SPC Training by D&H Engineers

Six Sigma - Variation

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SPC - Module 1Understanding variation and basic principles

SPC

AIM OF SPC COURSETo enable delegates to better understand variation and be able to

create and analyse control charts

OBJECTIVESDelegates will be able to:-

– Appreciate what variation is– Understand why it is the enemy of manufacturing– Know how we measure and calculate variation– Understand the basics of the normal distribution– Identify the two types of process variation– Understand the need for objective use of data– Produce I mR charts for variable data– Understand the basic theory behind control charts– Know how to analyse control charts

The History Of SPC

1924 - Walter Shewhart Of Bell Telephones Develops The Control Chart Still Being Used Today1950 - Dr W Edwards Deming Sells SPC To Japan After

World War II1965 - Ford Failed To Implement SPC Due To No Management Commitment1985 - Ford Finally Implement SPC1989 - Boeing roll out SPC1992 - BAe Decide To Implement SPC2002 - Airbus UK start SPC in key business areas

Variation

No two products or processes are exactly alike. Variation exists because any process contains

many sources of variation. The differences may be large or immeasurably small, but always

present.

They will vary due to common cause variation. If we introduce a special cause of variation into the process, then the process will vary more than usual.

Variation is a naturally occurring phenomenon inherent within any process.

Sign your name on a piece of paper three times, even if you sign it in the same pen, straight after one another, each one will vary slightly from the last one.

Variation

-------------Signature 1

-------------Signature 2

-------------Signature 3

-----------------Signature 4

Rank in order of desirability

Customer specification limits are the outside edge of yellow zone

Why do we need to improve our processes….

•To reduce the cost of manufacturing•Our competitors may already be leading the way•Our processes are not predictable•To improve quality

By improving processes we can….

•Reduce costs•Increase revenue (sales)•Have happier customers•Make our jobs more secure•Increase job satisfaction

So what to do….?•Commit to improving quality - make process capability measurable and reportable. So we will know we are getting better.

•Solve problems as a team rather than individuals. Teams get better and more permanent improvements than individual efforts.

•Gain better understanding of our process by studying measurement data in an informed way (control charts)

•Consider all possible pitfalls when implementing improvements.

•When improvements are made - make them permanent ones.

Quality of data:

We may have lots of data, but ….Does it represent the process outputs we are interested in ?

Is it representative of our current process ?Can we split it into subsets to aid problem solving ?

Can it be paired with process inputs ?Is the operational definition for how measurements are taken and

data recorded ?Has the measurement system been assessed for stability and

reliability (gauge R&R)

Garbage in, garbage out !

Attribute (discrete) data is that which can be countedExamples:

On or Off?

Variable (continuous) data is that which can be physically be measured on a continuous scaleExamples:

Temperature

Weight

Broken orunbroken?

Attribute Vs. Variable data

Attribute Vs. Variable dataWhich type of data ?

Length in millimetersSMC (standard manufacturing cost)

Number of breakdowns per dayAverage daily temperature

Proportion of defective itemsNumber of spars with concession

Lead time (days)Mean time between failure

Variable Attribute

Which is best ?

Variable data should be the preferred type as it tells us more about what is happening to a process.

Attribute - tells us little about the process

Variable - gives plenty of insight into the process

HistogramA GRAPHICAL REPRESENTATION OF DATA

SHOWING HOW THE VALUES ARE DISTRIBUTED BY:

•Displaying The Distribution Of Data•Displaying Process Variability (Spread)• Identifying Data Concentration

Histogram

• Graphic Representation of The Data

• Bar Chart• Vertical (y) axis shows the frequency of occurrence

• Horizontal (x) axis shows increasing values

01

2345

67

9.1 9.2 9.3 9.4 9.5 9.6

Note : To produce histograms quickly use Excel’s Data Analysis Tool pack.

The sample Average or Mean.

