Question 1

Which of the following statements are not true?

Accepted Answer

The answer of Which of the following statements are not...

Question 2

Suppose a control chart is constructed so that the probability of a point falling outside the control limits when the process is actually in control is .005.
a. What is the probability that ten successive points (based on independently selected samples) will be within the control limits?
b. What is the probability that 25 successive points will all lie within the control limits?
c. What is the smallest number of successive points plotted for which the probability of observing at least one outside the control limits exceeds .10?

Accepted Answer

The answer of Suppose a control chart is constructed so...

Question 3

A manufacturer of dustless chalk instituted a quality control program to monitor chalk density. The sample standard deviations of densities of n = 8 chalk specimens, were as follow: $$\begin{array} { l l l l l l l l } 
.165 & .231 & .073 & .165 & .292 & .371 & .179 & .234 \
.408 & .207 & .170 & .249 & .296 & .138 & .111 & .076 \
.224 & .335 & .116 & .204 & .250 & .232 & .342 & .307
\end{array}$$ Calculate limits for an S chart, and check for out-of-control points. If there is an out-of-control point, delete it and repeat the process.

Accepted Answer

The answer of A manufacturer of dustless chalk instituted a...

Question 4

A sample of ROM computer chips was selected on each of 30 consecutive days, and the number of nonconforming chips on each day was as follows: $$\begin{array} { l l l l l l l l l l } 
30 & 16 & 17 & 22 & 19 & 18 & 16 & 23 & 13 & 21 \
18 & 19 & 13 & 25 & 31 & 17 & 12 & 21 & 15 & 29 \
11 & 19 & 25 & 18 & 38 & 20 & 8 & 26 & 12 & 25
\end{array}$$ Determine control limits for a 3-sigma p chart and specify any out-of-control points.

Accepted Answer

The answer of A sample of ROM computer chips was...

Question 5

Consider a double-sampling plan with $n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6$ Which of the following equalities are not correct if the lot will be accepted?

Accepted Answer

In a double-sampling plan, the lot is accepted in the first stage if $x_1 \leq c_1$, which means if the number of defects in the first sample ($x_1$) is less than or equal to the acceptance number for the first sample ($c_1$). Given $c_1 = 2$, any $x_1 > 2$ would not lead to acceptance in the first stage. For option A, $x_1 = 5$, which is greater than $c_1$, so the lot would not be accepted based on the first sample alone, making the conditions for acceptance in option A incorrect.

Question 6

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

Statement D is not true because the larger the proportion of defective items in the lot (p), the smaller the probability of accepting the lot (P(A)). This is because a higher proportion of defects makes it more likely that the sample will contain enough defects to reject the lot.

Question 7

Subgroups of power supply units are selected once each hour from an assembly line, and the high-voltage output of each unit is determined.
a. Suppose the sum of the resulting sample ranges for 30 subgroups, each consisting of four units, is 84. Calculate control limits for an R chart.
b. Repeat part (a) if each subgroup consists of eight units and the sum is 105.

Accepted Answer

The answer of Subgroups of power supply units are selected...

Question 8

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

Accepted Answer

The answer of In the case of known \(\mu \text...

Question 9

For what $$\bar { x }$$ values will the LCL in a 3-sigma c chart be negative?

Accepted Answer

The answer of For what $$\bar { x }$$ values...

Question 10

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

The answer of The accompanying observations are numbers of defects...

Question 11

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

The answer of The accompanying table gives sample means and...

Question 12

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

Accepted Answer

When accepting a lot without thoroughly inspecting it, there is a risk of accepting poor quality, which is referred to as consumer's risk. It is a Type II error where the lot is accepted as good but is actually bad. Type I error refers to rejecting a good lot while producer's risk is the risk of rejecting a good lot. Bad luck lot is not a recognized term in acceptance sampling.

