SPC Basics

Presented By: Tariq Khurshid

LSL

NOMINAL

USL
UCLx X LCLx

Goode Consulting International, Inc 6/15/2012 Tariq Khurshid

Company Confidential 2011

Slide: 1

SPC Implementation Model

Pareto of SRR by P/N

Build a system that allows problem solving based on quality data

Cells, process improvement teams,

PEOPLE

MACHINES

MEASUREMENT

Identify key process elements & variables (i.e., inputs & outputs)

PROBLEM

Brainstorm Ideas!!

MATERIAL

METHODS

ENVIRONMENT

UCLx X LCLx

Use SPC to bring key variables into control

Can I predict where the next measurement will be? Can we meet the Engineering Tolerance 100% of the time? Am I targeted to the nominal dimension?

CONTROL:

CAPABILITY:

CENTERING:

Measure process capability. Can we meet requirements (i.e., Cpk > 1.33)?

No

Implement a plan of process improvement

Yes

UCLx X LCLx

We win this round. Use SPC as a defect prevention tool for sustaining control of quality.

SPC Data Collection

Data Allows the process to talk to you Is the window to making better decisions about the process Allows you to describe the process behavior Gives a picture of the process

Provides factual information about the process, operation, product, cause, problem or improvement
Eliminates guesswork Changes problem solving from dealing with OPINIONS to dealing with FACTS People can usually agree on facts

SPC Data Collection - continued

Planning for Ask the following questions: Data 1 What is the purpose? Why are we doing it? Collection
3 Is valid data already available? 4 How will data be gathered?
Measuring device Special form Special instructions

2 What is the exact nature of the problem we are trying to solve?

5 What is the PLAN? Who, what, when, where and how? 6 How will the data be analyzed and presented? 7 Should we measure the entire POPULATION or a SAMPLE of the population?

8 Should the sample data consist of random measurements or consecutive measurements? 9 How much data is needed?

Examples of Variation - Accuracy vs. Precision

1. Small Variation Not Targeted

2. Large Variation Not Targeted

EXERCISE: Which bullseye represents: Accuracy & No Precision _____ Precision & No Accuracy _____ Accuracy & Precision _____ No Accuracy & No Precision _____

3. Small Variation Properly Targeted

4. Large Variation Properly Targeted

A small variation not targeted can be adjusted to hit the bulls eye. A large variation not targeted must be improved before it can hit the bull seye.

Quick Review of Some SPC Basics

Sigma ( )
The measure a variability (spread and/or precision) within a set of data. Range (R) Another measure of variability in a set a data, arrived at by taking the difference of the highest value in the sample and subtracting the lowest value from it. The range is less sensitive at determining process variability than Sigma.

X-bar (X)
The measure of the average (mean and/or accuracy) of a set of data.

Assessing Accuracy and Precision

Measures of Variation
Accuracy Refers to the location of the process Measured by the average (or mean) of the data
Symbol X
Data Precision Refers to the variability of the process Measured by either the range or standard deviation (sigma)
X = Center of

Range

Range = R = high value - low value Sigma = S = n-1 = more precise measure of variation than the range
* Sigma is used to make predictions about a process performance * Sigma is calculated using all data from a sample, not just the high and low values n-1 = S = sample standard deviation *

Standard Deviation
Measures of Variation (cont.)
Standard deviation is the square root of the average squared deviation of each measurement from the mean.

Sx =

(Xi - X)2 n-1

x x x x x x x x x x
11 12 13 14

X = 15
4 3 2 1 0 1 2 3 4 Distance from X

M
x x x x x x x x

x x x x x x x x x x
16 17 18 19

Calculating the Standard Deviation

Measures of Variation (cont.)
Xi X1 = 12 X2 = 14 X3 = 13 X4 = 15 X5 = 18 X6 = 16 X7 = 18 X8 = 16 X9 = 14 X10 = 14 Xi - X (Xi - X)2

Data = 12, 14, 13, 15, 18, 16, 18, 16, 14, 14

M
Sx =
i

Xi = 150 n = 10 150 = 10

(Xi - X)2 =

X =

Xi n

(Xi - X)2 n-1

Quick Review of Some SPC Basics

WHAT ARE THE THREE "C's OF SPC?
CONTROL, CAPABILITY and CENTERING
What are the three questions they ask?
UCLx

CONTROL Measures: Process behavior

asks:

Am I able to predict where the next part will be?