• Example

• A set of numbers:

• 3,6,9,7,5,9,10,0,4,3

• Total = 56

• Average = 56 = 5.6 10

The Sample Range

Use The Following Dataset 5,2,9,12,3,19,7,5

The Sample Range is the largest value minus the smallest value

19-2=17The Range = 17

The Normal Distribution Curve

Typical process range

The normal curve illustrates how most measurement data is distributed around an

average value.

Probability of individual values are not uniform

Examples Weight of componentWing skin thickness

–Single peaked–Bell shaped–Average is centred–50% above & below the average

–Extends to infinity (in theory)

Characteristics Of The Normal Curve

How do we measure variation ?

Variation in a process can be measured by calculating the ‘standard deviation’

The Formula = ² n-1

The Standard DeviationoUse The Following Dataseto5,2,9,12,3,19,7,5

oThe Formula = x-x )² n-1

o (5-7.75)²+(2-7.75)²+(9-7.75)².....(5-7.75)² 7

i

Note : In excel you can use the STDEV function. It’s quicker than pen & paper !

Normal Distribution Proportion

68.3%

+/- 1 Std Dev = 68.3%

-4 -3 -2 -1 0 1 2 3 4

2


95.5%

+/- 2 Std Dev = 95.5%

-4 -3 -2 -1 0 1 2 3 4

4


99.74%

+/- 3 Std Dev = 99.74%

-4 -3 -2 -1 0 1 2 3 4

6

Control chartsA control chart is a run chart with control limits plotted on it.

A control chart can be used to check whether a process is predictable within a range of values

Control limits are an estimation of 3 standard deviations either side of the mean.

99.74% of data should be within 3 standard deviations of the mean if no ‘special cause’ variation is present.

Different types of variationCommon cause - random variation

Special cause variation

•The variation that naturally exists in your process assuming ‘nothing’ changes. This type of variation is predictable in so far as you can predict the range that your process will operate within•Difficult to reduce (advanced problem solving tools required)

•This is the type of variation is unpredictable and is exhibited in an unstable process. Variation may not look ‘normal’. No one knows what is going to happen next !•Easy to detect and reduce (but only if robust control systems are in place)

Examples of different types of variationCommon cause - random variation

Special cause variation

•Temperature•Humidity•Standard operating methods•Measurement systems•Normal running speed

•Sudden breakdown of equipment•Power failure•Unskilled operator•Tool breakage

Objective use of data

Reacting to a single item of data without first considering the normal variation expected from a process can :

...waste time and effort correcting a problem that may be due to random variation.

...increase the process variation by tampering with it thus making the process worse

Using data objectively can ensure you :...have the facts to back up your decisions.

...can quantify any improvements you make statistically

Objective use of data…

In God we trust….

….for everything else show us the data !

Upper spec limit = 8.Is this process in control ?

2468

10

12

14

Yes , the process is in control but not capable.

2468

10

12

14

UCL

LCL

Attribute data is that which can be countedExamples:

On or Off?

Variable data is that which can be physically be measuredExamples:

Temperature

Weight

Broken orunbroken?

Attribute Vs. Variable data

Variable Control Chart

–Establishes the values of a single component characteristic measured in physical units

Product Weight (kg) Curing Time (hrs) Component Length (mm)

Control Chart

Individual - Moving Range Charts(Also known as X-mR or I-mR)

Assumptions :

•Variable data.

•Normal distribution

Decide on operation to be measured

Decide on sample frequency

Establish characteristic

Record reading & date

Record any changes to the process on chart

Calculate range

Plot Graphs

Calculate control limits

Identify and take appropriate action if process out of control

Activity ExerciseGroups of 2 or 3 people

Objective: Represent a machine that cuts bar to length~cut drinking straws to 30mm length (approx. 20 off)

Operation: cut drinking strawsCharacteristic: LengthSample frequency: 100%

Cut by eye, 1 straw at a time to an estimated 30mmMeasure the straws in the order that they are cutRecord the information on a chart (remember to input data and update chart as you go)One person records, one person cutsNo communication between the operator and tester.

