Question 1

When a process variable is Normally distributed,there are two important process characteristics that need to be monitored: the mean,$\mu$,and the standard deviation,$\sigma$.Which control chart would be used to monitor the process spread?
A)The R chart
B)The  chart
C)The s chart
D)Any of the above charts would be appropriate to monitor process spread.
E)Only A and C monitor process spread.

Accepted Answer

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Question 2

Parts manufactured by an injection molding process are subjected to a compressive strength test.We monitor the compressive strength of the parts manufactured by this process using an and an s control chart.Samples of size 9 are taken at regular intervals,and their mean compressive strength (in psi = pounds per square inch)and standard deviation are plotted on the charts in time order.The overall mean of the sample means is = 81.2 psi,and the mean of the sample standard deviations is = 2.9 psi.The control chart constants are (partially)reproduced below. What is the lower control limit for the chart? A)0 psi B)18.8 psi C)78.2 psi D)78.7 psi

Accepted Answer

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Question 3

What do we call the ability of a process to meet or exceed the requirements placed on it?
A)Being in control
B)Being within tolerances
C)The stability
D)The capability

Accepted Answer

The ability of a process to meet or exceed the requirements placed on it is referred to as its capability. Choices A and B refer to the idea of a process being within acceptable limits or parameters, but do not capture the idea of the process's ability to meet requirements. Choice C refers to the stability of a process, which may or may not translate into the ability to meet requirements.

Question 4

Suppose we use a "run of eight" rule;that is,we declare the process out of control if eight consecutive points are all above the center line of the chart or if eight consecutive points are all below the center line of the Chart.If the process is in statistical control,what is the (approximate)probability that we declare the process out of control using this rule? A)0.001 B)0.004 C)0.008 D)0.05

Accepted Answer

Under statistical control, each point has an equal chance of being above or below the center line. Hence, the probability of eight consecutive points being above or below the center line is (0.5)^8 = 0.0039. However, we must consider both cases (above and below). Therefore, the approximate probability of declaring the process out of control is 0.0039 + 0.0039 = 0.0078, which is closest to option C (0.008).

Question 5

A bank is interested in improving the time it takes to complete transactions at teller windows.The goal is to have no transaction take more than 5 minutes.What name do we give the quantity "5 minutes"?
A)The upper control limit
B)The upper tolerance limit
C)The upper specification limit
D)The upper capability limit

Accepted Answer

The quantity "5 minutes" represents the upper specification limit, as it is the maximum time allowed for a transaction to be completed according to the bank's goal. The upper control limit and upper capability limit would be used in statistical process control, while the upper tolerance limit is typically used in quality assurance and defines the maximum acceptable deviation from a specified value.

Question 6

Piston rings for an automotive engine are produced by a forging process.We monitor the inside diameter of the rings manufactured by this process using an  and an s control chart.Samples of size 4 are taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The overall mean of the sample means is 73.812 millimeters,and the mean of the sample standard deviations is 0.022 millimeters.The control chart constants are (partially)reproduced below.  What is the value of the upper control limit for the  chart?
A)73.834 millimeters
B)73.848 millimeters
C)73.878 millimeters
D)154.119 millimeters

Accepted Answer

The answer of Piston rings for an automotive engine are...

Question 7

Which of the following statements about the use of control charts is/are FALSE?
A)The one point outside the control limits on the  chart is effective for detecting a gradual shift in the process mean.
B)To provide a quicker alarm when the process has gone out of control we can look for other patterns on the  chart,such as by adding a runs rule.
C)A pattern such as nine consecutive points,either above the center line or below the center line,can be used as a signal that a process has been disturbed by a special cause.
D)When additional patterns are looked for on a control chart,the false alarm rate,when the process is in control,will increase.
E)A false alarm occurs on a control chart when a plotted point gives an out-of-control signal,but the process is operating only with common cause variability.

Accepted Answer

The statement that the one point outside the control limits on the 11eab14b_c874_7415_9166_35d89d8e3f96_TB5065_11 chart is effective for detecting a gradual shift in the process mean is false. A single point outside the control limits is more effective at detecting a sudden shift or other out-of-control events, while a gradual shift would typically be detected by a trend or shift in the process over time on the chart.

Question 8

Piston rings for an automotive engine are produced by a forging process.We monitor the inside diameter of the rings manufactured by this process using an and an s control chart.Samples of size 4 are taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The overall mean of the sample means is 73.812 millimeters,and the mean of the sample standard deviations is 0.022 millimeters.The control chart constants are (partially)reproduced below. What value would we use for the center line of the chart? A)68.003 millimeters B)73.790 millimeters C)73.812 millimeters D)154.119 millimeters

Accepted Answer

The center line of an s control chart is calculated by taking the average of the sample standard deviations. The mean of the sample standard deviations is given in the problem as 0.022 millimeters, so we would use this value as the center line. Therefore, the answer is C)73.812 millimeters.

