Question 1

Control charts for variables are based on data that come from:
A) acceptance sampling.
B) individual items.
C) averages of small samples.
D) averages of large samples.
E) the entire lot.

Accepted Answer

Control charts for variables often use averages of small samples to monitor the process variability and mean. This approach allows for the detection of shifts in the process mean or increases in variability over time.

Question 2

A manager wants to build 3-sigma x-bar control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 3. If samples of size 9 are to be taken, what will be the upper and lower control limits, respectively?
A) 19 and 1
B) 16 and 4
C) 13 and 7
D) 4 and 16
E) 7 and 13

Accepted Answer

The upper and lower 3-sigma control limits for an x-bar chart are calculated using the formula: UCL = μ + Z(σ/√n) and LCL = μ - Z(σ/√n), where μ is the process mean, σ is the process standard deviation, Z is the Z-value for the desired sigma level (for 3-sigma, Z=3), and n is the sample size. Here, μ=10, σ=3, Z=3, and n=9. Thus, UCL = 10 + 3*(3/√9) = 10 + 3 = 13, and LCL = 10 - 3*(3/√9) = 10 - 3 = 7.

Question 3

An x-bar control chart was examined and no data points fell outside of the limits. Can this process be considered in control?
A) Not yet, there could be a pattern to the points.
B) Not yet, the R-chart must be checked.
C) Not yet, the number of samples must be known.
D) Yes.
E) Both A and B

Accepted Answer

An x-bar chart showing all points within control limits does not guarantee a process is in control. Patterns within the control limits, such as cycles or trends, can indicate a lack of control. Additionally, the R-chart (range chart) must also be checked for out-of-control signals to ensure process variability is stable.

Question 4

The number of late insurance claim payouts per 100 should be measured with what type of control chart?
A) x-bar chart
B) R-chart
C) p-chart
D) c-chart
E) either p-chart or c-chart

Accepted Answer

The number of late insurance claim payouts is a count data and the proportion of the late payouts out of 100 claims can be calculated. Hence, the appropriate control chart to use is a p-chart.

Question 5

Red Top Cab Company receives multiple complaints per day about driver behavior. Over 8 days the owner recorded the number of calls to be 3, 0, 8, 9, 6, 7, 9, and 8. What is the upper control limit for the 3-sigma c-chart?
A) 13.35
B) 8.45
C) 6.25
D) 0.00
E) 13.75

Accepted Answer

The upper control limit (UCL) for a c-chart is calculated using the formula UCL = $ \bar{c} + 3\sqrt{\bar{c}} $, where $ \bar{c} $ is the average number of complaints per day. The average $ \bar{c} $ is $ \frac{3 + 0 + 8 + 9 + 6 + 7 + 9 + 8}{8} = 6.25 $. Plugging this into the formula gives UCL = $ 6.25 + 3\sqrt{6.25} = 6.25 + 3(2.5) = 6.25 + 7.5 = 13.75 $.

Question 6

Ten samples of a process measuring the number of returns per 200 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, and 11. Find the standard deviation of the sampling distribution for the p-bar chart.
A) There is not enough information to answer the question.
B) .081
C) .0405
D) .0273
E) .0139

Accepted Answer

The answer of Ten samples of a process measuring the...

Question 7

If = 23 ounces, σ = 1.0 ounces, and n = 16, what will be the ± 3σ control limits for the x-bar chart? 
A) 21.8 to 24.2 ounces
B) 23 ounces
C) 22.70 to 23.30 ounces
D) 22.25 to 23.75 ounces
E) 22.90 to 23.10 ounces

Accepted Answer

The answer of If = 23 ounces, σ = 1.0...

Question 8

Assignable causes:
A) are not as important as natural causes.
B) are within the limits of a control chart.
C) depend on the inspector assigned to the job.
D) are also referred to as "chance" causes.
E) are causes of variation that can be identified and investigated.

Accepted Answer

Assignable causes, also known as "special causes," are specific factors that can be identified and corrected. They are distinct from natural or common causes of variation, which are inherent to the process.

Question 9

A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 28.5, and the average range is 3.9. From Table S6.1, the appropriate value of D₃ is 0, and D₄ is 2.115. What are the UCL and LCL, respectively, for this range chart? A) 30.75 and 26.25 B) 40.2 and 16.8 C) 11.2 and 0 D) 8.25 and 0 E) 32.4 and 24.6

Accepted Answer

The answer of A manager wishes to build a 3-sigma...

