Question 1

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

Accepted Answer

The x-bar chart is used to monitor the central tendency of a process output, typically the mean, to determine whether there is a significant change or shift in the process. This can help identify whether the process is stable or not and guide corrective actions if needed. The other options (A, B, D, E) each relate to different quality metrics and control charts (such as the R chart or p-chart) that are used for monitoring other aspects of the process output.

Question 2

Statistical process control charts:

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 do not display the 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 3

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

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 4

Natural variations:

Accepted Answer

The answer of Natural variations:
...

Question 5

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?

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 6

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?

Accepted Answer

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

Question 7

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

Accepted Answer

To calculate control limits for the x-bar chart, we use the formula:
Control limits = x-bar ± 3σ/√n
Here, x-bar = 23 ounces, σ = 0.4 ounces, and n = 16.
Plugging in the values, we get:
Control limits = 23 ± 3(0.4)/√16
= 23 ± 3(0.1)
= 23 ± 0.3
= 22.7 to 23.3 ounces
Therefore, the best choice is C.

Question 8

The Central Limit Theorem:

Accepted Answer

The Central Limit Theorem states that the distribution of the means of a large sample of data will be approximately normal, regardless of the underlying distribution of the population. This allows managers to use the normal distribution as the basis for building some control charts.

Question 9

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.

Accepted Answer

The standard deviation of the sampling distribution for a p-bar chart is calculated using the formula: sqrt[(p(1-p))/n], where p is the average proportion of returns and n is the sample size. Here, p = (10+9+11+7+3+12+8+4+6+11)/1000 = 0.081, and n = 10. Plugging these values into the formula gives approximately 0.0273.

Question 10

Assignable variation:

Accepted Answer

Assignable variation refers to variation that can be traced to a specific cause or source. It is important to identify and investigate this type of variation in order to improve the process and eliminate the cause of the variation. This is in contrast to random variation, which is inherent in any process and cannot be completely eliminated. Therefore, it is not a sign that a process is under control, nor is it the same as random variation. It also does not necessarily lead to a steep OC (operating characteristic) curve, which is a graphical representation of the relationship between a process's capability and the proportion of defects it produces.

Question 11

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?

Accepted Answer

To find the upper control limit for a 3-sigma c-chart, we use the formula UCL = c̄ + 3√c̄, where c̄ is the average number of calls per day.

c̄ = (3+0+8+9+6+7+4+9+8)/9 = 6.44

UCL = 6.44 + 3√6.44 = 13.35

Therefore, the upper control limit for the 3-sigma c-chart is 13.35. So, the best choice is A.

Question 12

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?

Accepted Answer

Since weight is a continuous variable, we need to use an x-bar chart to monitor the average weight of the jars and an R-chart to monitor the variability of the weights. A p-chart is used for discrete variables such as the proportion of defective items in a sample, while a c-chart is used for count data such as the number of defects per unit. Therefore, neither a p-chart nor a c-chart is appropriate for monitoring the weight of the jars of pickles.

Question 13

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

Accepted Answer

The p-chart is used to monitor the proportion of nonconforming items in a sample. In this case, the proportion of late insurance claim payouts can be measured and plotted on a p-chart. The c-chart is used for monitoring the number of defects per unit, which may not be applicable in this scenario.

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?

Accepted Answer

The control limits are calculated using the formula: Mean ± 3*(Standard Deviation/√n). Here, Mean = 10, Standard Deviation = 6, n = 9. So, the limits are 10 ± 3*(6/√9) = 10 ± 6, which gives 16 and 4.

Question 15

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

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 16

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

Accepted Answer

An R-chart is used to monitor the dispersion or variability of a process. It signals whether there has been a gain or loss in dispersion, indicating whether the process is becoming more or less predictable. A change in the percent defective, central tendency, or number of defects may also affect the process variability and be detected by an R-chart, but the primary purpose is to monitor dispersion.

Question 17

Assignable causes:

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 18

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

Accepted Answer

Up to three standard deviations above or below the centerline is the range of natural variation allowed in statistical process control. This range accounts for around 99.7% of all expected variation, leaving only 0.3% for assignable variation or errors beyond the control limits. Therefore, the correct answer is C - natural variation.

Question 19

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?

Accepted Answer

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

Question 20

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

Accepted Answer

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

Quiz 19: Statistical Process Control