Question 1

At time r, a process is judged out of control if any of the cumulative sum plotted values $\left( 1 , S _ { 1 } \right) , \left( 2 , S _ { 2 } \right) , \ldots \ldots , \left(y , S _ { \mathrm { r } } \right)$ lies outside the __________; either above the upper arm or below the lower arm.

Accepted Answer

The answer of At time r, a process is judged...

Question 2

The behavior of a sampling plan can be nicely summarized by graphing P(A); the probability that the lot is accepted, as a function of p; the proportion of defective items in the lot. Such a graph is called the __________ for the plan.

Accepted Answer

operating ...

Question 3

On each of the previous 25 days, 100 electronic devices of a certain type were randomly selected and subjected to a severe heat stress test. The total number of items that failed to pass the test was 570.
a. Determine control limits for a 3-sigma p chart.
b. The highest number of failed items on a given day was 40, and the lowest number was 12. Does either of these correspond to an out-of-control point? Explain.

Accepted Answer

a. The control limits are

; therefore ...

Question 4

When the out-of-control ARL corresponds to a shift of 1 standard deviation I the process mean, what are the characteristics of the CUSUM procedure that has ARL of 250 and 4.8 for the in-control and out-of-control conditions, respectively?

Accepted Answer

In- control ARL = 25...

Question 5

Which of the following are not examples of assignable causes of variation?

Accepted Answer

A)   Contaminated material
B)   Incorrect machine settings
C)   Environmental factors
D)   Unusual machine tools wear
E)   All of the aboveF) B) and E)
G) C) and E)

Question 6

Suppose there are 28 samples obtained at equally spaced time points, and n=7 observations in each sample. If the sum of the 28 sample ranges is 98, and that the tabulated values of  b7b _ { 7 }b7​  and  c7c _ { 7 }c7​  are 2.706 and .833, respectively, then the 3-sigma control limits LCL and UCL for an R control chart are respectively

Accepted Answer

A)   0.0 and 6.73
B)   .27 and 6.73
C)   -30.61 and 37.61
D)   0.0 and 37.61
E)   None of the above answers are correct. F) C) and D)
G) All of the above

Question 7

Which of the following statements are not true?

Accepted Answer

A)   An in-control process is simply one that is operating in a stable fashion, reflecting only natural random variation.
B)   An out-of-control "signal" occurs whenever a plotted point falls outside the two control limits.
C)   There is a strong analogy between the logic of control charting and hypothesis testing. The null hypothesis here is that the process is out-of-control.
D)   The two control limits are designed so that an in-control process generates very few false alarms, whereas a process not in control quickly gives rise to a point outside the limits.
E)   All of the above statements are true.F) B) and C)
G) A) and E)

Question 8

Which of the following statements are not true?

Accepted Answer

A)   One important use of control charts is to see whether some measure of location of the variable's distribution remains stable over time.
B)   It is highly unlikely that for an in-control process, the sample mean will fall within 3 standard deviations  (3σ/n) ( 3 \sigma/ \sqrt { n } ) (3σ/nc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​)  Of the process mean  μ.\mu .μ. 
C)   The use of control charts based on 3 standard deviation limits is traditional, but tradition is certainly not inviolable.
D)   All of the above statements are true.
E)   None of the above statements are true. F) A) and B)
G) A) and C)

Question 9

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

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

Question 10

When n = 180, what is the smallest value of $\bar { P }$ for which the LCL in a 3-sigma p chart is positive?

Accepted Answer

LCL > 0 when <img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> . Afte...

Question 11

Which of the following statements are true?

Accepted Answer

A)   The p control chart for the fraction of items not conforming to specifications is based on the binomial probability distribution.
B)   The c control chart for the number of defectives is based on the Poisson probability distribution.
C)   If the random variable X has a binomial distribution with parameters n and p, then when p is small the transformation  Y=h(X) =sin⁡−1(X/n) Y = h ( X )  = \sin ^ { - 1 } ( \sqrt { X / n } ) Y=h(X) =sin−1(X/nc34,79.3,68.167,158.7,102.5,238c34.3,79.3,51.8,119.3,52.5,120c340,-704.7,510.7,-1060.3,512,-1067l0 -0c4.7,-7.3,11,-11,19,-11H40000v40H1012.3s-271.3,567,-271.3,567c-38.7,80.7,-84,175,-136,283c-52,108,-89.167,185.3,-111.5,232c-22.3,46.7,-33.8,70.3,-34.5,71c-4.7,4.7,-12.3,7,-23,7s-12,-1,-12,-1s-109,-253,-109,-253c-72.7,-168,-109.3,-252,-110,-252c-10.7,8,-22,16.7,-34,26c-22,17.3,-33.3,26,-34,26s-26,-26,-26,-26s76,-59,76,-59s76,-60,76,-60zM1001 80h400000v40h-400000z'/>​)  Is recommended and that the points  y1,y2,…,yny _ { 1 } , y _ { 2 } , \ldots , y _ { n }y1​,y2​,…,yn​ Should be used to construct the p chart.
D)   If the random variable X has a Poisson distribution with parameter  λ,\lambda ,λ, And  λ\lambdaλ Is small, then the transformation  Y=h(X) =2XY = h ( X )  = 2 \sqrt { X }Y=h(X) =2Xc-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​ Is recommended and that the points  y1,y2,……y _ { 1 } , y _ { 2 } , \ldots \ldotsy1​,y2​,…… Should be used to construct the c chart.
E)   All of the above statements are correct F) All of the above
G) A) and E)

