spc training

1

HEIL

INTRODUCTION TO SPC (Statistical Process Control)

2

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.

3

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.

4

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?

5

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?

6

SPECIFICATION

Great!!!I'm in spec.

7

SPECIFICATION

Hey!!!!!But I'm in spec.

8

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.

9

SCREW SPECIFICATION

TARGET= .25UPPER SPEC = .27

LOWER SPEC = .23

SCREW TOLERANCE = +/- .02"

10

NUT SPECIFICATION


LOWER SPEC = .24

NUT TOLERANCE = +/- .02"

11


LOWER SPEC = .24


LOWER SPEC = .23

SCREW

NUT

SCREW = 26.8"

NUT = 24.8"

COMBINED TOLERANCE

12

Meeting specification is not enough

we need a way to communicate more.

What ???

LEANRING 1

13

Average Income

Country X Country Y

10,000 Rs/Month 11000 Rs/Month

Which country is ECONOMICALLY more stable ???

Example

14

Country X Country Y

8000 4600012000 300010000 10009000 300011000 2000

Avg. 10000 11000

Std dev. 1414 17516

15

Meeting specification is not enoughwe need a way to communicate

How close to target

How spread out the results were

LEANRING 2

16

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?

17

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?

18

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……

19

JUST KIDDING!

SPC quantifies variability and allowsyou to determine if a process changed.

It is simple and easy to understand.

20

First order

lowerspec.

Upperspec.size

DISCUSSION ON VARIABILITY

21

Second order

lowerspec.

Upperspec.size

22

After 6 orders

lowerspec.

Upperspec.size

23

After 12 orders

lowerspec.

Upperspec.size

24

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

25

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

26

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?

27

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

28

Distribution Patterns

Saw tooth Positively SkewedNegatively Skewed

Sharp Drop Twin Peak Bell Shape

29

Average different Spread same

A B

30

Average same Spread different

AB

31

A B

Average differentSpread different

32

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

35

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

36

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.....

37

•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

38

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

40

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?

41

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

42

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

43

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.

44

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.

45

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

46

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

47

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx x

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

48

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

49

x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

+/- 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

50

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.

51

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

53

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.

54

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.

55


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

56


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.

57

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)

58

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

=

59

x


x


+/- 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.

60

LOCATION SHIFTS

Process spreadremains samewhile center increases

let's see what that looks likein a control chart

61

+/- 3 sigma

+/- 3 sigma

X-bar chart

Range chart

Spread remains sameCenter shifts up

62

SPREAD CHANGE

Process spreadincrease whilecenter remain same let's see what

that looks likein a control chart

63

+/- 3 sigma

+/- 3 sigma

X-bar chart

Range chart

Spread increasedCenter remain same

?

64

+/- 3 sigma

+/- 3 sigma

X-bar chart

Range chart

Spread increasedCenter remain same

65

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

66

+/- 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.

67

+/- 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.

68

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

69

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

70

8:06 8:128:007:547:487:42

Lowerspec.

Upperspec.

CpCpk

TAR

GE

T Cp Cpk..... Say what?

71

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

72

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

73

X-bar chart

x


xx

xxxxxxxxx

xxx

xxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x

xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

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

74

xx

xxxxxxxxx

xxx

xxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

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

75

xxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxxxxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

machine capabilit y

Upper spec

Lower spec

xxxx = x

x

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

76

xxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxxxxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

machine capabilit y

Upper spec

Lower spec

xxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxxxxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

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

77

xx

xxxxxxxxx

xxx

xxxxxxxxx

x xxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

xx

xxxxxxxxx

xxx

xxxxxxxxx

x xxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

xx

x

xx

x

x

xx

xxxxxxxxx

xxx

xxxxxxxxx

x xxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

xx

xxxxxxxxx

xxx

xxxxxxxxx

x xxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxx

xxxxxxxxx

xxxxxxxx

x

xx

xx

x

xx

x

x

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

78

xxxxxxxxxxx

xxxxxxxxxxxx

xxxxxxxxxxx

xxxxxxxxxxx

x

xx

xxxx

xxxxxxxxx

xxxxxxxx x


xx x

x xx

xxxxx

xxxxxxxxxxxx

xxxxxxxx

x

xx

x xx

xx

x

x

machine capabilit y

Upper spec

Lower spec

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.

x


x

xx = xx

x

UpperControl Limit

LowerControl Limit

LEANRING 14

79

ATTRIBUTE CONTROL CHARTS

p-Chart c - Chart np-Chart u - Chart

Variable Sample

FixedSample

DefectsDefectives

80

Measurement System

Analysis

(MSA)

spc training

Automotive