SPC Basics X LSL USL NOMINAL UCLx LCLx X.

SPC Basics X LSL USL NOMINAL UCLx LCLx X

SPC Implementation Model
Pareto of SRR by P/N Cells, process improvement teams, MCABS, etc. A B C D PEOPLE MACHINES MEASUREMENT MATERIAL METHODS ENVIRONMENT PROBLEM Brainstorm Ideas!! UCLx LCLx X Can I predict where the next measurement will be? CONTROL: Can we meet the Engineering Tolerance 100% of the time? Am I targeted to the nominal dimension? CAPABILITY: CENTERING: UCLx LCLx X

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 Data Collection Ask the following questions: What is the purpose? Why are we doing it? What is the exact nature of the problem we are trying to solve? Is valid data already available? How will data be gathered? Measuring device Special form Special instructions What is the PLAN? Who, what, when, where and how? How will the data be analyzed and presented? Should we measure the entire POPULATION or a SAMPLE of the population? Should the sample data consist of random measurements or consecutive measurements? 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 bullseye. A large variation not targeted must be improved before it can hit the bullseye.

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 Range Symbol  X Precision Refers to the variability of the process Measured by either the range or standard deviation (sigma) Range = R = high value - low value Sigma = S = = 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 = S = sample standard deviation X = Center of Data n-1 n-1

Standard Deviation M (Xi - X)2 Sx = n-1 Measures of Variation (cont.)
Standard deviation is the square root of the average squared deviation of each measurement from the mean. (Xi - X)2 n-1 M Sx = x x x x x x x x x x x x x x x x x x X = 15 Distance from X

Calculating the Standard Deviation
Measures of Variation (cont.) Data = 12, 14, 13, 15, 18, 16, 18, 16, 14, 14 M Xi = 150 M (Xi - X)2 = n = 10 M Xi n 150 10 Sxi = X = = M (Xi - X)2 n-1

WHAT ARE THE THREE "C's OF SPC? CONTROL, CAPABILITY and CENTERING What are the three questions they ask? UCLx LCLx X CONTROL Measures: Process behavior asks: Am I able to predict where the next part will be? 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 LSL NOMINAL USL asks: Am I targeted to my NOMINAL dimension? X

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.

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

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).

Importance of Valid Data GARBAGE IN GARBAGE OUT!! The most powerful statistical analysis cannot change bad data into good information. 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 SOME CONSEQUENCES OF INVALID DATA

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 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: Cutting fluids breakdown, temperature changes, tool wear, etc. EXAMPLE: Power surges, tool breaks, power outage, out-of-round bushing, etc.

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

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

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 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 short-term 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: 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? Cpl Cpu Cpk = Minimum Process Average (Xbar) - Lower Spec. Limit (LSL) Three Sigma ( ) or Upper Spec. Limit (USL) - Process Average (Xbar) Three Sigma ( ) GOAL: Cpk greater than or equal to 1.33 (equates to a 63 DPM rate or better).

What is Process Capability?
LSL USL CAPABLE, CENTERED, AND MEETING SPECIFICATIONS CAPABLE, NOT POTENTIALLY MAKING NON- CONFORMING MATERIAL NOT CAPABLE, NOT CENTERED, AND POTENTIALLY

Cp & Cpk LSL USL Cp MEASURES PRECISION OF A PROCESS Cp > 1.0
ET = USL - LSL Cp MEASURES PRECISION OF A PROCESS Cp > 1.0 X NT = 6o Cpk MEASURES ACCURACY OF A PROCESS Cp > 1.0 Cpk < 1.0 USL - X Cpk measures the distance between Xbar and the nearest spec and compares that to 3-sigma (one-half of the bell curve). 3o X 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.) Cp NOTES: Let's say that: Natural Tolerance = NT = 6
Engineering Tolerance = ET = USL - LSL Cp = ET/NT then: Cp = USL - LSL 6 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.) Cpk NOTES:
Therefore, another index was designed to help us determine if the process is centered. We call this index Cpk. Cpl = X - LSL 3 Use the smaller Cpk = MINIMUM (Cpl, Cpu) = MINIMUM of these two Cpu = USL - X formulas . 3 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 two-sided tolerances? BILATERAL dimensions (i.e., diameters, linear dimensions, etc.) How do we handle capability analysis for one-sided tolerances? UNILATERAL MAXIMUM dimensions (i.e., runout, flatness, etc.) UNILATERAL MINIMUM dimensions (i.e., wall, thickness, etc.)