Question 12

Suppose there are 10 sample obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 20 sample standard deviations is 42, and that the tabulated value of  a4a _ { 4 }a4​  is .921, then the 3-sigma control limits LCL and UCL for an S control chart are respectively

Accepted Answer

A)   1.062 and 3.138
B)   3.138 and 4.765
C)   0.0 and 4.765
D)   -.354 and 4.554
E)   -.565 and 4.765 F) A) and E)
G) A) and B)

Question 13

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 14

__________ 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 15

In acceptance sampling, the risk of accepting a poor quality lot is considered a

Accepted Answer

A)   Type I error.
B)   consumer's risk.
C)   producer's risk.
D)   bad luck lot.
E)   None of the above.F) None of the above
G) B) and D)

Question 16

Let the random variable X denote the number of defective items in the lot, A denote the event that the lot is accepted, and p denote the proportion of defective items in the lot. Which of the following statements is not true?

Accepted Answer

A)   If the sample size n is large relative to the lot size N, then the probability of accepting the lot, P(
A)  , is calculated using the hypergeometric distribution.
B)   When the sample size n is small relative to the lot size N (the rule of thumb suggested in your text was  n≤.05 Nn \leq .05 \mathrm {~N}n≤.05 N ) , then the probability of accepting the , P(
A)  , is calculated using the binomial distribution.
C)   If the probability of accepting the lot, P(
A)  , is large only when p is small (this, of course, depends on the specified critical value c) , then the Poisson approximation to the binomial distribution is justified.
D)   The larger value of p, the larger the probability P(
A)   of accepting the lot.
E)   All of the above statements are true. F) A) and D)
G) A) and C)

Question 17

The accompanying observations are numbers of defects in 25 1-square-yard specimens of woven fabric of a certain type: 3, 7, 5, 3, 4, 2, 8, 4, 3, 3, 6, 6, 2, 3, 2, 4, 7, 3, 2, 3, 4, 1, 5, 4, 6. Determine control limits for a 3-sigma c chart for the number of defects, and discuss the behavior of the chart.

Accepted Answer

<img  loading="lazy" src="/assets/images/blured-textbook.svg" class="d-inline m-1" alt="blured image" width="139" height="30"> Thus LCL = 0 and UC...

Question 18

Consider the single-sample plan that utilizes n = 50 and c = 1 when N = 2000. Determine the values of AOQ and ATI for selected values of p and graph each of these against p. Also determine the value of AOQL.

Accepted Answer

P(A) =

Since

then multiplying each en...

Question 19

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 20

The accompanying table gives sample means and standard deviations, each based on n = 6 observations of the refractive index of fiber-optic cable. Calculate the control limits for an $$\bar { X }$$ chart based on the sample standard deviations given, and comment on the behavior of the chart. [Hint: $$\sum \bar { x } _ { 2 } = 2317.07 \text { and } \sum s _ { 2 } = 30.34$$ ]

Accepted Answer

Since

=

, then the control ...

Exam 16: Quality Control Methods

Correct Answer
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a. The control limits are ; therefore ...
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In acceptance sampling, the risk of accepting a poor quality lot is considered a

Correct Answer
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Which of the following statements are true?

Correct Answer
verified

Correct Answer
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Since = , then the control ...
View Answer

Which of the following are not examples of assignable causes of variation?

Correct Answer
verified

Consider the single-sample plan that utilizes n = 50 and c = 1 when N = 2000. Determine the values of AOQ and ATI for selected values of p and graph each of these against p. Also determine the value of AOQL.

