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# Cp, CpK, average and variation control chart

Topics include:
MRP
Calculate Cp and Cpk
Average and Variation Control Charts
Little's Law

1 Explain why it is possible that a process is in control as measured by a control chart, but is not capable as measured
by either Cp, Cpk or Sigma value.

SCENARIO A process has a mean of 14.0, and a standard deviation of 0.19. It's lower specification limit is 13.8 and its upper
specification limit is 14.8.
2 Calculate its Cp.

3 Calculate its Cpk.

4 Calculate the Sigma value of the above process.

5 Explain why the same customer service can be provided (i.e., the number in line) by system 1 which has a higher utilization
than system 2 given that the variance is lower in system 1 than in system 2. HINT: It might be useful to draw a graph.

SCENARIO: You are the manager of a retail clothing store. The manufacturer will ship some lots of clothing to you if they are standards.
The average demand for an item is 510 units a week. The lead time is two (2) weeks. The standard deviation of demand
is 20 units a week. The desired customer service level is 85% (z=1.045). The cost of placing an order is \$15. You currently order
1,000 items at a time. The holding cost per year of each item is \$20 a year. Assume 50 weeks in a year.
10 What is the current annual ordering cost and the current annual holding cost for the scenario above?
11 What is the reorder point for the scenario above if you are using the continuous reorder system?
12 What is the economic order quantity in the scenario above?
13 Use the samples in the table below to calculate the center line, and the upper and lower control limits needed for the
both the Average and Variation control charts. Note that there are 5 in each sample. (Please take z=3, s=0.06 and sV=0.041).
Item Sample Numbers 1 to 20
No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
1 3.1 3.1 3.1 2.9 3.0 2.9 2.9 3.0 3.0 3.0 3.1 3.1 3.1 3.0 3.0 2.9 3.0
2 3.0 3.0 2.9 3.0 3.0 3.1 3.1 2.9 3.1 3.1 3.1 3.0 3.0 3.0 3.0 2.9 3.0
3 3.0 3.0 2.9 3.1 3.0 3.1 3.0 2.9 3.1 3.0 2.9 3.0 3.1 3.1 3.0 3.0 2.9
4 3.0 3.1 2.9 3.0 3.0 2.9 3.1 3.0 3.0 3.0 3.0 3.1 2.9 2.9 3.0 3.0 3.1
5 3.0 3.0 3.0 2.9 3.0 3.1 3.0 2.9 3.1 2.9 3.0 3.0 3.1 2.9 3.0 2.9 3.0
16 Solve MRP problem in sheet labeled MRP

0 A LT 1 B LT 2 C LT 2

LT 2 LT 1
1 D(3) E(1) D(2) E(2) D(1) E(3)

2 F(2) LT 2 F(2) F(2)

A: OQA = L4L: SSA = 0 0 1 2 3 4 5 6 7 8 9 10
Gross Req. 100 100 50 50 50 20 20 20 50
Sched. Rec. 50
On Hand 100
Net Requirements
Planned Order Receipt
Plan Order Release.
B: OQB = L4L SSB = 0 0 1 2 3 4 5 6 7 8 9 10
Gross Req. 200 200 200 200
Sched. Rec.
On Hand 250
Net Requirements
Planned Order Receipt
Plan Order Release.
C: OQC = L4L SSC = 0 0 1 2 3 4 5 6 7 8 9 10
Gross Req. 100 100 100 100 50 200
Sched. Rec. 50
On Hand 100
Net Requirements
Planned Order Receipt
Plan Order Release.
D: OQD = L4L SSD = 0 0 1 2 3 4 5 6 7 8 9 10
Gross Req.
Sched. Rec. 250
OH 200
Net Requirements
Planned Order Receipt
Plan Order Release.
E: OQE = L4L SSE = 0 0 1 2 3 4 5 6 7 8 9 10
Gross Req.
Sched. Rec. 100
OH 200
Net Requirements
Planned Order Receipt
Plan Order Release.
F: OQF: =L4L SSF=0: 0 1 2 3 4 5 6 7 8 9 10
Gross Req.
Sched. Rec. 800
OH 600
Net Requirements
Planned Order Receipt
Plan Order Release.

#### Solution Preview

See the attached file. Thanks

13 Use the samples in the table below to calculate the center line, and the upper and lower control limits needed for the
both the Average and Variation control charts. Note that there are 5 in each sample. (Please take z=3, s=0.06 and sV=0.041).

Item Item No. 1 2 3 4 5
Sample Numbers 1 to ...

#### Solution Summary

This post shows how to calculate Cp, CpK, average and variation control chart

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