Question 1

The 3-sigma lower control limit (LCL) for an S chart is given by LCL = $\bar { s } - 3 \bar { s } \sqrt { 1 - a _ { n } ^ { 2 } } / a _ { n }$ where the values of $a _ { n }$ for n=3, ….., 8 are tabulated in your text. This expression for LCL will be negative if $n \leq$ __________, in which case it is customary to use LCL = __________.

Accepted Answer

5, 0

Question 2

The two control limit for 3 sigma $\bar { x }$ chart have been calculated. If the variable of interest is normally distributed, and 3 is replaced by 3.09 in the control limits formulas, then probability of Type I error $( \alpha )$ __________, but for any fixed n and $\sigma$ , probability of Type II error $( \beta )$ will __________.

Accepted Answer

decreases, increase

Question 3

An $\bar { x }$ control chart is based on control limits $\mu \pm 2.5 \sigma / \sqrt { n }$ When the process is in control, then the probability that a point falls outside the limits is __________.

Accepted Answer

.0124

Question 4

Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as contaminated material, are referred to as __________ in the quality control literature.

Accepted Answer

The answer of Sources of variation that may have a...

Question 5

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

Accepted Answer

The answer of An $\bar { x }$ control chart...

Question 6

Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to __________.

Accepted Answer

The answer of Suppose there are 25 samples obtained at...

Question 7

For a sample of size 5, the tabulated value of $a = .94$ If the population standard deviation $\sigma = 2.50$ then the standard deviation of the sample standard deviation S is $\sigma _ { 2 } =$ __________, rounded to 3 decimal places.

Accepted Answer

The answer of For a sample of size 5, the...

Question 8

When an in-control process yields a point outside the control limits (an out-of-control signal), a type __________ error has occurred.

Accepted Answer

The answer of When an in-control process yields a point...

Question 9

If the points on a control chart all lie between the two central limits, the process is deemed to __________.

Accepted Answer

The answer of If the points on a control chart...

Question 10

When an out-of-control process produces a point inside the control limits, a type __________ error has occurred.

Accepted Answer

The answer of When an out-of-control process produces a point...

Question 11

__________ are now used extensively in industry as diagnostic techniques for monitoring production processes to identify instability and unusual circumstances.

Accepted Answer

The answer of __________ are now used extensively in industry...

Question 12

An $\bar { x }$ control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard deviation control limits are LCL = __________ and UCL =__________.

Accepted Answer

The answer of An $\bar { x }$ control chart...

Question 13

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

Accepted Answer

The answer of Suppose there are 24 samples obtained at...

Question 14

In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a __________ and two__________.

Accepted Answer

The answer of In addition to the plotted points themselves...

Question 15

The 3-sigma lower control limit (LCL) for an R chart is given by LCL = $\bar { r } - 3 c _ { n } \bar { r } / b _ { n }$ where the values of $b _ { n } \text { and } c _ { n }$ for n=3,…..,8 are tabulated in your text. This expression for LCL will be negative if $n \leq$ __________, in which case it is customary to use LCL = __________.

Accepted Answer

The answer of The 3-sigma lower control limit (LCL) for...

Question 16

The two control limits for 3=sigma $\bar { x }$ chart have been calculated. If the variable of interest is normally distributed, and 3 is replaced by 2.5 in the control limits formulas, then probability of Type I error $( \alpha )$ __________, but for fixed n and $\sigma$ , probability of Type II error $( \beta )$ will __________.

Accepted Answer

The answer of The two control limits for 3=sigma \(\bar...

Question 17

The sample variance $S ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ that is, __________ = __________.

Accepted Answer

The answer of The sample variance \(S ^ { 2...

Question 18

Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma $\bar { x }$ chart suggests that the process may have been __________ at that time, so a search for __________ should be initiated.

Accepted Answer

The answer of Any point outside the lower control limit...

Question 19

The term __________ data is used in quality control to describe situations such as each item produced conforms to specifications or does not, or a single item (e.g., one automobile) may have one or more defects, and the number of defects is determined.

Accepted Answer

The answer of The term __________ data is used in...

Question 20

The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g., blemishes on a set of four tires) is based on the __________ probability distribution.

Accepted Answer

The answer of The c control chart for the number...

Quiz 16: Quality Control Methods

An $\bar { x }$ control chart is based on control limits $\mu \pm 2.5 \sigma / \sqrt { n }$ When the process is in control, then the probability that a point falls outside the limits is __________.

Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as contaminated material, are referred to as __________ in the quality control literature.