X LCLx

LSL

NOMINAL

USL

CAPABILITY (Cp, Pp) Measures: Precision Key parameter: Range or Sigma

asks:

Can I meet the required engineering tolerance from the B/P or operation sheet 100% of the time.
X

CENTERING (Cpk, Ppk) Measures: Accuracy Key parameter: Xbar, the Mean

asks:

Am I targeted to my NOMINAL dimension?

LSL

NOMINAL

USL

SPC Data Collection - continued

Sampling
POPULATION
Refers to all persons, objects, items, dimensions, etc., under consideration.

POPULATION

SAMPLE

SAMPLE
Refers to a portion of the population.
Samples are taken to represent the population. Samples save time, money, or product when seeking information about the population.

SPC Data Collection - continued

Advantages of Sampling
REDUCED COST
- Fewer expensive tests - Destructive tests are costly

LESS TIME
- Urgency - Lead time

MORE COMPLETE AND ACCURATE DATA

- Less fatigue - Fewer measurements, less likely to make an error

LESS DAMAGE TO THE PRODUCT

- Less handling

SPC Data Collection - continued

Sample Size
How large a sample is necessary?

Too small a sample size increases the risk of not getting a true picture of the population. Too small a subgroup may not detect a change in the process. Sampling tables based on the laws of probability are used for evaluation of lots.

If the proper sampling method is used, 20 subgroups of data provides a representative picture of most populations (20 subgroups of data should be the minimum collected).

SPC Data Collection - continued

Importance of Valid Data
GARBAGE IN.....................GARBAGE OUT!!
The most powerful statistical analysis cannot change bad data into good information.
SOME CONSEQUENCES OF INVALID DATA Shipping defective material to the customer Scrapping or reworking good product Accepting defective supplier material Returning bad supplier material when it was actually good Incorrectly stopping or adjusting a process when you shouldn't Not stopping or adjusting a process which is making bad product

SPC Data Collection - continued

Types of Variation
VARIATION is the inevitable difference among individual outputs of a process. The source of variation can be grouped into two major classes:

COMMON CAUSES
- Predictable - Stable over time - Accounts for 85% of process problems (Deming) - Can only be removed by changing the system
EXAMPLE: Cutting fluids breakdown, temperature changes, tool wear, etc.

SPECIAL CAUSES
- Unpredictable - Local in nature - Specific to a certain tool, person, fixture, etc. - Accounts for 15% of process problems (Deming) - Can be identified and removed at the local level
EXAMPLE: Power surges, tool breaks, power outage, out-of-round bushing, etc.

SPC Data Collection - continued

Process Stability
STABLE
A STABLE process contains only COMMON CAUSE variations and remains centered on the targeted value over time:

SMALL VARIATION

TIME

LARGE VARIATION

TIME

SPC Data Collection - continued

Process Stability (cont.)
UNSTABLE
An UNSTABLE process is affected by SPECIAL CAUSE variations which cause the process to move away from the targeted value, or change in the amount of variation.

CONSTANT VARIATION, CHANGING LOCATION (SHIFTING)

TIME

CHANGING VARIATION, CONSTANT LOCATION

TIME

SPC Data Collection - continued

Variation is the Enemy of Quality
BENEFITS OF REDUCING VARIATION
1. More uniform product 2. Reduce cost by economic targeting of process average 3. Design optimization 4. Less costly to control 5. Process can tolerate minor disturbances 6. Avoid scrap, rework and repair (SRR) 7. Reduce internal & external costs of quality 8. Improved reliability 9. Reduce appraisal costs of quality 10. Customer satisfaction

EXCESSIVE VARIATION IS NON-COMPETITIVE LARGE VARIATION IS EXPENSIVE

SMALL VARIATION IS THE GOAL

NO VARIATION IS IMPOSSIBLE

Process Capability - Cp
Cp = Process Potential Index Formula: Cp = Engineering Tolerance (ET)/Natural Tolerance (NT) Where: ET = Upper Specification Level - Lower Specification Level NT = Natural Tolerance = 6 X Sigma Sigma = Average Range/d2 What's it used for: Measures the short-term process precision for a given Key Characteristic essentially it measures Machine Capability Short-term process capability is computed using the short-term process variation (Rbar/d2). This is the machine and gage variation at a certain moment in time (last 2030 pieces made) If the gauge variation, as measured by a gauge capability study, is less than 20%..... .....we can conclude the key process input driving the variation in the shortterm is the machine. What question does Cp ask? Does the process have the precision to potentially make every part 100% to blueprint specification at this moment in time?

