spc training
DESCRIPTION
Spc trainingTRANSCRIPT
1
HEIL
INTRODUCTION TO SPC (Statistical Process Control)
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TRAINING AGENDA
HANDS ON LEARNING!! Limitation of Inspection Specification discussion What is SPC? Why SPC is a better? How SPC works? Control Chart You may learn to like statistics.
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F EXERCISE F EXERCISE
IMAGINE FOR ONE BRIEF MOMENT THAT EACH OF THE ONE HUNDRED AND FORTY-ONE WORDS OF THIS PARAGRAPH IS A SEPARATE COMPONENT FORM A FIRST SHIFT RUN OF FOURTEEN-INCH FLYWHEELS. YOU ARE ONE OF FIVE INSPECTORS PERFORMING THE FINAL INSPECTION OF THSES FINSISHED COMPONENTS WHICH WERE PRODUCED ON FOUR FAIRLY SMALL DIAL INDEX MACHINES THAT ARE NOT BEING CONTROLLED BY THE USE OF STATISTICAL TECHNIQUES. AS CAN BE EXPECTED FROM AN OPERATION OF THIS NATURE, THERE ARE A NUMBER OF DEFECTIVES COMPONENTS BEING MADE. EACH WORD THAT CONTAINS AN F REPRESENTS A DEFECTIVE COMPONENT. HOW MANY OF THE DEFECTIVES ARE YOU ABLE TO FIND? CHECK AGAIN AND INSPECT FOR THE PRESENTS OF F'S. WRITE YOUR FINAL COUNT IN THE BOTTOM LEFT HAND CORNER OF THIS PAGE. THIS EXAMPLE SHOULD GIVE YOU A FAIR IDEA OF HOW RELIABLE 100% INSPECTION CAN BE.
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INSPECTIONDraw sample
Meets spec. ?
ACCEPT REJECT
YES
NO
How good was it?Barely meet spec?middle of spec? Same as before?
How bad was it?Just outside spec?Way out of spec? Same as before?
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INSPECTION
Lower Spec.
AB
What's the difference between ball A and B?Why is the spec there and not somewhere else?What is the purpose of the spec?
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SPECIFICATION
Great!!!I'm in spec.
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SPECIFICATION
Hey!!!!!But I'm in spec.
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TARGETEvery specification has a TARGET.The upper and lower specificationis meant to serve as a guide line. What you really want is the stuffthat hits the TARGET.
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SCREW SPECIFICATION
TARGET= .25UPPER SPEC = .27
LOWER SPEC = .23
SCREW TOLERANCE = +/- .02"
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NUT SPECIFICATION
TARGET= .26UPPER SPEC = .28
LOWER SPEC = .24
NUT TOLERANCE = +/- .02"
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TARGET= .26UPPER SPEC = .28
LOWER SPEC = .24
TARGET= .25UPPER SPEC = .27
LOWER SPEC = .23
SCREW
NUT
SCREW = 26.8"
NUT = 24.8"
COMBINED TOLERANCE
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Meeting specification is not enough
we need a way to communicate more.
What ???
LEANRING 1
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Average Income
Country X Country Y
10,000 Rs/Month 11000 Rs/Month
Which country is ECONOMICALLY more stable ???
Example
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Country X Country Y
8000 4600012000 300010000 10009000 300011000 2000
Avg. 10000 11000
Std dev. 1414 17516
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Meeting specification is not enoughwe need a way to communicate
How close to target
How spread out the results were
LEANRING 2
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Statistical Process Control A monitoring tool that let's us know when a process is changing before products become unacceptable
It is a prevention tool– Inspection = defect detection– SPC =detect process change
defect prevention
What is SPC?
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Inspection does not assure quality inspection is too late, its after the fact need to detect process change before defectives are produced
Meeting specification does not go far enough
WHY SPC?