Correct Answer
verified
P(A) = Since then multiplying each en...
View Answer

Correct Answer
verified

The behavior of a sampling plan can be nicely summarized by graphing P(A); the probability that the lot is accepted, as a function of p; the proportion of defective items in the lot. Such a graph is called the __________ for the plan.

Correct Answer
verified
operating ...
View Answer

Which of the following statements are not true?

Correct Answer
verified

Let the random variable X denote the number of defective items in the lot, A denote the event that the lot is accepted, and p denote the proportion of defective items in the lot. Which of the following statements is not true?

Correct Answer
verified

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

Correct Answer
verified

Correct Answer
verified
Thus LCL = 0 and UC...
View Answer

When n = 180, what is the smallest value of $\bar { P }$ for which the LCL in a 3-sigma p chart is positive?

Correct Answer
verified
LCL > 0 when . Afte...
View Answer

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

Correct Answer
verified

Which of the following statements are not true?

Correct Answer
verified

Suppose there are 10 sample obtained at equally spaced time points, and n=4 observations in each sample. If the sum of the 20 sample standard deviations is 42, and that the tabulated value of $a _ { 4 }$ is .921, then the 3-sigma control limits LCL and UCL for an S control chart are respectively

Correct Answer
verified

At time r, a process is judged out of control if any of the cumulative sum plotted values $\left( 1 , S _ { 1 } \right) , \left( 2 , S _ { 2 } \right) , \ldots \ldots , \left(y , S _ { \mathrm { r } } \right)$ lies outside the __________; either above the upper arm or below the lower arm.

Correct Answer
verified

Correct Answer
verified

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.

Correct Answer
verified

When the out-of-control ARL corresponds to a shift of 1 standard deviation I the process mean, what are the characteristics of the CUSUM procedure that has ARL of 250 and 4.8 for the in-control and out-of-control conditions, respectively?

Correct Answer
verified
In- control ARL = 25...
View Answer

Exam 16: Quality Control Methods

Correct Answerverified a. The control limits are ; therefore ...View AnswerShow Answer

In acceptance sampling, the risk of accepting a poor quality lot is considered a

Correct AnswerverifiedShow Answer

Which of the following statements are true?

Correct AnswerverifiedShow Answer

Correct Answerverified Since = , then the control ...View AnswerShow Answer

Which of the following are not examples of assignable causes of variation?

Correct AnswerverifiedShow Answer

Consider the single-sample plan that utilizes n = 50 and c = 1 when N = 2000. Determine the values of AOQ and ATI for selected values of p and graph each of these against p. Also determine the value of AOQL.

Correct AnswerverifiedP(A) = Since then multiplying each en...View AnswerShow Answer

Correct AnswerverifiedShow Answer

The behavior of a sampling plan can be nicely summarized by graphing P(A); the probability that the lot is accepted, as a function of p; the proportion of defective items in the lot. Such a graph is called the __________ for the plan.

Correct Answerverifiedoperating ...View AnswerShow Answer

Which of the following statements are not true?

Correct AnswerverifiedShow Answer

Let the random variable X denote the number of defective items in the lot, A denote the event that the lot is accepted, and p denote the proportion of defective items in the lot. Which of the following statements is not true?

Correct AnswerverifiedShow Answer

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

Correct AnswerverifiedShow Answer

Correct Answerverified Thus LCL = 0 and UC...View AnswerShow Answer

When n = 180, what is the smallest value of Pˉ\bar { P }Pˉ for which the LCL in a 3-sigma p chart is positive?

Correct AnswerverifiedLCL > 0 when . Afte...View AnswerShow Answer

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

Correct AnswerverifiedShow Answer

Which of the following statements are not true?

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

Correct AnswerverifiedShow Answer

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.

Correct AnswerverifiedShow Answer

When the out-of-control ARL corresponds to a shift of 1 standard deviation I the process mean, what are the characteristics of the CUSUM procedure that has ARL of 250 and 4.8 for the in-control and out-of-control conditions, respectively?

Correct AnswerverifiedIn- control ARL = 25...View AnswerShow Answer

Correct Answer
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a. The control limits are ; therefore ...
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Correct Answer
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Correct Answer
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Correct Answer
verified
Since = , then the control ...
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Correct Answer
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Correct Answer
verified
P(A) = Since then multiplying each en...
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Correct Answer
verified

Correct Answer
verified
operating ...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified
Thus LCL = 0 and UC...
View Answer

When n = 180, what is the smallest value of $\bar { P }$ for which the LCL in a 3-sigma p chart is positive?

Correct Answer
verified
LCL > 0 when . Afte...
View Answer

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

Correct Answer
verified

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.

Correct Answer
verified

Correct Answer
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In- control ARL = 25...
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