Question 1

The value of the process capability index, (Cp), depends on the mean of the process.

Accepted Answer

The process capability index, Cp, is calculated based on the specification limits and the process variation, but it does not directly depend on the process mean. It is a measure of the potential capability of a process to meet its specification limits if the process were centered within those limits.

Question 2

The relationship between the natural variation and specifications is quantified by a measure known as the _____.
A) net promoter score
B) process capability index
C) net detractor score
D) process design index

Accepted Answer

The relationship between the natural variation and specifications is quantified by a measure known as the process capability index. This index is a statistical measure that compares the natural variation of a process to the specification limits. A high process capability index indicates that the process has low variation relative to the specification limits, while a low process capability index indicates that the process has high variation relative to the specification limits.

Question 3

Which of the following is true of control charts
A) Control charts can only be used for processes that have a very high sigma level.
B) The use of small sample sizes in control charts increases the chances that a process may have changed during the sampling interval.
C) Conventional statistical process control charts have the lowest frequency of false alarms.
D) Standard control charts are not effective when the rate of defects is extremely low.

Accepted Answer

D

Question 4

A bottling machine fills water bottles with an average of 12.000 ounces of water. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine.
A) Less than or equal to 1
B) More than 1 but less than or equal to 2
C) More than 2 but less than or equal to 3
D) More than 4

Accepted Answer

The process capability index (Cpk) is calculated as the minimum of (USL - mean)/(3*standard deviation) and (mean - LSL)/(3*standard deviation). Here, USL = 12.015, LSL = 11.985, mean = 12.000, and standard deviation = 0.002. Cpk = min((12.015-12.000)/(3*0.002), (12.000-11.985)/(3*0.002)) = min(2.5, 2.5) = 2.5, which is more than 2 but less than or equal to 3.

Question 5

The task of__________is to ensure that a good or service conforms to specifications and meets customer requirements by monitoring and measuring processes and making any necessary adjustments to maintain a specified level of performance.
A) job design
B) visual control
C) quality control
D) forecasting

Accepted Answer

Quality control is responsible for ensuring that a product or service meets a certain level of quality, which is achieved by monitoring and measuring the manufacturing or delivery process and making necessary adjustments to maintain a specified level of performance. Job design pertains to determining the tasks, responsibilities, and requirements of a position or role, while visual control refers to using visual cues, such as signs or markings, to communicate important information or instructions. Forecasting involves estimating future demand or trends for a product or service.

Question 6

In the context of the net promoter score (NPS), scores of 7 or 8 are associated with__________, customers who are satisfied but may switch to competitors.
A) detractors
B) passives
C) promoters
D) proponents

Accepted Answer

Scores of 7 or 8 are classified as passives in the NPS system, which means they are satisfied customers who may switch to competitors. Detractors give scores of 0-6 and are unhappy customers who may spread negative word-of-mouth about the company. Promoters give scores of 9-10 and are highly satisfied customers who are loyal and likely to recommend the company to others.

Question 7

Keeping special cause variation from occurring is the essence of statistical quality control.

Accepted Answer

Statistical quality control aims to maintain consistency and stability in a process by identifying and controlling sources of special cause variation. By doing so, the process becomes more predictable and produces more consistent and reliable results. Therefore, the statement is true.

Question 8

Which of the following is true of common cause variation
A) It can be controlled and described using nonstatistical methods.
B) It appears at random, and individual sources cannot be identified or explained.
C) It accounts for about 10 to 15 percent of the observed variation in a process.
D) It arises from external sources that are not inherent in a process.

Accepted Answer

Common cause variation is also known as random variation and appears at random without any identifiable or explainable individual sources. It cannot be controlled by nonstatistical methods and accounts for the majority of variation in a process. It is inherent to the process and arises from internal sources. Therefore, options A, C, and D are incorrect.

Question 9

The 1:10:100 Rule states that if a defect is first detected during the production process, it might cost $1 to fix.

Accepted Answer

The answer of The 1:10:100 Rule states that if a...

Question 10

The time taken for guests to check out at a hotel front desk was measured over the course of several weeks. The management believes that the target time for checking out guests should be between 2 and 3 minutes with a target of 2.5 minutes. The data gathered for the actual process had a mean time of 2.75 minutes with a standard deviation of 0.45 minutes. The process capability index will be:
A) less than or equal to 1.
B) more than 3 but less than or equal to 5.
C) more than 4 but less than or equal to 5.
D) more than 5.

Accepted Answer

The process capability index (Cpk) can be calculated using the formula:
Cpk = min[(USL - Mean)/3*SD, (Mean - LSL)/3*SD]
where USL is the upper specification limit (3 minutes), LSL is the lower specification limit (2 minutes), Mean is the mean time taken for checkout (2.75 minutes) and SD is the standard deviation (0.45 minutes).