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Quantitify the Mue and the Sigma of a process and detects change from the standard deviation by calculating the
control limit by estimating the Rbar over d2 to estimate the inherent variation of a process for a given alpha and beta risks.
SPC, how does it work
Ooopps tough to understand……
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JUST KIDDING!
SPC quantifies variability and allowsyou to determine if a process changed.
It is simple and easy to understand.
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First order
lowerspec.
Upperspec.size
DISCUSSION ON VARIABILITY
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Second order
lowerspec.
Upperspec.size
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After 6 orders
lowerspec.
Upperspec.size
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After 12 orders
lowerspec.
Upperspec.size
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Over the long run a pattern begins to develop. Notice there is a large cluster in the middle. As further from the middle you go, there are less and less
lowerspec.
Upperspec.size
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lowerspec.
Upperspec.size
If the source of the material is stable, over a long time period, a bell like shaped curve will emerge from the inspection. The Bell shape curve is alsocommonly referred to as the Normal distribution
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4.2 12.4 65.2 14.8 7.85.4 18 112.1 17 11.89 19 9.4
9.6 15.5 10.813 2 1014 5 1115 7 10.19.6 10.1 8.8
DataPlot HISTOGRAM for following DATA
What is HITOGRAM?
Why we need it to understand?
What is this BELL shape and normal distribution?
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CHARACTERISTICS OF A NORMAL DISTRIBUTION
LOCATION
SPREAD
LEANRING 3
LOCATION: The central tendencyit is usuallyexpressed as theAVERAGE
SPREAD:The dispersion it is
usually expressed as SIGMA
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Distribution Patterns
Saw tooth Positively SkewedNegatively Skewed
Sharp Drop Twin Peak Bell Shape
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Average different Spread same
A B
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Average same Spread different
AB
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A B
Average differentSpread different
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SIGMA -measure of spread
sigm
a
LEANRING 4
3332%32% 14%14%2% 2%
+/- 1 sigma
+/- 2 sigma
+/-3 sigma
3432%32% 14%14%2% 2%
64.25%
96.45%
99.73%+/-3 sigma
+/-2 sigma
+/-1 sigma
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34.13%34.13% 13.6%13.6%2.14% 2.14%
+/- 1 sigma
+/- 2 sigma
+/-3 sigma
68.26%
95.45%
99.73%
LEANRING 5
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64%
96%99.7%+/-3 sigma
+/-2 sigma
+/-1 sigma
14 2
32 gallons
IF the upside-down bell curve could hold100 gallons of water.....
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•It is symmetrical , unimodel and bell shaped.•It is uniquely determined by the two parameters , namely mean and standard deviation.•In the family of normal curves smaller the standard deviation , higher will be the peak.•If the original observations follow a normal model with mean mu and std dev sigma then the averages of random sample of size n drawn from this distribution will also follow a normal distribution. •The mean of the new model is same as the original model I.e mu but the standard deviation gets reduced to (sigma)/root "n"
Properties of a normal model curve :-LEANRING 6
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Sources of Variation
Common Cause
Special Cause
39TIME
PREDICTION
If only common cause of variation are present, the output of a process forms a distribution that isstable over time and is PREDICTABLE.
LEANRING 7
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That's great, we can make prediction basedon sigma, So what?
Once we know the sigma of a process then;Process has not changed if it is inside +/- 3 sigma. If outside +/- 3 sigma, process has changed
SO WHAT?
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SINCE WE CAN NOT SAMPLE 100 UNITS TODETERMINE IF OUR MANUFACTURING PROCESSHAS CHANGED WE NEED A QUICK EFFECTIVE WAY TO MEASURE THE TWO ATTRIBUTE OFA PROCESS; THE CENTER AND THE SPREAD
CENTER = AVERAGESPREAD = RANGE
= (MAXIMUM - MINIMUM)
Why Average ????
LEANRING 8
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The Central Limit Theorem
The Central Limit Theorem states that the mean values of samples taken from ANY distribution
tend towards a normal distribution as the sample size increases.