GOAL: Cp greater than or equal to 1.33 (equates to a 63 DPM rate or better).

Process Capability - Cpk

Cpk = Process Potential Index that Accounts for Centering Formula: Cpl
Process Average (Xbar) - Lower Spec. Limit (LSL) Three Sigma (3 )

Cpu

Cpk = Minimum

or

Upper Spec. Limit (USL) - Process Average (Xbar) Three Sigma (3 )

What's it used for: Measures the short-term process accuracy for a given Key Characteristic - essentially it measures how close to the targeted value the process is running at. Cpk is the smaller of Cpl or Cpu, depending which side of the tolerance the process is shifted towards. Cpk should be compared to Cp. The closer Cpk is to Cp, the more centered the process is running. Cpk is affected by different operators, shifts, raw materials, tool adjustments as well as machine and gage error. What questions does Cpk ask? Is the process targeted to the NOMINAL dimension, i.e.., is the process centered? If a shift is present within the process, should I be concerned?

GOAL: Cpk greater than or equal to 1.33 (equates to a 63 DPM rate or better).

What is Process Capability?

LSL
CAPABLE, CENTERED, AND MEETING SPECIFICATIONS

USL

CAPABLE, NOT CENTERED, AND POTENTIALLY MAKING NONCONFORMING MATERIAL

NOT CAPABLE, CENTERED, AND POTENTIALLY MAKING NONCONFORMING MATERIAL

NOT CAPABLE, NOT CENTERED, AND POTENTIALLY MAKING NONCONFORMING MATERIAL

Cp & Cpk

LSL

ET = USL - LSL

USL
Cp MEASURES PRECISION OF A PROCESS

Cp > 1.0
X NT = 6o

Cpk MEASURES ACCURACY OF A PROCESS Cp > 1.0 Cpk < 1.0

Cpk measures the distance between Xbar and the nearest spec and compares that to 3-sigma (one-half of the bell curve).

USL - X 3o

Cp RATIO ANSWERS THE QUESTION: "CAN I MEET THE ENGINEERING TOLERANCE 100% OF THE TIME?" Cpk RATIO ANSWERS THE QUESTION: "AM I TARGETED TO THE NOMINAL DIMENSION?"

Cp & Cpk (cont.)

Let's say that: Natural Tolerance = NT = 6 Engineering Tolerance = ET = USL - LSL Cp = ET/NT then: Cp = USL - LSL

Cp NOTES:
If Cp = 1.0 then the process is capable (but barely!).
If Cp < 1.0, then the process is not capable. If Cp > 1.0, then the process is more than capable. GOAL: Cp greater than or equal to 1.33. Cp tells us if the process is capable of meeting specs. However it does not tell us if the process is centered in the middle of the specs.

Cp & Cpk (cont.)

Therefore, another index was designed to help us determine if the process is centered. We call this index Cpk.

Cpk = MINIMUM (Cpl, Cpu) = MINIMUM

Cpl = X - LSL 3 Cpu = USL - X

Use the smaller of these two formulas .

Cpk NOTES:
Cpk can never be greater than Cp (mathematically impossible).
If Cpk = Cp, then the process is centered in the middle of the specs. If Cpk < Cp, then the process is not centered. If Cpk > 1.0, then even if the process is not centered properly nothing will be out-of-spec. GOAL: Cpk greater than or equal to 1.33.

Process Capability (cont.)

Unilateral vs. Bilateral Tolerances How do we handle capability analysis for twosided tolerances?
BILATERAL dimensions (i.e., diameters, linear dimensions, etc.)

How do we handle capability analysis for onesided tolerances?

UNILATERAL MAXIMUM dimensions (i.e., runout, flatness, etc.) UNILATERAL MINIMUM dimensions (i.e., wall, thickness, etc.)

Process Capability (cont.)

Bilateral Tolerances
BILATERAL Dimensions (i.e., Diameters, Linear Dimensions, etc.)
LSL NOMINAL USL

X
CONVENTIONAL CONTROL CHART CAPABILITY ANALYSIS:

Cp

USL - LSL 6 )

Cpk = MINIMUM { Cpl, Cpu }, where: Cpl = X - LSL 3 and Cpu = USL - X 3

=R (Where d2

GOAL: Cp & Cpk > 1.33

Process Capability (cont.)