Substituting the values, we get:
Cpk = min[(3-2.75)/3*0.45, (2.75-2)/3*0.45]
Cpk = min[0.1667, 0.1667]
Cpk = 0.1667

Since the Cpk value is less than or equal to 1, the process is not capable of meeting the target time of 2.5 minutes. Therefore, the answer is A.

Question 11

In the context of designing control charts, which of the following is true of a sample size
A) A large sample allows small changes in process characteristics to be detected with higher probability than a small sample size.
B) A small sample is used to detect process shifts of two standard deviations or smaller.
C) A large sample size is desirable to keep the cost associated with sampling low.
D) A small sample size provides greater degrees of statistical accuracy in estimating the true state of control than a large sample size.

Accepted Answer

A large sample size allows for a higher probability of detecting small changes in process characteristics. This is because a larger sample size provides more information and reduces the influence of random variation. B is incorrect because a large sample size may still be needed to detect small shifts. C is incorrect because a large sample size can increase sampling costs. D is incorrect because a larger sample size generally provides more statistical accuracy in estimating the true state of control.

Question 12

In the context of quality control practices in manufacturing, if supplier documentation is done properly, incoming inspection can be completely eliminated.

Accepted Answer

If supplier documentation is done properly, it can provide evidence of quality control processes that the supplier has in place, and the quality of the product being delivered. This can eliminate or significantly reduce the need for incoming inspection. However, it is still important for the purchasing organization to have a sampling plan in place to verify the quality of the product, even if incoming inspection is eliminated.

Question 13

The lower and upper specification limits for a mustard filling machine are 10.50 and 12.00 ounces, respectively. The standard deviation is 0.05. The process capability index of the machine will be:
A) less than or equal to 3.
B) more than 3 but less than or equal to 5.
C) more than 4 but less than or equal to 5.
D) more than 5.

Accepted Answer

The process capability index (Cpk) can be calculated as:
Cpk = min[(USL - μ)/(3σ), (μ - LSL)/(3σ)]
where USL is the upper specification limit, LSL is the lower specification limit, μ is the mean of the process and σ is the standard deviation.

In this case, the mean of the process is not given. Therefore, we assume that the process is centered between the upper and lower specification limits, which gives us:
μ = (USL + LSL)/2 = (12.00 + 10.50)/2 = 11.25

Substituting the given values, we get:
Cpk = min[(12.00 - 11.25)/(3*0.05), (11.25 - 10.50)/(3*0.05)]
Cpk = min[5, 5]
Cpk = 5

Since the Cpk is greater than 4 but less than or equal to 5, the best choice is C. This indicates that the machine is very capable of producing mustard fillings within the specified range.

Question 14

In the context of the net promoter score (NPS), scores of 6 or below represent__________, unhappy customers who may spread negative comments.
A) detractors
B) passives
C) promoters
D) campaigners

Accepted Answer

In the net promoter score (NPS) system, scores of 6 or below indicate detractors, who are unhappy customers who are likely to spread negative comments about a company or product.

Question 15

In the context of statistical process control and variation, if no special causes affect the output of a process, we say that the process is__________.
A) inconsistent
B) out of control
C) in control
D) overadjusted

Accepted Answer

When no special causes affect the output of a process, we say that the process is in control. This means that the process operates within predictable and expected ranges, and any variation is due to common causes that are inherent in the process. In statistical process control, the goal is to keep the process in control to produce consistent, high-quality output.

Question 16

A cell phone manufacturer has been experiencing physical quality control problems. The back case of phones does not always fit and snap into place on the phone body. The dimensions of the case have constantly been in statistical process control (SPC). To monitor process control, the company uses -charts. Seven samples, each containing three phone cases, were selected from different batches. The data is presented in Table 1 below.
Table 1: Cell Phone Plastic Case Widths in Centimeters Data*
$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline \text { Observation } & \text { Sample 1 } & \text { Sample 2 } & \text { Sample 3 } & \text { Sample 4 } & \text { Sample 5 } & \text { Sample 6 } & \text { Sample 7 } \
\hline 1 & 6.02 & 5.92 & 5.88 & 5.99 & 6.05 & 5.94 & 6.00 \
\hline 2 & 5.97 & 5.83 & 5.97 & 6.08 & 6.06 & 5.96 & 5.95 \
\hline 3 & 5.90 & 5.87 & 5.88 & 6.08 & 5.98 & 5.99 & 5.82 \
\hline \text { Average } & 5.963 & 5.873 & 5.912 & 6.051 & 6.035 & 5.963 & 5.923 \
\hline \text { Range } & 0.12 & 0.09 & 0.09 & 0.09 & 0.08 & 0.05 & 0.18 \
\hline
\end{array}$
*The sample averages and ranges help avoid simple math errors and quicken the time to complete the SPC analysis.
If 
for the
-chart is 1.023, the lower control limit for the
-chart (LCL) will be:
A) less than or equal to 3.0.
B) greater than 3.0 but less than or equal to 4.0.
C) greater than 4.0 but less than or equal to 5.0.
D) greater than 5.0.

