Statistical Process Control Preparation Grade Level: 6-12
Group Size: 20-30
Time: 50-60 Minutes
Presenters: 3-5
Objectives
This lesson will enable students to: •
Demonstrate and explain the concepts of Statistical Process Control and standard variations.
• •
Measure, calculate, record, and plot variation patterns from product testing. Adjust product specifications to satisfy client parameters.
Standards This lesson aligns with the following National Science Content Standards: • •
Materials • •
Science and Technology, grades 5-8, 9-12
Science in Personal and Social Perspectives, grades 5-8, 9-12
Scrap memory parts
SPC PowerPoint® presentation – http://www.micron.com/k12/resources.aspx
•
“SPC Worksheet” – Appendix A
•
“SPC Sample Data” – Appendix B
• • • • • • • •
Sharpened pencils
Target – 1 per group Deck of cards
Small paper clips
Large paper clips
Small binder clips
Large binder clips
Calculator – 1 per group
•
Marker – 2 colors per group
•
Yardstick – 1 per group
•
Quincunx
Revision Date: 02/06/2007 1 © 2002 Micron Technology Foundation, Inc. All Rights Reserved
Preparation Prepare targets and overhead transparencies. Prepare the materials for each group: 1 target, yardstick, markers, calculator, two playing cards, appropriate clips for each card, and the “SPC Worksheet” (Appendix A).
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Introduction Micron’s memory and imaging products comply with extremely rigid specification. An error of even a hundredth of a micron (1/700th of the size of human hair) can cause a product to be
faulty. In order to prevent failure when they reach the consumer, Micron uses the process of Statistical Process Control, monitoring increases and decreases in variation that can affect product quality.
Distribute Memory devices and discuss the variety of applications which contain memory. Q: What products do you have that use memory?
A: Answers will vary. Examples might include cell phones, digital cameras, DVD players, MP3 players, computers, handhelds, global positioning units, vehicles, etc.
Q: What would happen if the memory in the products didn’t meet specifications and failed?
A: Answers will vary, but might include: nothing, car problems, loss of work, not able to make phone calls …
The activity we are going to do today helps explain what Micron does to prevent failures with our products.
Introduce key terms and examine the meaning of each word. Refer to the Statistical Process Control PowerPoint available at: http://www.micron.com/k12/resources.aspx . Q: What does Statistical Process Control stand for?
A: Statistical – We collect large amounts of data about our memory products from experiments. We study that data to learn how our actions affect the performance of our products.
Process – The method of doing something. Control – We use the data to adjust the process to achieve the desired results. Those results are dependent on customer requirements, efficiency, quality, and reliability.
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Statistical Process Control Simulation For this activity we’re going to pretend that Micron makes playing cards. One of our customers has asked that his cards meet certain performance standards: Dropped from shoulder height, they have to fall on a target. We will record variation from the target. Q: How do we give the customer what he/she wants?
A: Answers will vary – brainstorm possible solutions with the students. Micron engineers came up with a process of putting three different weights on the cards: 1) a
paper clip, 2) a small binder clip, and 3) a large binder clip. Will one of these options meet the customer’s requirement?
Ask the teacher to divide the class into groups of three to four students per group. Give each team the materials for the activity (cards, targets, rulers, clips, markers, worksheet, pencil, and calculator.)
Process
1. Demonstrate the proper technique for dropping the cards. Stand with toes at end of the
target, arm extended at shoulder height, card grasped between thumb and fore finger, and weight at the top. Drop the cards individually.
2. Explain the process for dropping the cards, measuring and recording the information. 3. Instruct each team to place its target flat on the floor.
4. Have one student stand over the target one at a time and drop the cards as demonstrated. 5. Have the students take turns dropping the cards.
6. Once the card is dropped, the students measures the distance from the target (100) to the spot
each card lands and records the measurement on the worksheet. Measure to where the card first hits the floor to the nearest quarter inch.
7. Repeat steps 4, 5, and 6 ten times with team members taking turns.
8. Once all of the measurements are recorded have the students calculate the following: •
Process statistics: Average ( x ) and Range (R)
•
Process summary statistics: Average of averages ( x ) and Average of the ranges ( R )
•
Control limits: Standard deviation (S x ); Upper Control Limit (UCL) and Lower Control Limit (LCL)
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9. Have the students draw the upper and lower control limits on the target sheet.
10. Next instruct the students to plot the averages on the target sheet and draw a line graph to connect each average.
11. Have each group plot its results on a trend chart. Compare their trend charts against the required distance parameters. Share the example on page 13 of the PowerPoint
presentation.
Trend Charts A trend chart allows us to do three things: •
Observe results that fall outside control limits, so we can adjust the process to address the variation.
•
Determine if the “scrap” factor (those results that fall outside the control limits) for any of the three options is acceptable.
•
Observe how our process changes over time.
Trend charts are analyzed and monitored throughout the process.
Discussion Now let’s compare the charts that each group created.
For each group’s chart ask the entire class the following questions. Q: Do the control limits fall within product specifications? A: Answers will vary based on the chart. Q: Is the process capable? A: Answers will vary.
Q: What process would you suggest using for the card production? A: In most of the exercises just completed, the large binder clips will have produced the best results simply because they’re heavier.
