart
C)x-chart and r-chart together
D)c-chart

Accepted Answer

An x-chart and r-chart together are used to monitor the mean and variability of a process, respectively. In the context of ensuring cookies average a specific number of chocolate chips, these charts would help in controlling both the average number of chips per cookie (x-chart) and the consistency of that number across batches (r-chart).

Question 14

Control charts are typically used
A)at every step in a production or service process
B)at the beginning and end of a production or service process
C)at critical points where it is particularly costly if the process goes out of control
D)at labor intensive points in the process

Accepted Answer

Control charts are used at critical points where it is particularly costly if the process goes out of control. This allows for early detection and correction of any issues, ensuring that the process stays within acceptable limits and reducing the likelihood of costly errors or failure.

Question 15

If 20 samples of a production process are taken and there are 240 total defects,the upper and lower control limits for a 3-sigma c-chart are
A)UCL = 16.472,LCL = 7.528
B)UCL = 15.464,LCL = 8.536
C)UCL = 22.392,LCL = 1.608
D)UCL = 18.728,LCL = 5.272

Accepted Answer

The average number of defects per sample is calculated as total defects divided by the number of samples, which is 240/20 = 12. For a c-chart, the control limits are calculated using the formula: UCL = $ \bar{c} + 3\sqrt{\bar{c}} $ and LCL = $ \bar{c} - 3\sqrt{\bar{c}} $, where $ \bar{c} $ is the average number of defects. Substituting $ \bar{c} = 12 $, we get UCL = 12 + 3√12 ≈ 22.392 and LCL = 12 - 3√12 ≈ 1.608.

Question 16

A p-chart and R-chart are control charts for
A)variables
B)attributes
C)attributes for a p-chart and variables for a R-chart
D)attributes for a R-chart and variables for a p-chart

Accepted Answer

A p-chart is used for attributes (proportions), and an R-chart is used for variables (range of a sample).

Question 17

At a fast-food restaurant,if the average time to serve a customer is 3.75 minutes for 10 samples of size 5,and the average range for the samples is 0.50 minutes,the upper and lower control limits for a 3-sigma x-chart are
A)UCL = 4.04,LCL = 3.46
B)UCL = 5.08,LCL = 4.94
C)UCL = 5.75,LCL = 1.75
D)UCL = 3.91,LCL = 3.60

Accepted Answer

To calculate the control limits for the x-chart:
Mean (X-Bar) = 3.75 minutes
Range (R-Bar) = 0.5 minutes

Upper Control Limit (UCL) = X-Bar + A2 * R-Bar
Lower Control Limit (LCL) = X-Bar - A2 * R-Bar

Here, for a sample size of 5, the value of A2 from the standard normal distribution table is 0.577.

Using the formula:
UCL = 3.75 + 0.577 * 0.5 = 4.04
LCL = 3.75 - 0.577 * 0.5 = 3.46

Therefore, the correct answer is (A).

Question 18

In an Excel spreadsheet for a c-chart,if the population process average for 20 samples,c,is in cell H4,the Excel formula for the upper control limit is
A)=H4+3*SQRTH4*1-H4))/100))
B)=H4+3*SQRTH4/20)
C)=H4+3*SQRTH4)
D)=H4+SQRT3*H4)

Accepted Answer

The correct formula for the upper control limit (UCL) in a c-chart is given by UCL = c + 3*sqrt(c), where c is the average number of defects per unit (in this case, located in cell H4). Option C correctly represents this formula in Excel syntax.

Question 19

An attribute control chart that uses the actual number of defects per item in a sample is a
A)p-chart
B)mean chart
C)range chart
D)c-chart

Accepted Answer

The c-chart is used for attribute control charts where the number of defects per item in a sample can vary. It is the best choice for monitoring the number of defects in a process when the sample size of the items being inspected is consistent. The p-chart is used when the sample size of items being inspected can vary, while the mean chart and range chart are used for variable control charts to monitor process mean and process variation, respectively.

Question 20

In general,sample sizes for attribute control charts are
A)smaller than for variable control charts
B)larger than for variable control charts
C)the same as for variable control charts
D)larger or smaller than variable control charts

Accepted Answer

Attribute control charts typically require larger sample sizes than variable control charts because attribute data (categorical) is less informative per observation than variable data (measurable), necessitating larger samples to achieve a similar level of statistical confidence.

Quiz 4: Statistical Process Control

For a process control chart a process is generally considered to be in control if

In a process where a large number of defects are likely to occur

In order to determine if the time required for students to take a final exam is excessive,five students were selected at random from each of six classes.If the process average is 123.77 minutes and the average range is 66.83 minutes,the upper and lower control limits of a 3-sigma x-chart are

An example of a product or service quality attribute is

If samples of 100 for a process are taken and p is 0.15,the upper and lower control limits for a 3-sigma p-chart are

In order to determine if the time required for students to take a final exam is excessive,five students were selected at random from each of six classes.If the process average is 123.77 minutes and the average range is 66.83 minutes,the upper and lower control limits of a 3-sigma R-chart are

In a "zone" pattern test each zone is how many standard deviations wide?

In an Excel spreadsheet for a p-chart,if the total number of defectives for 20 samples of 100 observations each is in cell F26,the Excel formula for p is

One of the general guidelines for identifying a pattern in a control chart is

Wider control limits on a process control chart i.e. ,3 sigma as opposed to 2 sigma limits) makes the chart

If the process capability index,C_pk_.is greater than 1.00_,then

Statistical process control is a tool primarily for

A cookie company makes chocolate chip cookies and it wants them to average 8 chocolate chips apiece.To control the quality of the production process the company should use a

Control charts are typically used

If 20 samples of a production process are taken and there are 240 total defects,the upper and lower control limits for a 3-sigma c-chart are

A p-chart and R-chart are control charts for

At a fast-food restaurant,if the average time to serve a customer is 3.75 minutes for 10 samples of size 5,and the average range for the samples is 0.50 minutes,the upper and lower control limits for a 3-sigma x-chart are

In an Excel spreadsheet for a c-chart,if the population process average for 20 samples,c,is in cell H4,the Excel formula for the upper control limit is

An attribute control chart that uses the actual number of defects per item in a sample is a

In general,sample sizes for attribute control charts are