Question 9

Parts manufactured by an injection molding process are subjected to a compressive strength test.We monitor the compressive strength of the parts manufactured by this process using an and an s control chart.Samples of size 9 are taken at regular intervals,and their mean compressive strength (in psi = pounds per square inch)and standard deviation are plotted on the charts in time order.The overall mean of the sample means is = 81.2 psi,and the mean of the sample standard deviations is = 2.9 psi.The control chart constants are (partially)reproduced below. What is the value of the center line for the chart? A)18.8 psi B)78.7 psi C)81.2 psi D)138.6 psi

Accepted Answer

The center line for an s chart is calculated as the mean of the sample standard deviations, which is given as 2.9 psi. Therefore, the value of the center line for the s chart is 2.9 psi. The overall mean of the sample means is not used in the calculation of the center line for an s chart.

Question 10

Piston rings for an automotive engine are produced by a forging process.We monitor the inside diameter of the rings manufactured by this process using an and an s control chart.Samples of size 4 are taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The overall mean of the sample means is 73.812 millimeters,and the mean of the sample standard deviations is 0.022 millimeters.The control chart constants are (partially)reproduced below. The overall mean of the sample means is given as 73.812 millimeters.What symbol do we use to represent this value? A) B) C)$\mu$ D)

Accepted Answer

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Question 11

An important characteristic in the proper operation of ignition keys for automobiles is the groove width of the key.In a large manufacturing plant that produces thousands of keys,control charts have been established to monitor the process of cutting the groove.It is believed that the measurement (in inches)of the groove width is Normally distributed.Over a period of time,20 samples,each of size n = 5,were selected in order to establish 3-sigma and s charts.From these samples the following were determined: = 0.15932 and = 0.0193438.Examination of the chart and the s chart for the samples led to the conclusion that the process was in control at this time.Because this process is in a state of statistical control,we are able to predict what to expect in the finished product.What will be the natural tolerances for the grooves in the ignition keys? A)(0.00659,0.00935) B)(0.00488,0.01105) C)(0.00506,0.01087) D)(0.13337,0.18527) E)This cannot be determined with the given information.

Accepted Answer

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Question 12

An important characteristic in the proper operation of ignition keys for automobiles is the groove width of the key.In a large manufacturing plant that produces thousands of keys,control charts have been established to monitor the process of cutting the groove.It is believed that the measurement (in inches)of the groove width is Normally distributed.Over a period of time,20 samples,each of size n = 5,were selected in order to establish 3-sigma and s charts.From these samples the following were determined: = 0.15932 and = 0.0193438.What is the value of the center line on the chart and on the s chart,respectively? A)0.00797;0.001028 B)0.15932;0.019344 C)0.00797;0.000967 D)0.15932;0.000967 E)0.00797;0.019344

Accepted Answer

The answer of An important characteristic in the proper operation...

Question 13

What is an R chart used for?
A)To monitor the center of a process
B)To monitor the spread of a process
C)To monitor both the center and spread of a process
D)To monitor the correlation of a process

Accepted Answer

An R chart, or range chart, is used to monitor the spread of a process by tracking the range of variation within subgroups of data. It is not used to monitor the center of a process, correlation of a process, or both the center and spread of a process (which would require an X-R chart or individuals and moving range chart).

Question 14

Parts manufactured by an injection molding process are subjected to a compressive strength test.We monitor the compressive strength of the parts manufactured by this process using an and an s control chart.Samples of size 9 are taken at regular intervals,and their mean compressive strength (in psi = pounds per square inch)and standard deviation are plotted on the charts in time order.The overall mean of the sample means is = 81.2 psi,and the mean of the sample standard deviations is = 2.9 psi.The control chart constants are (partially)reproduced below. What is the center line for the s chart? A)2.8 psi B)2.9 psi C)3 psi D)5.0 psi

Accepted Answer

The center line for the s chart is calculated using the formula (3.267 * average range), where the average range is the mean of the sample standard deviations. Thus, the center line for the s chart is 3.267 * 2.9 = 9.46 psi. However, the options given do not include this value. The closest option is B, which is 2.9 psi, the mean of the sample standard deviations. This is not the correct formula for calculating the center line for the s chart, but it is the closest option available, and it is a reasonable estimate for the center line.

Question 15

An important characteristic in the proper operation of ignition keys for automobiles is the groove width of the key.In a large manufacturing plant that produces thousands of keys,control charts have been established to monitor the process of cutting the groove.It is believed that the measurement (in inches)of the groove width is Normally distributed.Over a period of time,20 samples,each of size n = 5,were selected in order to establish 3-sigma and s charts.From these samples the following were determined: = 0.15932 and = 0.0193438.For the chart that is being set up,what are the appropriate 3-sigma lower and upper control limits, (LCL,UCL)? A)(0.00667,0.00927) B)(-0.02289,0.03883) C)(0.13337,0.18527) D)(0.00659,0.00935) E)None of the above

Accepted Answer

The answer of An important characteristic in the proper operation...

