Exam 13: Attribute Control Charts

To reduce the costs associated with an accident and its consequences, returning the employee to work, even in a limited capacity is critical. The safety engineer wants management to understand the importance of managing the days it takes to return employees to work. In order to show their past performance, he wants to create an np chart for his boss. What level of return to work days can be expected in the future?

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Question 1

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$\begin{array}{ll}\text { Sample } & \text { \# of days to } \\\text { Size n } & \text { return to work } \\10 & 6\\10 & 14 \\10 & 6 \\10 & 3 \\10 & 8 \\10 & 22 \\10 & 4 \\10 & 3 \\10 & 24\\10 & 2 \\10 & 6 \\10 & 17 \\10 & 1 \\10 & 5 \\10 & 6 \\10 & 3 \\10 & 2 \\10 & 6 \\10 & 16 \\10 & 1 \\10 & 2 \\10 & 1\end{array}$
$n p-b a r=\frac{\sum n p}{m}=\frac{158}{22}=7$
$\text { p-bar }=\frac{\sum n p}{\sum n}=\frac{158}{220}=0.72$
$\begin{array}{l}\mathrm{UCL}=7+3 \sqrt{7}(1-0.72)=11 \\\mathrm{ICJ}=7-3 \sqrt{ }(7(1-0.72)=3\end{array}$

Lawnmower decks are composed of metal sheets that have been spot-welded together. For obvious safety reasons, as the lawnmower decks are prepared for priming and painting, the operator performs an inspection to check for weld defects that need to be corrected before the deck is painted. Use the following information to create a c chart.

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Question 2

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$\begin{array}{cc}\text { Deck } & \text { Defects } \\1 & 5 \\2 & 6 \\3 & 4 \\4 & 7\\5 & 5 \\6 & 7 \\7 & 4 \\8 & 6 \\9 & 5 \\10 & 4 \\11 & 5 \\12 & 5 \\13 & 4 \\14 & 6 \\15 & 3 \\16 & 2\\17 & 0 \\18 & 1 \\19 & 2 \\20 & 1 \\21 & 2 \\22 & 0 \\23 & 1 \\24 & 2 \\25 & 1\\26 & 2 \\27 & 1 \\28 & 0 \\29 & 1 \\30 & 2\end{array}$
$\text { c-bar }=-\frac{\sum c}{m}=\frac{93}{30}=3$
$\begin{array}{l}\mathrm{UCL}=3+3 \sqrt{3}=8 \\\mathrm{UCL}=3-3 \sqrt{3}=0\end{array}$

Sometimes container ships carrying goods across the ocean have rough trips. When this happens, the cargo master instructs the owners of the goods to carefully inspect the items in the containers for breakage and file the appropriate forms with their insurance company. In order to protect themselves, one importer performs a dock audit on the containers they receive. They consider a container a single unit and inspect 8 such units each time a ship docks. Due to their type of business, products that receive minor damage are classified as defects and are sold at an outlet store. Use the following information to create the centerline and control limits for an appropriate chart.

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Question 3

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$\begin{array}{ll}\text { Subgroup } & \text { Defects } \\\text { Size } & \\8 & 8 \\8 & 12\\8 & 17 \\8 & 8 \\8 & 18 \\8 & 15 \\8 & 23 \\8 & 9 \\8 & 10 \\8 & 51 \\8 & 8 \\8 & 2 \\8 & 7 \\8 & 8 \\8 & 4 \\8 & 7 \\8 & 8 \\8 & 9 \\8 & 10 \\8 & 13\end{array}$
$\text { u-bar }=\frac{\sum c}{\sum n}=\frac{247}{160}=1.5$
$\begin{array}{l}\mathrm{UCL}=1.5+3 \sqrt{1}.5 / 8=2.8 \\U C L=15-3 \sqrt{1} .5 / 8=02\end{array}$

For a doctor's office, the processing of forms in order to receive payment is a necessary part of doing business. If a form is filled out incorrectly, the form can not be processes and is considered defective. Within each office, an individual is responsible for inspecting and correcting the forms before filing them with the appropriate insurance company. Every week, a particular doctor's office samples 20 forms and creates a p chart to monitor how many forms have mistakes. They plan on using this information to justify changing the form. Create a p control chart. What is the process capability? Should they change the form?

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Question 4

What does the upper control limit of either a p, np, c, or u chart tell us about the process? What does the lower control limit tell us?

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Question 5

As container ships get ready to leave to begin their careers on the high seas, a final inspection is held in order to create a list containing the defects that need to be corrected before the ship can put to sea. The following in formation and chart is data for these final inspections. Each sample represents one ship (n = 1). Create a c chart.

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Question 6

For the following information, create an np control chart:

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Question 7

Ships number 2 and 17 have a larger number of problems due to the new engine crews assigned to these ships. The manufacturer of the ships has instituted a rigorous training program and doesn't expect these problems to resurface. They are still investigating the high number of defects for ship 22, as yet, no specific cause has been found. Use the information provided and revise the chart.

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Question 8

How is the process capability of a p, np, u, or c chart determined?

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Question 9

A state tracks a variety of performance measures including: the number of childhood immunizations given each year, the preventive dental care given in two age ranges (3-21 years and 21+ years), and blood lead toxicity in infants ages 0 - 72 months. The following data, covering the past 11 years, is based on blood level toxicity in infants. This information is for one county only, which samples 25,075 infants each year. Create a p chart.

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Question 10

What does the upper control limit of either a p, np, c, or u chart tell us about the process? What does the lower control limit tell us?

For the following information, create an np control chart:

How is the process capability of a p, np, u, or c chart determined?

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