Question 1

Which of the following is most closely related to a discrete metric?

Accepted Answer

C-charts are used for counting the number of defects in an item or process and are based on discrete data, which aligns with the concept of a discrete metric.

Question 2

If one was monitoring the average time to load a web page, the chart to use would be a(n) _____.

Accepted Answer

The R- or x-bar chart would be the best choice as it is used for monitoring process variation over time and measuring the average time to load a web page is a measure of process variation. The sample-size chart is used to track the sample size over time and would not be appropriate for this scenario. The p-chart and c-chart are used for monitoring proportion and count, respectively, and are not suitable for measuring page load times.

Question 3

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times
 $\begin{array} { | c | c | c | c | } 
\hline \begin{array} { c } 
\text { Sample } \
\text { Number }
\end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \
\hline & 1 & 2 & 3 \
\hline 1 & 9.6 & 10.2 & 9.8 \
\hline 2 & 9.4 & 10.0 & 10.4 \
\hline 3 & 9.9 & 9.6 & 9.0 \
\hline 4 & 9.3 & 10.5 & 9.9 \
\hline 5 & 9.7 & 9.2 & 9.7 \
\hline
\end{array}$
-Given the previous results and analysis for the R-chart regarding service waiting times, one would:

Accepted Answer

The R-chart, or range chart, is used to monitor the variation within a process. The data provided does not show any sample with extreme variation compared to others, and there's no indication of non-random patterns or trends in the range values across the samples. Therefore, it's reasonable to conclude that the process variation is in control, allowing the next step of developing the x-bar chart to monitor the process mean.

Question 4

The center line (p-bar) for a p-chart is 0.50 with an ULC = 0.70 and a LCL = 0.35. The results of the next eight sample means are 0.45, 0.60, 0.39, 0.44, 0.48, 0.58, 0.54, and 0.64. Which of the following actions should be taken in this scenario?

Accepted Answer

The answer of The center line (p-bar) for a p-chart...

Question 5

Identify the chart that is also known as fraction nonconforming or fraction defective chart.

Accepted Answer

The p-chart, also known as the fraction nonconforming or fraction defective chart, is used to monitor the proportion of nonconforming units or defects in a process. The chart plots the fraction of nonconforming units or defects over time and helps to identify if the process is stable or if there are any changes in the proportion of nonconforming units or defects.

Question 6

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times $\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Sample } \ \text { Number } \end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \ \hline & 1 & 2 & 3 \ \hline 1 & 9.6 & 10.2 & 9.8 \ \hline 2 & 9.4 & 10.0 & 10.4 \ \hline 3 & 9.9 & 9.6 & 9.0 \ \hline 4 & 9.3 & 10.5 & 9.9 \ \hline 5 & 9.7 & 9.2 & 9.7 \ \hline \end{array}$ -In Table 1, the sample values represent service waiting times in minutes. For the R-chart, what is the value of UCL_R?

Accepted Answer

The UCL for an R-chart is calculated using the formula UCL_R = D4 * R-bar, where D4 is a constant that depends on the sample size. For a sample size of 3, D4 is approximately 2.114. The average range (R-bar) is calculated as the average of the ranges of each sample. The ranges are 0.6, 1.0, 0.9, 1.2, and 0.5, with an average of 0.84. Thus, UCL_R = 2.114 * 0.84 = 1.776, which falls in the range greater than 1.5 but less than or equal to 2.0.

Question 7

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of six was used.
 $\begin{array} { c c c } 
\text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
2 & 16.10 & 0.38 \
3 & 16.02 & 0.08 \
4 & 15.95 & 0.15 \
5 & 16.12 & 0.42 \
6 & 16.18 & 0.23 \
7 & 15.87 & 0.36 \
8 & 16.20 & 0.40
\end{array}$ Worksheet (this will not be graded but will help you answer exam questions)
  
-For the Proctor and Gamble detergent box problem, based on the control charts it can be said that _____.

Accepted Answer

The answer of A Proctor and Gamble factory process fills...

Question 8

The center line (p-bar) for a p-chart is 0.50 with an ULC = 0.65 and a LCL = 0.35. The results of the next eight sample means are 0.45, 0.60, 0.39, 0.44, 0.48, 0.58, 0.54, and 0.64. Which of the following is the best action to take?

Accepted Answer

The answer of The center line (p-bar) for a p-chart...

Question 9

A c-chart _____.

Accepted Answer

A c-chart is specifically designed to monitor the number of nonconformances (defects) per unit or item, which is a count of occurrences rather than a measurement of a continuous metric.

Question 10

Which is NOT related to a discrete metric?

Accepted Answer

Time is a continuous metric, not a discrete metric. Discrete metrics involve distinct, separate values, such as counting or visual yes or no inspection. Good or bad can also be considered a discrete metric as it is binary (either good or bad), but time is not.

Question 11

Indications in a control chart of an out-of-control situation include all of the following EXCEPT:

Accepted Answer

A control chart is a tool used in quality control to monitor a process and detect any deviations from the expected performance. An out-of-control situation is indicated by points that lie outside the upper and lower control limits or a cyclical pattern in the chart, indicating a variation that is not random. A shift in the average value is also an indication of an out-of-control situation. However, having the same number of points above and below the centerline is not a reliable indicator of an out-of-control situation.