This computer demonstration provides convincing evidence of this surprising fact. Thus, taking samples from a distribution and averaging the observationswithin the samples effectively eliminates the effect of the underlying distribution, however 'non-normal' it may be.This demonstration works with two symmetrical distributions: one is triangular and has some features in common with the normal distribution while the other is a 'V'-shaped notch - almost the total opposite of the type of distributions we see in applied statistics. Both distributions have a mean of 50.00. We can model these distributions by supposing we have two packs containing cards numbered 1 - 99. The first pack would have: One 1, two 2s .... fifty 50s, forty nine 51s, .... two 98s, and one 99 While the second would have:Fifty 1s, forty nine 2s ... two 48s, one 50, two 51s, ..... fifty 99sThe computer draws cards according to these distributions for sample sizes of 1 (to verify the concept of 'distribution'), 2, 5 and 10. When the sample size is 1, we are really confirming that the data 'in the long run' will behave like the distribution - which is in itself an important statistical lesson.The case {Sample Size = 2} is particularly interesting. It is not easy to to 'outguess' the computer and predict the shape of the lower curve; however, once the curve is seen, it can be readily explained in terms of basic probability.Although the second case is very extreme (literally!) compared with the first, it eventually falls into a 'normal' shape although it takes longer to do so.
LEANRING 9
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The Arithmetic mean :
Most of the time when we refer to the average of something we are talking about arithmetic mean only. To find out the arithmetic mean , we sum the values and divide by the number of observation.
Advantages : it's a good measure of central tendency.It easily understood by most people
Disadvantages :- Although the mean is reliable in that it reflects all the values in the data set, it may also be affected by extreme values that are not representative of the rest of the data.
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The Median :The median is a single value from the data set that measures the central item in the set of numbers.Half of the item lie above this point and the other half lie below it.
We can find median even when our data are qualitative descriptions.
For example we have five runs of the printing press the results of which must be rated according to the sharpness of the image.Extremely sharp, very sharp, sharp slightly blurred, and very blurred.
Mode :-The mode is a value that is repeated most often in the data set. Infect it is the value with highest frequency.
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23CONTROL CHART TEMPLATE
23242627
12345
AverageRange
How was our process behavingover time? Let's calculate theaverage and range of each set
average = (23+23+24+26+27)/5 = 24.6
Range = 27 - 23 = 4
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12345
avgMin.MaxRange
aver
age
rang
eCONTROL CHART TEMPLATE
2323242627
24.6
4
2225252627
25.0
5
2323242727
2224242526
24.8 24.2
4 4Plott the average and the range on the controlchart template
Notice the center and the spreadof the process varies much likewhen we looked at the histogram
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x-bar Chart
If you thought of the control charts as a stretched outslinky, it would look like a histogram if you collapsedit. Since the control chart is nothing more than ahistogram expressed over time, what we said aboutSIGMA applies to the control chart as well.
LEANRING 9
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64%
96%99.7%+/-3 sigma
+/-2 sigma
+/-1 sigma
14 2
32 gallons
IF the upsidedown bell curve could hold 100 gallons of water.....
Reminder, what we said about sigma
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+/- 3 sigma
We can calculate the sigma of all the points in the control charts and draw lines at +/- 3 sigma. Since 99.7% of the vaules are suppose to fit in the linewe can say that a process has changed if it one of the points are outside the +/- 3 sigma lines. Wewill call the +/-3 sigma lines the CONTROL LIMIT
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HOW DO YOU CALCULATE CONTROL LIMITS?
In the past it was important for operators and auditorsto be able to calculate the control limit. Today, in most
manufacturing plants the computer calculates the control limits and people interpret them.
This makes sense because computers are excellentat calculating number. However, computers are not too intelligent. They can not reason and make gooddecisions. People are very capable of reasoning andmaking good decision. However, people need good
information. SPC is a tool that converts process data toinformation allowing people to focus on what they do best.
