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Before starting production, the quality control manager made sure that there are no assignable causes in existence. He then took samples of 8 items every hour and found the following mean and range values.
Sample mean range
1) 59.2

4.2

2)61.2

3.7

3) 61.6

5.1

4) 59.5

3.1

5) 59.0

5.0

6) 61.1

4.1

7) 60.0

5.1

8) 61.1

6.4

9) 59.9

4.0

10) 60.0

4.5

a) Use this data and draw x-bar and R control charts.
b) If customer speci?cations are 60+1.0, is this process capable of meeting the speci?cation?

2) The chief security of?ce at the Houston International believes that a large number of bags that are checked in are oversized. He therefore orders to draw samples of 100 bags every hour and identify how many bags are oversized. The data is collected in the following table.
No. of oversized bags 2

TIME
8 a.m.
9 a.m.
10 a.m.
11 a.m.
12 noon

# of oversized bags
2
6
5
5
0

01 p.m.

6

2 p.m.

3

3 p.m.

0

4 p.m.

4

5 p.m.

7

a)Use

this date to develop appropriate control chart(s). Is this process in control?
b)If the sample size was 200 bags and gave us the same data as above, what would have your conclusion?

3. Alpha Of?ce supplies orders papers from NeverTear Paper Wholesalers (NPW). Being a long-term customer, NPW offers decent price discounts on large purchases to Alpha. Generally, the cost of 10 boxes of paper is \$12.50.
A discount is given as per the following table.

Order (Q)

Discount Rate

1-99 boxes

0%

100-499

6%

500-1999

10%

2000 +

20%

Alpha has experienced demand of 30,000 boxes per year. It is estimated a box has a holding cost \$0.50 per year. The ordering cost is \$20 per order.
1. a) How many boxes should Alpha order every time?

4.Your engineering team has developed a new product. You have to make a decision whether to manufacture it in-house or outsource from a reliable supplier. After doing necessary homework, you come up with these numbers for in-house production. The machine to manufacture will cost \$150,000.
This cost will be amortized over 15 years. The variable production cost = \$25, production rate = 30/day
The supplier will charge \$40 per unit.
The inventory holding cost of this product is estimated is \$10 per unit per year. If you manufacture in- house, the set up cost is \$200, whereas ordering cost when you order with the supplier is only \$50 per order. Annual demand is estimated to be 1,000. [For convenience, assume 300 days in a year.]

5. Suppose you are managing a furniture rental store. Your customers rent different type of furniture from your company for a period ranging from a few days to a few months. List ?ve issues that will be most critical in managing your (furniture) inventory.Before starting production, the quality control manager made sure that there are no assignable causes in existence. He then took samples of 8 items every
hour and found the following mean and range values.
Sample mean range
1) 59.2

4.2

2)61.2

3.7

3) 61.6

5.1

4) 59.5

3.1

5) 59.0

5.0

6) 61.1

4.1

7) 60.0

5.1

8) 61.1

6.4

9) 59.9

4.0

10) 60.0

4.5

a) Use this data and draw x-bar and R control charts.
b) If customer speci?cations are 60+1.0, is this process capable of meeting the speci?cation?

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