Accepted Answer

The lower control limit (LCL) for the R-chart can be calculated using the formula LCL = D4 * R̄, where D4 is a constant that depends on the sample size (in this case, 1.023 for the R-chart) and R̄ is the average range of the samples. Given the ranges provided in the table, the average range (R̄) can be calculated, and it will be a positive number. Since D4 is also positive, the product of D4 and R̄ will be a positive number, which, when considering the typical scale of measurements for such manufacturing processes, will likely place the LCL greater than 5.0, especially since the ranges are relatively small and the constant 1.023 would not reduce the value significantly to fall below 5.0.

Question 17

A detergent company periodically tests its products for variations in the fill weight. To do this, the company uses -charts. Eight samples, each containing six detergent boxes, were selected from different batches. Historical data for fill weight (in ounces) of the eight samples is presented below.
$\begin{array} { | l | l | l | } 
\hline \text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
\hline 2 & 16.10 & 0.38 \
\hline 3 & 16.02 & 0.08 \
\hline 4 & 15.95 & 0.15 \
\hline 5 & 16.12 & 0.42 \
\hline 6 & 16.18 & 0.23 \
\hline 7 & 15.87 & 0.36 \
\hline 8 & 16.20 & 0.40 \
\hline
\end{array}$
If A2>for the
-chart is 0.483, the upper control limit for the
-chart (UCL) will be:
A) less than or equal to 14.
B) more than 14 but less than or equal to 16.
C) more than 16 but less than or equal to 18.
D) more than 18.

Accepted Answer

To find the upper control limit (UCL) for the -chart, we need to use the formula:

UCL = Sample Mean + A2 x Sample Range

We are given A2=0.483, and we can find the maximum sample range from the given data as 0.42. So, the UCL will be:

UCL = 16.02 + 0.483 x 0.42
UCL ≈ 16.22

Since the UCL is calculated as 16.22, which is more than 16 but less than or equal to 18, the best choice is C.

Question 18

Customer waiting time and order lead time are examples of__________.
A) discrete metrics
B) countable metrics
C) isolated metrics
D) continuous metrics

Accepted Answer

Customer waiting time and order lead time are continuous metrics, meaning they are measured on a continuous scale and can have any value within a range. Discrete metrics are only measured in whole numbers or categories, countable metrics can be measured in whole numbers but also have an upper limit, and isolated metrics are not commonly used terms in the field of metrics.

Question 19

In-process control is typically performed by people who run the back-end processes.

Accepted Answer

In-process control is usually performed by personnel involved in the actual production process or by a quality control department, not specifically by those who run back-end processes. It involves monitoring and controlling the manufacturing process to ensure product quality and compliance with specifications.

Question 20

An operator wants to determine the standard deviation for a machine she operates. To do this, she wants to create a p-chart. Over a month's time, she collects 30 samples of 75 observations each and records the number of errors. The average proportion defective is found to be 0.024. Which of the following is the standard deviation ( ) of the machine?
A) Less than or equal to 0.1
B) More than 0.1 but less than or equal to 0.5
C) More than 0.5 but less than or equal to 1.0
D) More than 1.0

Accepted Answer

The standard deviation (σ) for a p-chart is calculated using the formula σ = sqrt[p(1-p)/n], where p is the average proportion defective, and n is the number of observations per sample. Substituting the given values, σ = sqrt[0.024(1-0.024)/75], which results in a value less than 0.1.

Quiz 16: Quality Control and SPC

The value of the process capability index, (Cp), depends on the mean of the process.

The relationship between the natural variation and specifications is quantified by a measure known as the _____.

Which of the following is true of control charts

A bottling machine fills water bottles with an average of 12.000 ounces of water. The standard deviation is 0.002 ounces. If the design specification for the fill weight of the bottles is 12.000 ounces plus or minus 0.015 ounces, calculate the process capability index of the machine.

The task of__________is to ensure that a good or service conforms to specifications and meets customer requirements by monitoring and measuring processes and making any necessary adjustments to maintain a specified level of performance.

In the context of the net promoter score (NPS) , scores of 7 or 8 are associated with__________, customers who are satisfied but may switch to competitors.

Keeping special cause variation from occurring is the essence of statistical quality control.

Which of the following is true of common cause variation

The 1:10:100 Rule states that if a defect is first detected during the production process, it might cost $1 to fix.

In the context of designing control charts, which of the following is true of a sample size

In the context of quality control practices in manufacturing, if supplier documentation is done properly, incoming inspection can be completely eliminated.

The lower and upper specification limits for a mustard filling machine are 10.50 and 12.00 ounces, respectively. The standard deviation is 0.05. The process capability index of the machine will be:

In the context of the net promoter score (NPS) , scores of 6 or below represent__________, unhappy customers who may spread negative comments.

In the context of statistical process control and variation, if no special causes affect the output of a process, we say that the process is__________.

Customer waiting time and order lead time are examples of__________.

In-process control is typically performed by people who run the back-end processes.