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Control Limits for
Average and Range Chart
X =X+X+X+…X1 2 3 n
nR =
R+R+R+…R1 2 3 n
n
UCL = X + A2R
CL = X
LCL = X - A2R
UCL = D4R
CL = R
LCL = D3R
LEANRING 10
52HOW LONG DOES IT TAKE TO GET TO WORK?
WE USE STATISTICS EVERYDAY
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TYPES OF VARIABILITY
Common cause= normal, InherentArrive work between 7:55 to 8:01due to number traffics lights that you stopped at on your way to work.
Special cause = assignableArrived to work today at 8:45 because;
a) flat tire on the way to workb) Accident on the interstatec) I met up with an old drinking buddy and I stayed out later than I should have.
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PROCESS CAPABILITY ANALOGY
Bill, Nice guy. works in the accounting department. He lives 10 miles away from work. In order to get to work he takes the interstate I-95 and gets off at exit 23 and zips right into work. He never hits any trafficand there is no traffic light between his home and work.He's never late to work.
Judge Lance Ito. Nice guy. Works in Los Angeles. He lives 5 miles from work. In order to get to work he has to get through 5 traffic light onto interstate I-5(which is frequently backed up) to downtown Los Angeles. There he has to find parking and then fight the reporters on his way into the court to preside over the O.J. Simpson trial. He is late to work quite frequently.
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PROCESS CAPABILITY ANALOGY
BillArrives to work between7:48 to 7:56 AM.
Judge Lance ItoArrives to work between 7:48 to 8:06 AM
8:06 8:128:007:547:487:42
Late to work
Arrival time at work
Early to work
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PROCESS CAPABILITY ANALOGY
Bill
Judge Ito
8:06 8:128:007:547:487:42
Late to work
Arrival time at work
Early to work
If we thought of being early or late to work as our specification, then we can say that Bill IS capable meeting the specification. Judge Ito IS NOT capable of meeting the specification.
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PROCESS CAPABILITY ANALOGYBillArrives to work between7:48 to 7:56 AM 99.7% of time. 6 sigma = 7:56 -7:48 = 8 min.
Judge Lance ItoArrives to work between 7:48 to 8:06 AM 99.7% of time. 6 sigma = 8:06 - 7:48 = 18 min.
Tolerance = late - early = 8:00 - 7:46 = 14 minutes
Capability = tolerance if greater than 1 we say it 6 sigma is capable of meeting spec.
Bill's Capability = 14 / 8 = 1.75 (Bill is capable)Ito's Capability = 14/18 = .78 (Ito IS NOT capable)
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LEANRING 11
Cp = Tol band / 6 sigma
Cpk = Min of (Avg - LSL) or (USL - Avg) / 3 sigma
(n-1)=√(x-x ) + (x-x ) + … (x-x )
(n - 1)
_ _ _
1 2 n2 2 2
(R abr) R
d2
=
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+/- 3 sigma
+/- 3 sigma
X-bar chart
Range chart
The control limits can be drawn around both the average (x-bar) and the Range chart. Therefore, you can detect several different types of change.
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LOCATION SHIFTS
Process spreadremains samewhile center increases
let's see what that looks likein a control chart
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+/- 3 sigma
+/- 3 sigma
X-bar chart
Range chart
Spread remains sameCenter shifts up
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SPREAD CHANGE
Process spreadincrease whilecenter remain same let's see what
that looks likein a control chart
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+/- 3 sigma
+/- 3 sigma
X-bar chart
Range chart
Spread increasedCenter remain same
?
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+/- 3 sigma
+/- 3 sigma
X-bar chart
Range chart
Spread increasedCenter remain same
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Note that when the process variation increased the Range chart points shifted to a higher level. However, the process center (X-bar) seems to swing wildly going out of both Upper and Lowercontrol limit while the average is still the same.