Unilateral Maximum Tolerances
ZERO USL = MAX EXAMPLES:

Runout Flatness True Position Roundness Straightness Perpendicularly

X CAPABILITY ANALYSIS: Now it is time to change the rules for Cpk analysis as illustrated for Bilateral tolerances. Since it is assumed smaller values are always superior to larger values, the most meaningful capability index for MAXIMUM tolerances will be:
Cpu ANSWERS: Is there a probability of making product beyond the Maximum tolerance allowed?

Cpu = USL - X 3

GOAL: Cpu > 1.33

Process Capability (cont.)

Unilateral Minimum Tolerances
LSL = MIN

EXAMPLES:

Wall Thickness MTBF MTTF Horsepower X

CAPABILITY ANALYSIS: Since it is assumed larger values are always superior to smaller values, the most meaningful capability index for MINIMUM tolerances will be:
Cpl ANSWERS: Is there a probability of making product below the Minimum tolerance allowed?

Cpl = X - LSL 3

GOAL: Cpl > 1.33

UCLx X LCLx

Control Charts...
are a graphic representation of a process.

show plotted values of some statistic gathered from that process. have one or two control limits.
Control limits define the maximum and minimum values expected to be produced by the process.

have two basic uses:

Determines if a process is in control, I.e., is the process predictable. Used as a level two mistake-proofing device in order to maintain control.

Control Charts (cont.)

UPPER CONTROL LIMIT (UCL)

The maximum value expected to be seen. The average value expected to be seen. The minimum value expected to be seen.

CENTRAL LINE (X)

LOWER CONTROL LIMIT (LCL)

TIME

Plotted points from an in-control process will behave in a statistically predictable manner.

Control limits define the amount of variation to be expected in plotted points if the process is consistent over time.

Questions In Control Charting

What sources of variation are to be detected by the Control Chart?

How valid is the measurement process used to collect the data?

How does an Operator react to an out-of-control point/situation?

How does management react to processes that are out-of-control or not capable?

Will the data collected on the Control Chart answer the questions people have about the process? What other groups will utilize this Control Chart data for constructive purposes?

Where To Apply Control Charts

As required by the Customer based on form, fit, function and or complaints.

Problem areas (initiated from QCPC turnbacks, high scrap & rework).
Critical locating dimensions.

Ones goal in life is not to wallpaper the walls of our companys manufacturing and office areas with charts.

Cautions in Over-Adjusting a Process

Control chart also tells the Operator when to leave the process alone or there will be a risk of incurring the following losses due to over-correcting:
1. The labor required to make the adjustments and the downtime of the assembly area. 2. Unnecessary adjustments will increase the variability of a stable process. An excessive number of adjustments (over-correcting or knob twiddling) can increase the 6-sigma (natural) tolerance by up to 41%.
Shift Distribution from Unnecessary Adjustments Original Distribution LSL NOMINAL USL

X
Original 6-Sigma Spread

Spread Resulting From Unnecessary Adjustments

Control Chart Interpretation Below summarizes the patterns on a control chart that might indicate a Special Cause of variation may be present in the process. Investigate for a special cause if one of these patterns should develop on a control chart you are using to monitor a process.
SEVEN POINTS IN A ROW STEADILY INCREASING (OR DECREASING) POSSIBLE CAUSES Gradual deterioration of equipment Operator Fatigue Tool Wear Etc. STRATIFICATION - POINTS HUGGING THE CENTERLINE POSSIBLE CAUSES Inadequate Gauge Resolution Improvement to Process Gauge Sticking Etc.

POINT OUTSIDE CONTROL LIMIT Fixture Moved UCLx

A B C
X

LCLx

C B A
RUN OF EIGHT POINTS ON THE SAME SIDE OF THE CENTER LINE POSSIBLE CAUSES Sticky Gauge Worn Die Drift in Controls Etc. FOURTEEN POINTS IN A ROW ALTERNATING UP & DOWN POSSIBLE CAUSES Over adjustment of the process Control of two or more processes on the same chart Fixtures or holders not holding work in position Etc.

Quick Review of Some SPC Basics WHAT ARE THE THREE "C's OF SPC?

CONTROL, CAPABILITY and CENTERING

What are the three questions they ask?
UCLx

CONTROL Measures: Process behavior

asks:

Am I able to predict where the next part will be?