Q: What types of variation did you observe?
A: Answers may include: difference in height of team members, arm length, technique used,
difference in the weights, and bent cards.
Expected – Differences in the weights and how they’re dropped will make cards fall in
different places.
Unexpected – Unforeseen outside forces (height of person dropping the cards, air
conditioning currents, etc.) make cards fall in different places.
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Q: Why do we use Statistical Process Control?
A: It can tell us if our process is doing what we expect it to do. It can identify unexpected variation.
It can help us make real-time decisions about how to adjust our process.
Sources of Variation (The Six Ms) Review the sources of variation using the PowerPoint slides for reference. • •
Man (people) – everybody does things differently.
Machines – using different machines – even different individual machines of the same
model – might produce different results. • •
Method – different training emphasizes different things.
Materials – different materials (paper clips vs. large binder clips) produce different results.
•
Mother Nature (Environment) – differences in temperature, humidity, etc., can affect results.
•
Measurement system – the more accurate and precise the measurement tools the
smaller the range of variation.
Demonstration of Variation Use the Quincunx to demonstrate the randomness inherent in Statistical Process Control. In this example, the metal pegs represent the six sources of variation. The funnel represents the process center.
1. Set up the Quincunx with the beads at the top. 2. Using a transparency marker write a T (for Target) in the center. 3. Move the funnel away from the target. 4. Using your hand or a piece of paper, cover the funnel. Drop one bead and see how far away from the target it lands. Q: Based on this first run would we want to adjust our process?
A: Answer will vary. Based on where the bead lands, if it is a long way from the target adjusting it might be in order. If it is close then it would be good to drop additional beads before adjusting the target.
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5. Drop additional beads and adjust the funnel towards the target according to the results from the first drop. Repeat as necessary to center the funnel. 6. Drop the remaining beads. Note how the beads spread out into a Bell curve. This is what random variation looks like. Q: Where are the upper and lower control limits on this spread?
A: Identify visually the upper control limits and the lower control limits. Q: What would be considered unexpected variation? A: Any beads that fall outside the limits.
In production we would stop the process to investigate the cause of unexpected variation.
Meeting Customer Parameters Before Micron builds a new device, a product review team made up of people from the design, product engineering, and marketing departments analyzes customers’ needs. They review design concepts and marketing studies to match new device ideas to the equipment
manufacturer’s anticipated memory needs. Once the team is confident a new device will gain market acceptance, the design process begins.
Card Customers Parameters Our card customer has introduced a new parameter, price, which must be “y.” The following are the prices for our weights: Paper clip = x
Small binder clip = 1.5 x
Large binder clip = 2.0 x Q: How does that effect decision-making with regard to which option is more acceptable? A: We probably wouldn’t want to use the large binder clip because of the increased cost.
Q: How do we change the process to meet the customer’s requirements without incurring the increased cost of large binder clips?
A: Answers will vary – brainstorm possible solutions. Q: What effect does the amount of product that will need to be scrapped or reworked have on the decision?
A: That will add to the total cost. We will want to find a way to drop the cards that meets all of
the customer parameters.
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Conclusion At Micron our design, research, and development teams are constantly looking for new and better ways to fabricate memory devices. Research Challenge Q: What new options can your team engineer without increasing cost? A: Answers will vary.
Demonstrate the student’s ideas to the entire group and discuss the outcome of each idea.
At the end of the lesson demonstrate one possible process change that improves the rate at which the card hits the target. It is to drop the card by holding it flat and facing down. Lesson adapted from: Alloway, James A., Jr. “The Card Drop Show.” Quality Progress. July 1994: 99-104.
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Appendix A – Statistical Process Control
SPC Experiment Clip Size: ___________________________
Date:_______________
Measurements Sub-
1
2
R
x
group 1 2 3 4 5 6 7 8 9 10
X=
Subgroup Size: n = 2
sx =
d2 = 1.128
R= R d2
n
=
X-Bar Chart:
UCL = X + 3 s x = ______ 9
LCL = X − 3 s x = ______
Appendix A – Statistical Process Control
Control Charts X-Bar Chart
UCL = ( x +3sx) = _____ ( x +2s x) = _____ ( x +1s x) = _____ CL = ( x ) = _____ ( x -1s x) = _____ ( x -2s x) = _____ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10
LCL = ( x -3sx) = _____
Appendix B – Statistical Process Control
Sample Data Measurements Sub-
1
2
x
R
1
103
100
101.5
3
2
98
96
97
2
3
98
95
96.5
3
4
107
94
100.5
13
5
95
98
96.5
3
6
94
99
96.5
5
7
103
101
102
2
8
97
93
95
4
9
102
106
104
4
10
101
100
100.5
1
group
X=
Subgroup Size: n = 2
sx =
d2 = 1.128
R=
99
R d2
n
=
4
2.51
X-Bar Chart:
UCL = X + 3 s x = ______
LCL = X − 3 s x = ______
Upper Control Limit (UCL) = 106.5 Centerline = 99.0 11
Appendix B – Statistical Process Control
Lower Control limit (LCL) = 91.5
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Appendix B – Statistical Process Control
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