Question 12

Which of the following statements is TRUE?

Accepted Answer

B is true because p-charts are used for attributes data representing proportions, and c-charts are used for count data, both of which are types of discrete data.

Question 13

Given that 20 samples are taken in a control chart initiative, the probability that 5 consecutive samples are below the center line in an R- or x-bar chart is _____.

Accepted Answer

The probability of a single point being below the centerline is 0.5 (assuming the process is in control and centered on the centerline). 
The probability of 5 consecutive points being below the centerline is (0.5)^5 = 0.03125. 
Since there are 16 groups of 5 consecutive samples (20-5+1), we need to multiply 0.03125 by 16 to get the total probability of observing 5 consecutive samples below the centerline. 
This gives us 0.03125 x 16 = 0.5. So the answer is B.

Question 14

A Proctor and Gamble factory process fills boxes with detergent. Construct an appropriate set of control charts to monitor the process. Historical data for fill weight (in ounces) of eight samples is presented below. A sample size of six was used.
 $\begin{array} { c c c } 
\text { Sample } & \text { Sample Mean } & \text { Sample Range } \
\hline 1 & 15.80 & 0.42 \
2 & 16.10 & 0.38 \
3 & 16.02 & 0.08 \
4 & 15.95 & 0.15 \
5 & 16.12 & 0.42 \
6 & 16.18 & 0.23 \
7 & 15.87 & 0.36 \
8 & 16.20 & 0.40
\end{array}$ Worksheet (this will not be graded but will help you answer exam questions)
  
-For the Proctor and Gamble detergent box problem, the lower control limit for the x-bar chart is _____.

Accepted Answer

The lower control limit (LCL) for an x-bar chart is calculated using the formula: LCL = X̄ - A2 * R̄. Without specific values for X̄ (the process mean) and R̄ (the average range), we can infer from the options that the LCL is more than 14 but less than or equal to 16.

Question 15

Which of the following is NOT related to a continuous metric?

Accepted Answer

Length, x-bar and R-charts, and time are all continuous metrics that can be measured with precise numerical values. A p-chart, on the other hand, is used to monitor the proportion of nonconforming items in a sample, which is a categorical or discrete metric.

Question 16

Table 1-Statistical Process Control (SPC) Problem Data for Service Waiting Times $\begin{array} { | c | c | c | c | } \hline \begin{array} { c } \text { Sample } \ \text { Number } \end{array} & \multicolumn{3}{|c|} { \text { Observation Number } } \ \hline & 1 & 2 & 3 \ \hline 1 & 9.6 & 10.2 & 9.8 \ \hline 2 & 9.4 & 10.0 & 10.4 \ \hline 3 & 9.9 & 9.6 & 9.0 \ \hline 4 & 9.3 & 10.5 & 9.9 \ \hline 5 & 9.7 & 9.2 & 9.7 \ \hline \end{array}$ -Using Table 1, for the R-chart, what is the value of LCL_R?

Accepted Answer

The answer of Table 1-Statistical Process Control (SPC) Problem Data...

Question 17

Honda wants to monitor the number of blemishes (scratches, blisters, etc.) on the fenders of its cars using a statistical process control chart. The most appropriate type of statistical process control (SPC) chart that can be used in this scenario is a(n) _____.

Accepted Answer

The most appropriate SPC chart to monitor the number of blemishes on the fenders of cars is the c-chart. This chart is used to control the count of defects or nonconformities in a given sample or unit. Since the number of blemishes can be counted and the occurrence rate may vary between cars, a c-chart would be the most suitable choice for monitoring the number of blemishes. The x-bar chart and R-chart are more suitable for continuous data, while the Cpk chart is used to measure how well a process meets a set of specifications.

Question 18

To monitor the fraction of printed circuit boards that do not pass a functional test, a(n) _____ is used.

Accepted Answer

The p-chart would be the best choice for monitoring the fraction of printed circuit boards that do not pass a functional test. The p-chart is used for monitoring the proportion of nonconforming units in a sample. In this case, the sample would be the total number of printed circuit boards that have been tested, and the nonconforming units would be the ones that fail the functional test.

Question 19

A p-chart _____.

Accepted Answer

A p-chart is a statistical process control chart that is used to monitor the proportion of nonconforming items in a sample. It is typically used with categorical data, where each item is classified as either conforming or nonconforming. The chart plots the proportion of nonconforming items for each sample taken over time, and allows organizations to detect when the proportion of nonconforming items is outside of an acceptable range. Answers B, C, and D are all incorrect as they do not accurately describe a p-chart.

Question 20

Which of the following suggests a process that is NOT in control?

Accepted Answer

A process that is in control will have points that fall randomly above and below the center line, not follow a smooth pattern from one control limit to the other. This smooth pattern suggests a systematic variation, indicating the process is not in control.

Quiz 16: Quality Control and Spc