X LCLx

LSL

NOMINAL

USL

CAPABILITY (Cp, Pp) Measures: Precision Key parameter: Range or Sigma

asks:

Can I meet the required engineering tolerance from the B/P or operation sheet 100% of the time?
X

CENTERING (Cpk, Ppk) Measures: Accuracy Key parameter: Xbar, the Mean

asks:

Am I targeted to my NOMINAL dimension?

LSL

NOMINAL

USL

Xbar-R Control Charts

Works with small subgroups of data plotted over time.
Subgroup sizes are typically 3, 4 & 5. Subgroups composed of similar pieces (homogeneous). Time between plotted subgroups may vary based on experience.
More time between plotted subgroups for consistent and capable processes . Less time for processes more susceptible to inconsistencies.

Collect at least 20 subgroups of data prior to calculating control limits. Plotted points are the average values from each subgroup measured. The Range Chart is independent of the Averages Chart.
Range = High value - low value (for each subgroup).

Xbar-R Control Charts (cont.)

Terminology:
Subgroup: A sample of a number of consecutive pieces from the process (I.e., measuring the coating thickness of the last three circuit boards). k: Total number of subgroups. n: Number of pieces in each subgroup. X: Measurement on one individual piece. X: Subgroup mean. R: Subgroup range. X: Mean of all the subgroup means. R: Mean of all the subgroup ranges. UCL: Upper control limit, the maximum subgroup average expected to be seen. LCL: Lower control limit, the minimum subgroup average expected to be seen.

X-R Chart Preliminaries

X Chart UCL

X LCL

Averages variation is due to long-term, between subgroup sources that include Temperature, Raw Material., People, Shift, Method, Measurement System, Tooling, etc.

R Chart UCLR
Range variation is due to short-term, within subgroup sources that include the Measurement System and the Machine.

An out-of-control range chart (problem of PRECISION) situation is a more difficult problem to resolve than an out-of-control averages chart (problem of ACCURACY) situation.

Introduction to X-R Charts

Bowling is a sport many people participate in, whether on a league or for occasional recreation. For the serious league bowler who wants to attain a high average, they must practice often to become consistent. You can see by the Fishbone Diagram below there are many inputs that make up the bowling process. The following page shows 20 subgroups of data collected by one particular bowler looking to improve their game. The data is plotted on a Xbar-R Chart with assignable (special ) causes noted. At what point should control limits be calculated? What are the average, lowest & highest games expected?

BOWLING PROCESS INPUTS

PEOPLE
ATTITUDE ALCOHOL INTAKE AMOUNT OF BALL LIFT HOW MANY ON TEAM? - PACE EVERYONE SHOW UP? USE OF ALLEY ARROWS AMOUNT OF PRACTICE

METHODS

MEASUREMENT
USE WRIST BAND? LENGTH OF ARMSWING SCOREKEEPER - MANUAL OR AUTO

CURVE OR STRAIGHT BALL

# OF STEPS ON APPROACH USE RAG TO WIPE OFF BALL

PROBLEM:
ACHIEVE HIGHER BOWLING SCORES

TYPE OF WRIST BAND AUTO PINSETTER SHOES USED LANE OIL BALL CLEANER

TEMPERATURE BALL MATERIAL BALL WEIGHT

NOISE FROM OTHER BOWLERS TIME OF YEAR HUMIDITY

RAG CLEAN

MACHINES

MATERIALS

ENVIRONMENT

CHART FOR AVERAGES AND RANGE (X AND R)

NAME: Rodney D. Alley: BOWLORAMA
DATE LANE NO. NOTES
SAMPLE MEASUREMENTS

Chart No.: __ of __

Weeknight: MONDAY Team Name: THE BANANNAS

1/24 1/31 2/7 2/14 2/21 2/28 3/7 1

League Name: MILLER HIGH LIFE Key Characteristic: BOWLING SCORE

3/14 3/21 3/28 4/4
1-2 3-4 5-6

1/10 1/17 4/11 4/18 4/25 5/2

7-8

5/9

5/16 5/23

1-2 1 2 3 5

3-4

5-6

7-8

9-10 11-12 13-14 15-16 17-18 19-20

9-10 11-12 13-14 15-16 17-18 19-20

3 195 210 215 212 203 205 202 198 193 196 205 210 188 211 210

145 150 4 155

135 155 165

130 140 125 155 160 165 157 160 125 134 188 190 210 158 157 148 162 158 162 171 165 136 151 210 220 225 157 165 160 170 172 168 168 172 120 103 195 200 205