Question 10

Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for:
A) Type I errors.
B) about 95.5% variation.
C) natural variation.
D) all types of variation.
E) assignable variation.

Accepted Answer

This is known as the control limits or the range of natural variation in a process. It allows for a certain amount of variation that is inherent in the process, while flagging any data points that fall outside of this range as potentially indicating an issue with the process that needs to be addressed. Choice A is incorrect because Type I errors refer to errors made in hypothesis testing, and are not directly related to statistical process control. Choice B is incorrect because while 95.5% of data falls within three standard deviations of the mean in a normal distribution, this does not necessarily apply to all processes or forms of data. Choice D is incorrect because statistical process control does not allow for all types of variation – for example, any variation due to external factors that is not inherent to the process being measured should be eliminated or controlled for. Choice E is incorrect because assignable variation refers to fluctuations in a process that can be traced back to specific causes, and should be addressed rather than simply allowed for.

Question 11

The upper and lower limits for diving ring diameters made by John's Swimming Co. are 40 and 39 cm., respectively. John took 11 samples with the following average diameters (39, 39.1, 39.2, 39.3, 39.4, 39.5 39.6, 39.7, 39.8, 39.9, 40). Is the process in control?
A) Yes, no diameters exceeded the control limits.
B) No, some diameters exceeded the control limits.
C) No, there is a distinguishable pattern to the samples.
D) No, the range is not in control.
E) There is not enough information to make a decision.

Accepted Answer

The samples show a distinguishable pattern of increasing diameters, which may indicate a trend or systematic issue in the process.

Question 12

Statistical process control charts:
A) display the measurements on every item being produced.
B) display upper and lower limits for process variables or attributes and signal when a process is no longer in control.
C) indicate to the process operator the average outgoing quality of each lot.
D) indicate to the operator the true quality of material leaving the process.
E) are a graphic way of classifying problems by their level of importance, often referred to as the 80-20 rule.

Accepted Answer

Statistical process control charts display upper and lower limits for process variables or attributes and signal when a process is no longer in control. They are used to monitor and control a process, not to classify problems by their level of importance or indicate the true quality of material leaving the process.

Question 13

To set x-bar chart upper and lower control limits, one must know the process central line, which is the:
A) average of the sample means.
B) total number of defects in the population.
C) percent defects in the population.
D) size of the population.
E) average range.

Accepted Answer

The process central line for an x-bar chart is the average of the sample means. This is because the x-bar chart tracks the process mean over time, and the mean of the sample means is the best estimate of the process mean. The upper and lower control limits are set based on the variability of the process, which is measured by the average range.

Question 14

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?
A) Since there is no obvious pattern in the measurements, variability is in control.
B) One value outside the control limits is insufficient to warrant any action.
C) Lower than expected dispersion is a desirable condition; there is no reason to investigate.
D) The process is out of control; reject the last units produced.
E) Variation is not in control; investigate what created this condition.

Accepted Answer

When the most recent value is below the lower control limit, it indicates that the process is out of control and that variability is not in control. Therefore, it is necessary to investigate what has caused this condition to occur.

Question 15

The usual purpose of an R-chart is to signal whether there has been a:
A) gain or loss in dispersion.
B) change in the percent defective in a sample.
C) change in the central tendency of the process output.
D) change in the number of defects in a sample.
E) change in the consumer's risk.

Accepted Answer

The R-chart is used to monitor the variability or dispersion of a process. It tracks the range (R) of a sample and detects changes in dispersion. If there has been a gain or loss in dispersion, the R-chart will signal that there is a problem in the process.

Question 16

Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?
A) p-chart
B) c-chart
C) both an x-bar chart and an R-chart
D) an x-bar chart, but not an R-chart
E) both a p-chart and a c-chart

Accepted Answer

Since the weight of the jars of pickles is continuous data, an x-bar chart and an R-chart will be appropriate for monitoring the mean and range of the weights. The ideal weight should be precisely 11 oz, so we want to monitor any deviations from this value. A p-chart and c-chart are suitable for attribute data, where the focus is on the proportion of nonconforming items or the count of nonconforming items, respectively. Therefore, the best option is an x-bar chart and an R-chart.

Question 17

The purpose of an x-bar chart is to determine whether there has been a:
A) change in the dispersion of the process output.
B) change in the percent defective in a sample.
C) change in the central tendency of the process output.
D) change in the number of defects in a sample.
E) change in the AOQ.