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to __________.

For a sample of size 5, the tabulated value of $a = .94$ If the population standard deviation $\sigma = 2.50$ then the standard deviation of the sample standard deviation S is $\sigma _ { 2 } =$ __________, rounded to 3 decimal places.

When an in-control process yields a point outside the control limits (an out-of-control signal), a type __________ error has occurred.

If the points on a control chart all lie between the two central limits, the process is deemed to __________.

When an out-of-control process produces a point inside the control limits, a type __________ error has occurred.

__________ are now used extensively in industry as diagnostic techniques for monitoring production processes to identify instability and unusual circumstances.

An $\bar { x }$ control chart is constructed using 25 samples of size 3 each, when the process is in-control and the random variable of interest is normally distributed with a mean of 20 and standard deviation of 1.732. Then, the 3 standard deviation control limits are LCL = and UCL =.

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a and two.

The sample variance $S ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ that is, = .

Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma $\bar { x }$ chart suggests that the process may have been at that time, so a search for should be initiated.

The term __________ data is used in quality control to describe situations such as each item produced conforms to specifications or does not, or a single item (e.g., one automobile) may have one or more defects, and the number of defects is determined.

The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g., blemishes on a set of four tires) is based on the __________ probability distribution.

Quiz 16: Quality Control Methods

An xˉ\bar { x }xˉ control chart is based on control limits μ±2.5σ/n\mu \pm 2.5 \sigma / \sqrt { n }μ±2.5σ/n​ When the process is in control, then the probability that a point falls outside the limits is __________.

Sources of variation that may have a pernicious impact on the quality of items produced by some process, such as contaminated material, are referred to as __________ in the quality control literature.

An xˉ\bar { x }xˉ control chart is based on control limits μ0±2.88σ/n\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }μ0​±2.88σ/n​ When the process is in control, then the average run length (ARL) is __________.

Suppose there are 25 samples obtained at equally spaced time points, and n=5 observations in each sample. If the sum of the 25 sample standard deviations is 50, then the center line of the S chart will be at height equals to __________.

For a sample of size 5, the tabulated value of a=.94a = .94a=.94 If the population standard deviation σ=2.50\sigma = 2.50σ=2.50 then the standard deviation of the sample standard deviation S is σ2=\sigma _ { 2 } =σ2​= __________, rounded to 3 decimal places.

When an in-control process yields a point outside the control limits (an out-of-control signal), a type __________ error has occurred.

If the points on a control chart all lie between the two central limits, the process is deemed to __________.

When an out-of-control process produces a point inside the control limits, a type __________ error has occurred.

__________ are now used extensively in industry as diagnostic techniques for monitoring production processes to identify instability and unusual circumstances.

Suppose there are 24 samples obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 24 samples ranges is 108, then the center line of the R chart will be at height equals to __________.

In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a __________ and two__________.

The sample variance S2S ^ { 2 }S2 is an unbiased estimator of the population variance σ2\sigma ^ { 2 }σ2 that is, __________ = __________.

Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma xˉ\bar { x }xˉ chart suggests that the process may have been __________ at that time, so a search for __________ should be initiated.

The term __________ data is used in quality control to describe situations such as each item produced conforms to specifications or does not, or a single item (e.g., one automobile) may have one or more defects, and the number of defects is determined.

The c control chart for the number of defectives in a single item (e.g., one automobile) or a group of items (e.g., blemishes on a set of four tires) is based on the __________ probability distribution.

An $\bar { x }$ control chart is based on control limits $\mu \pm 2.5 \sigma / \sqrt { n }$ When the process is in control, then the probability that a point falls outside the limits is __________.

An $\bar { x }$ control chart is based on control limits $\mu _ { 0 } \pm 2.88 \sigma / \sqrt { n }$ When the process is in control, then the average run length (ARL) is __________.

For a sample of size 5, the tabulated value of $a = .94$ If the population standard deviation $\sigma = 2.50$ then the standard deviation of the sample standard deviation S is $\sigma _ { 2 } =$ __________, rounded to 3 decimal places.

In addition to the plotted points themselves (e.g., sample means or sample proportions), a control chart has a and two.

The sample variance $S ^ { 2 }$ is an unbiased estimator of the population variance $\sigma ^ { 2 }$ that is, = .

Any point outside the lower control limit (LCL) and/or the upper control limit (UCL) of a 3-sigma $\bar { x }$ chart suggests that the process may have been at that time, so a search for should be initiated.