Question 1

Ten samples of a process measuring the number of returns per 100 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)8.1
D).0273
E).0863

Accepted Answer

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

Question 2

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 answer of The upper and lower limits for diving...

Question 3

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 4

For a 3-sigma x-bar chart where the process standard deviation is known,the upper control limit:
A)is 3σ below the mean of sample means for a 3σ control chart.
B)is 3σ above the mean of sample means for a 3σ control chart.
C)is 3σ/  below the mean of sample means for a 3σ control chart.
D)is 3σ/  above the mean of sample means for a 3σ control chart.
E)cannot be calculated unless the average range is known.

Accepted Answer

The answer of For a 3-sigma x-bar chart where the...

Question 5

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

An R-chart (range chart) is used in statistical process control to monitor the variability of a process. It plots the range of a sample against the sample number or time. The purpose is to detect if there has been a gain or loss in dispersion, which could indicate that the process is out of control or that a change has occurred in the process. Therefore, option A is the best choice.

Question 6

Red Top Cab Company receives multiple complaints per day about driver behavior.Over 9 days the owner recorded the number of calls to be 3,0,8,9,6,7,4,9,and 8.What is the upper control limit for the 3-sigma c-chart?
A)13.35
B)8.45
C)24.00
D)0.00
E)9.03

Accepted Answer

1. Calculate the average: 
(3+0+8+9+6+7+4+9+8)/9 = 6.44

2. Calculate the standard deviation: 
First, find the variance:
[(3-6.44)^2+(0-6.44)^2+(8-6.44)^2+(9-6.44)^2+(6-6.44)^2+(7-6.44)^2+(4-6.44)^2+(9-6.44)^2+(8-6.44)^2]/9
= 5.91

Then, calculate the standard deviation: 
sqrt(5.91) = 2.43

3. Calculate the upper control limit: 
UCL = 6.44 + 3*(2.43) 
= 13.35

Therefore, the upper control limit for the 3-sigma c-chart is 13.35.

Question 7

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

The amount of variation that SPC allows for is known as natural variation, and it is typically measured by the standard deviation. It is generally accepted that up to three standard deviations above or below the centerline is a normal amount of variation that can be expected in a process. This range typically accounts for about 99.7% of all possible outcomes, which means that only 0.3% of all data points would fall outside this range. Therefore, option C is the correct choice.

Question 8

Natural variations:
A)are variations that are to be identified and investigated.
B)are variations that can be traced to a specific cause.
C)are the same as assignable variations.
D)lead to occasional false findings that processes are out of control.
E)play no role in statistical process control.

Accepted Answer

The answer of Natural variations:
A)are variations that are to be...

Question 9

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 10

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...

Question 11

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 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 help to maintain quality control by identifying variations in the process and helping to detect potential problems early on. They do not display measurements on every item being produced, indicate the average outgoing quality of each lot, indicate the true quality of material leaving the process, or classify problems by their level of importance.

Question 13

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 14

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 6.If samples of size 9 are to be taken,what will be the upper and lower control limits,respectively?
A)-8 and 28
B)16 and 4
C)12 and 8
D)4 and 16
E)8 and 12

Accepted Answer

The answer of A manager wants to build 3-sigma x-bar...

Question 15

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

As the weight of the pickles is measured continuously, and the ideal weight is a precise value, it is best to use both an x-bar chart and an R-chart to plot the sample measures. The x-bar chart will give the central tendency of the sample means while the R-chart will show the variability of sample ranges. Together, they will help to monitor and control the process, ensuring that the jars of pickles are within the desired weight range of 11 oz.

Question 16

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 17

If  = 23 ounces,σ = 0.4 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 formula for control limits for the x-bar chart is:
Upper control limit (UCL) = x-bar + ARL * σ/sqrt(n)
Lower control limit (LCL) = x-bar - ARL * σ/sqrt(n)

Where ARL (Average Run Length) is the constant value obtained from the ARL table for the desired control limit. For ±3σ control limits and n = 16, ARL = 2.574.

Substituting the given values:
UCL = 23 + 2.574 * 0.4/sqrt(16) = 23.3 ounces
LCL = 23 - 2.574 * 0.4/sqrt(16) = 22.7 ounces

Therefore, the ±3σ control limits for the x-bar chart are 22.70 to 23.30 ounces, which is option C.

Question 18

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

The purpose of an x-bar chart is to determine if there has been a change in the central tendency of the process output, which is usually indicated by the mean of the sample data. The chart plots the sample mean values against their corresponding sample numbers over time, allowing the process operator to detect any shifts or trends in the data that may indicate a change in the mean value of the process output. The other options (A, B, D, and E) are not relevant to the x-bar chart's purpose.

Question 19

Assignable variation:
A)is a sign that a process is under control.
B)is to be identified and investigated.
C)is the same as random variation.
D)is variation that cannot be traced to a specific cause.
E)leads to a steep OC curve.

Accepted Answer

Assignable variation refers to variation in a process that can be traced to a specific cause, such as a defect in a machine or a mistake made by an operator. It is important to identify and investigate this type of variation in order to improve the process and eliminate the root cause. Random variation, on the other hand, cannot be attributed to a specific cause and is inherent in any process. Therefore, assignable variation is not the same as random variation (choice C) and is not a sign that a process is under control (choice A). Additionally, there is no indication that assignable variation leads to a steep OC (operating characteristic) curve (choice E).

Question 20

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.

Quiz 19: Statistical Process Control

Ten samples of a process measuring the number of returns per 100 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.

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?

Assignable causes:

For a 3-sigma x-bar chart where the process standard deviation is known,the upper control limit:

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

Red Top Cab Company receives multiple complaints per day about driver behavior.Over 9 days the owner recorded the number of calls to be 3,0,8,9,6,7,4,9,and 8.What is the upper control limit for the 3-sigma c-chart?

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

Natural variations:

The Central Limit Theorem:

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?

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?

Statistical process control charts:

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

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 6.If samples of size 9 are to be taken,what will be the upper and lower control limits,respectively?

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?

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

If = 23 ounces,σ = 0.4 ounces,and n = 16,what will be the ±3σ control limits for the x-bar chart?

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

Assignable variation:

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