Because of the tendency of the X-bar chart to swing with increase variability, the Range chartmust be reviewed first to determine if the processvariability increased prior to looking at the X-barchart to determine if the process shifted.
LEANRING 12
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+/- 3
sig
ma target
TREND
Rule of thumb, if there are 7 points in a row all higher or lowerthan the preceeding point. In this case from the start of the trend to the time a point went outside the control limit there were12 samples. An experinced operator/auditor would begin lookingfor assignable cause much sooner.
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+/- 3
sig
ma target
SHIFT
Rule of thumb, if there are 6 consequetive points above or below the target line, a process shift has occurred. In this case, because the process shifted to somewhere between the target and the upper controllimit, there is a good chance that a point will be outside the control limit soon. In the above example, it took about 11 points to go outside thecontrol limit. An experienced operator/auditor would have looked forassignable cause sooner.
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Summary.. Process changes
Small shift .. in Center while Spread same in Spread while Center same
Large shift in Center up or down while Spread same
Spread increase while Center same
Center slowly trending up or down while spead same
Center shift up or down at the same time the spread increase
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So you now know how to detect change in a process. You even know how to detect different type of change to the process distribution. Up to now we have not talked about the QUALITY of the products being produced while the process is controlled using SPC methods.
If we control the process the process will produce parts with variation as the equipment is CAPABLE of producing. We call this PROCESS CAPABILITY.
PROCESS CAPABILITY
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8:06 8:128:007:547:487:42
Lowerspec.
Upperspec.
CpCpk
TAR
GE
T Cp Cpk..... Say what?
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8:06 8:128:007:547:487:42
Lowerspec.
Upperspec.
Cpk
TAR
GE
T
Cpk = Target - lower spec or Upper spec - Target 3 sigma 3 sigma
Cpk looks at the likelihood of making product outsideeither lower or upper specification
Cpk
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IT IS IMPORTANT TO KNOW WHAT YOUR MACHINE IS
CAPABLE OF PRODUCING. OTHERWISE YOU MAY BE
CHASING YOUR TAIL TRYING TO GET THE
MACHINE TO DO WHAT IT IS NOT CAPABLE OF DOING.
LEANRING
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X-bar chart
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x UPPER SPEC
LOWER SPEC Each point is an averageof five indivdual points
x
xx = xx
x
Each red x represents five individualreading (blue x) that are spread outmore than the average (red x)
Control chart will not differentiate a capable anda not capable process. it will only signal change.The control chart does not care what the spec is.
UpperControl Limit
LowerControl Limit
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xmachine capabilit y
Upper spec
Lower spec
If your process is not capable, then there is a good chance that some of your sample will have valuesoutside the specification. Chances are if you are notrunning SPC control chart, you may be tempted to make an adjustment. Let's see what would happen.
LEANRING
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machine capabilit y
Upper spec
Lower spec
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If by the luck of the draw you get a reading below the lower specification even though the process has not changed, and adjusted the machine up. The distribution will shift up.
Sample
Adjust
machin
e up
LEANRING
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machine capabilit y
Upper spec
Lower spec
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After the distribution shifted up, there is now amuch greater chance of getting a value outside upper specification. So the machine is adjusted down, slightly more than it was adjusted up.
Chance of out ofspec is now = 40%
Chance of out ofspec was = 10%
Adjust machine down
LEANRING
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Actual r an ge of pro duct pro duced
mach ine capability
Upper spec
Lower spec
The adjustments continues until, the actual products produced varies much more than the capability of the machine.
LEANRING 13
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machine capabilit y
Upper spec
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If you are controlling your process using SPC Method,even if your process is not capable, no adjustmentwould take place. Therefore, the product you producedis what the machine is capable of and not more.
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UpperControl Limit
LowerControl Limit
LEANRING 14
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ATTRIBUTE CONTROL CHARTS
p-Chart c - Chart np-Chart u - Chart
Variable Sample
FixedSample
DefectsDefectives
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Measurement System
Analysis
(MSA)