Bilateral Tolerances BILATERAL Dimensions (i.e., Diameters, Linear Dimensions, etc.) LSL NOMINAL USL X CONVENTIONAL CONTROL CHART CAPABILITY ANALYSIS: USL - LSL Cp = Cpk = MINIMUM { Cpl, Cpu }, where: 6  Cpl = X - LSL Cpu = USL - X (Where )  R and = d 3 3 2 GOAL: Cp & Cpk > 1.33

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: Is there a probability of making product beyond Cpu = USL - X Cpu ANSWERS: the Maximum tolerance allowed? 3 GOAL: Cpu > 1.33

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: Is there a probability of making product below Cpl = X - LSL Cpl ANSWERS: the Minimum tolerance allowed? 3 GOAL: Cpl > 1.33

Control Charts... …are a graphic representation of a process.
UCLx LCLx X …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.) The maximum value expected to be seen. UPPER CONTROL LIMIT (UCL) The average value expected to be seen. CENTRAL LINE (X) LOWER CONTROL The minimum value expected to be seen. 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. One’s goal in life is not to wallpaper the walls of our company’s 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. STRATIFICATION - POINTS HUGGING THE CENTERLINE SEVEN POINTS IN A ROW STEADILY INCREASING (OR DECREASING) POSSIBLE CAUSES Inadequate Gauge Resolution Improvement to Process Gauge Sticking Etc. POSSIBLE CAUSES Gradual deterioration of equipment Operator Fatigue Tool Wear Etc. POINT OUTSIDE CONTROL LIMIT Fixture Moved UCLx A B C X C B A LCLx RUN OF EIGHT POINTS ON THE SAME SIDE OF THE CENTER LINE FOURTEEN POINTS IN A ROW ALTERNATING UP & DOWN POSSIBLE CAUSES Sticky Gauge Worn Die Drift in Controls Etc. POSSIBLE CAUSES Overadjustment of the process Control of two or more processes on the same chart Fixtures or holders not holding work in position Etc.

WHAT ARE THE THREE "C's OF SPC? CONTROL, CAPABILITY and CENTERING What are the three questions they ask? UCLx LCLx X CONTROL Measures: Process behavior asks: Am I able to predict where the next part will be? 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 LSL NOMINAL USL asks: Am I targeted to my NOMINAL dimension? X

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

X-R Chart Preliminaries
X Chart UCL Averages variation is due to long-term, ”between subgroup” sources that include Temperature, Raw Material., People, Shift, Method, Measurement System, Tooling, etc. X LCL R Chart Range variation is due to short-term, “within subgroup” sources that include the Measurement System and the Machine. UCLR 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 PROBLEM: ACHIEVE HIGHER BOWLING SCORES PEOPLE METHODS MEASUREMENT MACHINES MATERIALS ENVIRONMENT ATTITUDE ALCOHOL INTAKE HOW MANY ON TEAM? - PACE EVERYONE SHOW UP? CURVE OR STRAIGHT BALL LENGTH OF ARMSWING USE OF ALLEY ARROWS AMOUNT OF PRACTICE # OF STEPS ON APPROACH SCOREKEEPER - MANUAL OR AUTO AUTO PINSETTER BALL CLEANER BALL MATERIAL BALL WEIGHT SHOES USED LANE OIL TEMPERATURE TIME OF YEAR HUMIDITY NOISE FROM OTHER BOWLERS RAG CLEAN USE RAG TO WIPE OFF BALL USE WRIST BAND? TYPE OF WRIST BAND AMOUNT OF BALL LIFT

CHART FOR AVERAGES AND RANGE (X AND R)
NAME: Rodney D. Alley: BOWLORAMA Weeknight: MONDAY Team Name: THE BANANNAS League Name: MILLER HIGH LIFE Chart No.: __ of __ Key Characteristic: BOWLING SCORE DATE LANE NO. NOTES SAMPLE MEASUREMENTS 1 2 3 4 (X) AVERAGE (R) RANGE SUM RANGE (X) (R) 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 1/10 1/17 1/24 1/31 2/7 2/14 2/21 2/28 3/7 3/14 3/21 3/28 4/4 4/11 4/18 4/25 5/2 5/9 5/16 5/23 1-2 3-4 5-6 7-8 9-10 11-12 13-14 15-16 17-18 19-20 1 2 3 145 150 155 135 165 130 158 157 140 125 148 160 162 170 172 168 171 136 120 134 151 103 188 210 195 190 220 200 225 205 215 203 212 202 198 193 196 211 450 455 445 462 433 487 490 495 496 497 381 388 593 610 640 613 627 611 609 152 154 144 163 166 127 129 213 204 209 10 30 28 25 35 15 14 6 12 16 48 22 20 7 9 23 40 180 240 CHANGED STYLE (Can't make spares, getting lots of strikes) STARTED THROWING PRACTICE GAME RECEIVED COACHING ON SPARES ELIMINATED POOR FIRST GAME

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: 1) Prepare Core 2) Wrap core with two layers of wool and polyester yarn 3) Wrap with thin, white cotton cord KC: 3.75” +/- .05” 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
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 _____ 2) What patterns seem to be present? Check all that apply. __ Saw tooth __ Trend __ 2 of of three points near Zone A __ Points outside the 3-sigma control limits Should the Operator take action or leave the process alone?

Collection and Analysis
Attribute Data Collection and Analysis UCLc LCLc c

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?

Collect Qualitative Data
Attribute Model Collect Qualitative Data Turnbacks Count Data (Defects) Classification Data (Defectives) QCPC Constant Subgroup Size Constant Subgroup Size N U-Chart N P-Chart Y Y C-Chart NP-Chart Quality Level Acceptable Y Certify N RRCA Pareto Top Opportunities 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 Basics X LSL USL NOMINAL UCLx LCLx X.

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