Question 13

A control chart for thickness of rolled-steel sheets is based on an upper control limit of .0525 inch and a lower limit of .0475 inch. The first ten values of the quality statistic (in this case $\bar { X }$ the sample mean thickness of n =5 sample sheets) are .0508, .0495, .0504, .0503, .0514, .0500, .0487, .0502, .0507, and .0485. Comment on the behavior of this control chart.

Accepted Answer

The answer of A control chart for thickness of rolled-steel...

Question 14

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

The answer of When n = 180, what is the...

Question 15

Consider a 3-sigma control chart with center line at $\mu _ { 0 }$ and based on n = 5. Assuming normality, calculate the probability that a single point will fall outside the control limits when the actual process mean is 
a. $\mu _ { 0 } + .5 \sigma$ 
b. $\mu _ { 0 } - \sigma$ 
c. $\mu _ { 0 } + 2 \sigma$

Accepted Answer

The answer of Consider a 3-sigma control chart with center...

Question 16

A control chart for thickness of rolled-steel sheets is based on an upper control limit of .0525 inch and a lower limit of .0475inch. Suppose the ten most recent values of the quality statistic are .0493, .0485, .0490, .0503, .0492, .0486, .0495, .0494, .0493, and .0488. Comment on the behavior of this control chart.

Accepted Answer

The answer of A control chart for thickness of rolled-steel...

Question 17

Consider the control chart based on control limits $\mu _ { 0 } \pm 2.575 \sigma / \sqrt { n }$ 
a. What is the ARL when the process is in control?
b. What is the ARL when n = 4 and the process mean has shifted to $\mu = \mu _ { 0 } + \sigma$ 
? 
c. How do the values of parts (a) and (b) compare to the corresponding values for a 3-sigma chart?

Accepted Answer

The answer of Consider the control chart based on control...

Question 18

In acceptance sampling, the risk of rejecting a good quality lot is considered a

Accepted Answer

The risk of rejecting a good quality lot is considered a producer's risk in acceptance sampling. This refers to the risk that a producer or supplier will have to bear the cost of rejecting a good lot due to a sample not being representative of the whole lot. This can be costly for the producer, as they may have to go through the entire production process again to produce a new lot that meets the customer's requirements.

Question 19

Which of the following statements are not true?

Accepted Answer

B) is incorrect because the Average Outgoing Quality (AOQ) refers to the expected proportion of defective items in the lot that are passed on to the customer after inspection, not before the sampling plan is employed.

Question 20

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

The answer of On each of the previous 25 days,...

Quiz 16: Quality Control Methods

Which of the following statements are not true?

Consider a double-sampling plan with $n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6$ Which of the following equalities are not correct if the lot will be accepted?

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?

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

For what $\bar { x }$ values will the LCL in a 3-sigma c chart be negative?

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

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

In acceptance sampling, the risk of rejecting a good quality lot is considered a

Which of the following statements are not true?

Quiz 16: Quality Control Methods

Which of the following statements are not true?

Consider a double-sampling plan with n1=80,n2=80,c1=2,r1=5, and c2=6n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6n1​=80,n2​=80,c1​=2,r1​=5, and c2​=6 Which of the following equalities are not correct if the lot will be accepted?

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?

In the case of known μ and σ,\mu \text { and } \sigma ,μ and σ, what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

For what xˉ\bar { x }xˉ values will the LCL in a 3-sigma c chart be negative?

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

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?

In acceptance sampling, the risk of rejecting a good quality lot is considered a

Which of the following statements are not true?

Consider a double-sampling plan with $n _ { 1 } = 80 , n _ { 2 } = 80 , c _ { 1 } = 2 , r _ { 1 } = 5 , \text { and } c _ { 2 } = 6$ Which of the following equalities are not correct if the lot will be accepted?

In the case of known $\mu \text { and } \sigma ,$ what control limits are necessary for the probability of a single point being outside the limits for an in-control process to be .003?

For what $\bar { x }$ values will the LCL in a 3-sigma c chart be negative?

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