Question 16

Piston rings for an automotive engine are produced by a forging process.We monitor the inside diameter of the rings manufactured by this process using an  and an s control chart.Samples of size 4 are taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The overall mean of the sample means is 73.812 millimeters,and the mean of the sample standard deviations is 0.022 millimeters.The control chart constants are (partially)reproduced below.  What is the value of the center line of the s chart?
A)0 millimeters
B)0.020 millimeters
C)0.022 millimeters
D)0.046 millimeters

Accepted Answer

The center line of an s chart is the average of the sample standard deviations. In this case, the mean of the sample standard deviations is given as 0.022 millimeters, which is the value of the center line of the s chart.

Question 17

An important characteristic in the proper operation of ignition keys for automobiles is the groove width of the key.In a large manufacturing plant that produces thousands of keys,control charts have been established to monitor the process of cutting the groove.It is believed that the measurement (in inches)of the groove width is Normally distributed.Over a period of time,20 samples,each of size n = 5,were selected in order to establish 3-sigma and s charts.From these samples the following were determined: = 0.15932 and = 0.0193438.Examination of the chart and the s chart for the samples led to the conclusion that the process was in control at this time.What,then,are the estimates of the process mean,$\mu$,and process standard deviation,$\sigma$? A) = 0.00797; = 0.000967 B) = 0.00797; = 0.019344 C) = 0.15932; = 0.020578 D) = 0.15932; = 0.001029 E) = 0.00797; = 0.001029

Accepted Answer

The answer of An important characteristic in the proper operation...

Question 18

The 68-95-99.7 rule tells us that if a process with mean $\mu$ and standard deviation $\sigma$ varies according to a Normal distribution,then almost all measurements on individual products will lie in the range $\mu$ ± 3$\sigma$.What do we call the values $\mu$ - 3$\sigma$ and $\mu$ + 3$\sigma$?
A)The control limits
B)The confidence limits
C)The natural tolerances
D)The capability limits

Accepted Answer

The values $ \mu - 3\sigma $ and $ \mu + 3\sigma $ define the range within which about 99.7% of the values of a normal distribution are expected to fall. This range is referred to as the natural tolerances of the process, indicating the natural variation limits within the process under normal conditions.

Question 19

Piston rings for an automotive engine are produced by a forging process.We monitor the inside diameter of the rings manufactured by this process using an  and an s control chart.Samples of size 4 are taken at regular intervals,and the sample means and standard deviations are computed and plotted on the charts in time order.The overall mean of the sample means is 73.812 millimeters,and the mean of the sample standard deviations is 0.022 millimeters.The control chart constants are (partially)reproduced below.  What is the lower control limit for the s chart?
A)-0.066 millimeters
B)0 millimeters
C)0.020 millimeters
D)0.022 millimeters

Accepted Answer

The answer of Piston rings for an automotive engine are...

Question 20

What is the definition of rational subgroups?
A)They are those parts of a process that are identified as most likely to be special causes.
B)They are samples chosen to reflect only item-to-item variation in a process.
C)They are those samples in an s chart that are in control.
D)They are the specific groups of charts that we use to monitor a process.

Accepted Answer

Rational subgroups are designed to minimize the variation within subgroups and maximize the variation between subgroups to effectively monitor and identify any special causes of variation in a process. They reflect item-to-item variation, helping in understanding the process variability more accurately.

Quiz 17: Statistics for Quality: Control and Capability

When a process variable is Normally distributed,there are two important process characteristics that need to be monitored: the mean, $\mu$ ,and the standard deviation, $\sigma$ .Which control chart would be used to monitor the process spread?

What do we call the ability of a process to meet or exceed the requirements placed on it?

A bank is interested in improving the time it takes to complete transactions at teller windows.The goal is to have no transaction take more than 5 minutes.What name do we give the quantity "5 minutes"?

Which of the following statements about the use of control charts is/are FALSE?

What is an R chart used for?

What is the definition of rational subgroups?

Quiz 17: Statistics for Quality: Control and Capability

When a process variable is Normally distributed,there are two important process characteristics that need to be monitored: the mean, μ\muμ ,and the standard deviation, σ\sigmaσ .Which control chart would be used to monitor the process spread?

What do we call the ability of a process to meet or exceed the requirements placed on it?

A bank is interested in improving the time it takes to complete transactions at teller windows.The goal is to have no transaction take more than 5 minutes.What name do we give the quantity "5 minutes"?

Which of the following statements about the use of control charts is/are FALSE?

What is an R chart used for?

What is the definition of rational subgroups?

When a process variable is Normally distributed,there are two important process characteristics that need to be monitored: the mean, $\mu$ ,and the standard deviation, $\sigma$ .Which control chart would be used to monitor the process spread?