# R- and x-Bar Charts

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1. Thermostats are subjected to rigorous testing before they are shipped to air conditioning technicians around the world. Results from the last five samples are shown in the table. Draw and R Chart and an x-bar chart. Based on the charts, is the process under control?

Observations

Sample 1 2 3 4 5

1 73.5 70.8 72.2 73.6 71.0

2 71.3 71.0 73.1 72.7 72.2

3 70.0 72.6 71.9 72.4 73.3

4 71.1 70.6 70.3 74.2 73.6

5 70.8 70.7 70.7 73.5 71.1

2. A professor records the number of students who complain each week throughout the semester. If the class size is forty students, what are 3-sigma control limits for this class? Construct a control p-chart and interpret the data. Is the process in control?

Week number Complaints

1 5

2 2

3 7

4 1

5 3

6 2

7 8

8 1

9 3

10 5

11 4

12 6

13 3

14 1

15 4

3. A department store chain is designing a layout for a new store. The store manager wants to provide as much convenience as possible for her customers. Based on historical data, the number of trips between departments per hour is given in the following closeness matrix. A block plan showing a preliminary layout is also shown.

Closeness Factors (Trips per hour)

1/O 2/S 3/H 4/T 5/A 6/E

1. Office Supplies (O) --- 40 100 50 20 10

2. Sporting Goods (S) --- 100 80 60 80

3. Hardware (H) --- 70 100 50

4. Toys (T) --- 70 90

5. Automotive (A) --- 60

6. Electronics (E) ---

CALCULATIONS TABLE:

Dept. Pair Closeness Factor (w) Origincal Distance (d_0) w X d_0 Revision #1 Distance(d_1) w X d_1

1 - 2

1 - 3

1 - 4

1 - 5

1 - 6

2 - 3

2 - 4

2 - 5

2 - 6

3 - 4

3 - 5

3 - 6

4 - 5

4 - 6

5 - 6

TOTAL

Complete the calculations and fill in the table above. Based on the table above answer the following questions.

a) What is the total expected weighted-distance score between Office Supplies and Hardware?

b) What is the total weighted-distance score between Hardware and Toys?

c) What is the total weighted-distance score for the entire store?

d) A suggestion has been made to switch Hardware and Automotive. What would the total weighted-distance score for the entire store if these two departments were switched

e) Based on your calculations, would you recommend that Hardware and Automotive be switched?

Answer 3:

4. Balance the assembly line for the tasks contained in the table. The desired output is 240 units per day. Available production time per day is 480 minutes.

Work Element Time (Sec.) Immediate Predecessor(s)

A 40 ---

B 45 ---

C 55 A

D 55 B

E 65 B

F 40 C,D

G 25 D,E

a) What is the desired Cycle time in seconds?

b) What is the theoretical minimum number of stations?

c) Use trial and error to work out a solution in the table below. Your efficiency should be at least 90%.

Station Candidates Choice Work-Element

Time (Sec) Cumulative Time (Sec) Idle Time

d) Calculate the efficiency of your solution.

5. A manufacturer's research and development center must expand by building a new facility. The search has been narrowed to five locations, all of which are acceptable to management. The assessment of these sites is being made on the basis of the five subjective location factors that follow. Management has agreed to use a five-point scale (Excellent = 5, and Poor = 1) to quantify and compare their subjective opinions about the relative goodness of the sites. The weight reflects the importance of each factor in the decision.

Locations

Factor Weight A B C D E

Labor climate 0.30 4 2 1 4 2

Proximity to markets 0.30 5 3 3 4 4

Quality of life 0.15 1 3 2 1 5

Proximity to suppliers 0.15 2 5 3 4 3

Taxes 0.10 4 4 4 1 3

Calculate the weighted score for each alternative. Which location would you recommend?

6. Complete the following MPS Record

Lot Size 130

Lead Time 1

Quantity on Hand 45 1 2 3 4 5 6 7 8 9 10

Forecast 25 25 25 25 50 50 50 50 40 20

Customer Orders (booked) 30 20 5 8 2

Projected On-Hand Inventory

MPS Quantity

MPS start

Available to Promise Inventory

7. Use the bill of materials and inventory records to determine the quantity of purchased items necessary to assemble 20 end items if the manufacturer uses lot-for-lot ordering. There are no end items currently on hand, and none of the components have any scheduled receipts.

Component On-hand Component On-hand

A 5 D 15

B 75 E 3

C 10 F 20

8. Use the table below to answer the following questions.

a) Use the information in the Table above, what is the throughput time for the process, assuming that the Call Center is always busy and has customers waiting to be processed?

b) Use the information in Table above, what is the process bottleneck?

c) Use the information in Table above, what is the 8-hour capacity for the process?

d) Use the information in Table above, where would you expect customer wait times to occur?

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#### Solution Summary

R- and x-Bar charts are examined. The processes under control are determined.

Awake Coffee Company Statistical Quality Control: R-chart and Xbar-chart

The Awake Coffee Company produces gourmet instant coffee. The company wants to be sure that the average fill of coffee containers is 12.0 ounces. To make sure the process is in control, a worker periodically selects at random a box of six containers of coffee and measures their weight. When the process is in control, the range of the weight of coffee samples average 0.6 ounces.

(a) Develop an R-chart and an xbar-chart for this process

(b) The measurements of weight from the last five samples taken of the six containers follow

Sample x-bar R

1 12.1 0.7

2 11.8 0.4

3 12.3 0.6

4 11.5 0.4

5 11.6 0.9

Is the process in control? Explain your answer

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