Accepted Answer

X-bar chart is used to monitor the central tendency of a process output. It helps to identify whether there has been a shift in the mean or not. The chart plots the sample means, and the control limits are based on the process variation. Hence, any point outside those limits signals a significant change in the central tendency of the process output.

Question 18

The Central Limit Theorem:
A) is the theoretical foundation of the c-chart.
B) states that the average of assignable variations is zero.
C) allows managers to use the normal distribution as the basis for building some control charts.
D) states that the average range can be used as a proxy for the standard deviation.
E) controls the steepness of an operating characteristic curve.

Accepted Answer

The Central Limit Theorem allows managers to use the normal distribution as the basis for building some control charts.

Question 19

The number of defects after a hotel room cleaning (sheets not straight, smears on mirror, missed debris on carpet, etc.) should be measured using what type of control chart?
A) x-bar chart
B) R-chart
C) p-chart
D) c-chart
E) either x-bar chart or R chart

Accepted Answer

A c-chart is used for counting the number of defects per unit when the number of opportunities for defects is constant. In this scenario, each hotel room cleaning session is a unit with various opportunities for defects (e.g., sheets not straight, smears on mirror, missed debris on carpet), making the c-chart the appropriate choice for monitoring the number of defects.

Question 20

A process that is assumed to be in control with limits of 89 ± 2 had sample averages for the x-bar chart of the following: 87.1, 87, 87.2, 89, 90, 88.5, 89.5, and 88. Is the process in control?
A) Yes.
B) No, one or more averages exceeded the limits.
C) Not enough information to tell.
D) No, there is a distinguishable trend.
E) No, two or more consecutive points are very near the lower (or upper) limit.

Accepted Answer

The answer of A process that is assumed to be...

Quiz 7: Process Strategies

Control charts for variables are based on data that come from:

A manager wants to build 3-sigma x-bar control limits for a process. The target value for the mean of the process is 10 units, and the standard deviation of the process is 3. If samples of size 9 are to be taken, what will be the upper and lower control limits, respectively?

An x-bar control chart was examined and no data points fell outside of the limits. Can this process be considered in control?

The number of late insurance claim payouts per 100 should be measured with what type of control chart?

Red Top Cab Company receives multiple complaints per day about driver behavior. Over 8 days the owner recorded the number of calls to be 3, 0, 8, 9, 6, 7, 9, and 8. What is the upper control limit for the 3-sigma c-chart?

Ten samples of a process measuring the number of returns per 200 receipts were taken for a local retail store. The number of returns were 10, 9, 11, 7, 3, 12, 8, 4, 6, and 11. Find the standard deviation of the sampling distribution for the p-bar chart.

If = 23 ounces, σ = 1.0 ounces, and n = 16, what will be the ± 3σ control limits for the x-bar chart?

Assignable causes:

A manager wishes to build a 3-sigma range chart for a process. The sample size is five, the mean of sample means is 28.5, and the average range is 3.9. From Table S6.1, the appropriate value of D₃ is 0, and D₄ is 2.115. What are the UCL and LCL, respectively, for this range chart?

Up to three standard deviations above or below the centerline is the amount of variation that statistical process control allows for:

The upper and lower limits for diving ring diameters made by John's Swimming Co. are 40 and 39 cm., respectively. John took 11 samples with the following average diameters (39, 39.1, 39.2, 39.3, 39.4, 39.5 39.6, 39.7, 39.8, 39.9, 40) . Is the process in control?

Statistical process control charts:

To set x-bar chart upper and lower control limits, one must know the process central line, which is the:

Plots of sample ranges indicate that the most recent value is below the lower control limit. What course of action would you recommend?

The usual purpose of an R-chart is to signal whether there has been a:

Jars of pickles are sampled and weighed. Sample measures are plotted on control charts. The ideal weight should be precisely 11 oz. Which type of chart(s) would you recommend?

The purpose of an x-bar chart is to determine whether there has been a:

The Central Limit Theorem:

The number of defects after a hotel room cleaning (sheets not straight, smears on mirror, missed debris on carpet, etc.) should be measured using what type of control chart?

A process that is assumed to be in control with limits of 89 ± 2 had sample averages for the x-bar chart of the following: 87.1, 87, 87.2, 89, 90, 88.5, 89.5, and 88. Is the process in control?