SUM (X) AVERAGE 450 (R) RANGE (X) MEASUREMENTS

150 10 1

455 152 30 2

445 462 433 487 490 495 496 497 381 388 593 610 640 613 627 593 611 609 148 154 144 162 163 165 165 166 127 129 198 203 213 204 209 198 204 203 28 25 35 15 14 6 14 12 16 7 918 14 3 4 5 6 7 8 9 10 11 48 12 22 13 30 14 20 15 20 16 17 19 23 20
CHANGED STYLE (Can't make spares, getting lots of strikes)

240 220 200 180

STARTED THROWING PRACTICE GAME

160
140 120 40 30 20 10 0
1 2 3 4 5 6 7 8 9 10 11 12 13 14
ELIMINATED POOR FIRST GAME

RECEIVED COACHING ON SPARES

(R) RANGE

15

16

17

18

19

20

Xbar-R Chart Exercise Baseball Winding Operation

The Rawlings Sporting Goods Company has been making baseballs for Major League Baseball for many years. Outlined below is the process:

SPC
2) Wrap core with two layers of wool and polyester yarn 3) Wrap with thin, white cotton cord KC: 3.75 +/- .05

1) Prepare Core

5) Stitch white leather cover

4) Glue outer windings

SPC is used to monitor the 3.75 +/- .05 diameter Key Characteristic at Operation #3, Final Winding Process. The Operator measures the diameter of four balls every hour and records the results on an Xbar-R Chart as seen on the next page.

Xbar-R Chart Exercise

Baseball Winding Operation
Xbar-R Chart for 3.75 +/- .05 Baseball Diameter at Winding Operation
3.78 3.77 3.76 3.75 3.74 3.73 3.72 3.71 3.70 3.69 3.68 0 5 1 1

Sample Mean

UCL=3.771 Mean=3.742 LCL=3.713 1 1 1 25

Based on the Xbar-R Chart results for 25 subgroups of 4 balls each (total of 100 balls), answer the following questions: 1) Does the process appear to be in control? YES _____ NO _____

1 1

Subgroup 0.10

10

15

20

Sample Range

UCL=0.09125

2) What patterns seem to be present? Check all that apply. __ Saw tooth __ Trend __ 2 of three points near Zone A __ Points outside the 3-sigma control limits

0.05 R=0.04

0.00

LCL=0

Should the Operator take action or leave the process alone?

Attribute Data Collection and Analysis

UCLc
c LCLc

Attributes Control Charts - Introduction

Attribute control charts are used when it is necessary to classify or count a particular characteristic of a process as opposed to measuring it. There are four types of Attribute control charts:
1) P-Chart, for the proportion defective, where each itemis either go/nogo, good/bad, yes/no, etc., and changing subgroup size. 2) NP-Chart, for the number proportion defective, where each item is either go/nogo, good/bad, yes/no, etc., with constant subgroup size. 3) C-Chart, for counting defects with a constant area of opportunity where the defects are drawn out of. 4) U-Chart, for counting proportion of defects per changing area of opportunity.

Which chart should I use? Ask:

1) Is there a maximum count for each group? 2) Is each subgroup the same size?

Attribute Model
Collect Qualitative Data

Turnbacks

Count Data (Defects)

Classification Data (Defectives)

QCPC Constant Subgroup Size N U-Chart Constant Subgroup Size N P-Chart

Y C-Chart

NP-Chart

Quality Level Acceptable

Certify

N Pareto Top Opportunities

RRCA

Mistake Proofing

Attributes Control Charts

Attributes ( or count ) data differs from variables data in that;

It is discrete ( yes/no, good/bad, pass/fail, etc. ) Count data must have a known area of opportunity (potholes per mile of road, defects per foot of video tape, knots per foot of board, etc. )

SPC Terms

Goode Consulting International, Inc 6/15/2012

Company Confidential

Slide: 47

SPC Terms

Goode Consulting International, Inc 6/15/2012

Company Confidential

Slide: 48

Attribute Chart

Goode Consulting International, Inc 6/15/2012

Company Confidential

Slide: 49

Variable Data Charts

Goode Consulting International, Inc 6/15/2012

Company Confidential

Slide: 50