UCL x = Xbar + 2.66 x mRbarLCL x = Xbar - 2.66 x mRbarUCL r = 3.267 x mRbar

222426283032343638404244

0123456789

10

_

Date Time XmR -----

Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100%Characteristic Length Chart No two Specification Limit 30mm +/- 6mmXbar = UCL= LCL=

mRbar = CL =


222426283032343638404244

0123456789

10

_

Date Time X 38 39 36mR ----- 1 3

Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100%Characteristic Length Chart No two Specification Limit 30mm +/- 6mm

Xbar = UCL= LCL=

mR bar = CL=

X XX

XX


222426283032343638404244

0123456789

10

_

Date Time X 38 39 36mR ----- 1 3

Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100%Characteristic Length Chart No two Specification Limit 30mm +/- 6mm

Xbar = UCL= LCL=

mR bar = CL=

MOVING RANGE CHART

AVERAGE CHART

_mR = ENTER mR FIGURES

INTO CALCULATOR

Upper ControlLimit of mR = _D4 X mR

=

_ D4 X mR

=

_X =

ENTER X FIGURESINTO CALCULATOR

=_X

ucl X+ (E2_X

ucl mR

lcl XmR)_X

X+ =

=

x

-

-

X

XX

Lower ControlLimit of X = _ X - (E2 x mR)

Upper ControlLimit of X = _ X + (E2 x mR)

mR)

(E2

_mR

X AND mR CONTROL CHART CALCULATING CONTROL LIMITS

_

_

_

_

Table of Constantsfor Control Charts

X and R Charts Charts for Individuals

Chart forAverages

_(X)

Charts forIndividuals

(X)Chart for Ranges (R)

Factors forControlLimits


Divisors forEstimate ofStandardDeviation


SubgroupSize

A2

d2

D3

E2

D4

n

1

2

3

4

5

6

7

8

9

10

1.880

1.880

1.023

0.729

0.577

0.483

0.419

0.373

0.377

0.308

1.128

1.128

1.693

2.059

2.326

2.534

2.704

2.847

2.970

3.078

-

-

-

-

-

-

0.076

0.136

0.184

0.223

3.267

3.267

2.574

2.282

2.144

2.004

1.924

1.864

1.816

1.777

2.660

2.660

1.772

1.457

1.290

1.184

1.109

1.054

1.010

0.975

MOVING RANGE CHART

AVERAGE CHART

_mR = ENTER mR FIGURES

INTO CALCULATOR

Upper ControlLimit of mR =

_D4 X mR

=

_ D4 X mR

=

_X =

ENTER X FIGURESINTO CALCULATOR

=_X

ucl X+ (E2_X

ucl mR

lcl XmR)_X

X+ =

=

x

-

-

X

XX

Lower ControlLimit of X = _ X - (E2 x mR)

Upper ControlLimit of X = _ X + (E2 x mR)

mR)

(E2

_mR

8.363.267 2.56

2.562.66 39.4

25.8

32.6

2.56

2.562.66

32.6

32.6

_

_

_

_

X AND mR CONTROL CHART CALCULATING CONTROL LIMITS


222426283032343638404244

0123456789

10

_

Date Time X 38 39 36 34 38 37 40 36 34 32 29 31 28 32 31 27 28 29 32 35 29 30 30 27mR ----- 1 3 2 4 3 3 4 2 2 3 2 3 4 1 4 1 1 3 3 6 1 0 3

Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100%Characteristic Length Chart No two Specification Limit 30mm +/- 6mmXbar = 32.6 UCL= 40.2 LCL= 26.7

mR bar = 2.56 CL= 8.38

Analysing Control ChartsShake Down

To Convert a control chart into the form of a Histogram

Turn the control chart on its side And imagine that the points would fall into a normal distribution curve

Control Chart Analysis

– Any Point Outside Control Limits

– A Run of 8 Points Above or Below the mean

– Any Non-Random Patterns

1 34

25

6 7 89

10

13

14

121516

17

181119

20

1 34

256 7

8

9

10131412

151617

18

11

1 34

25 6

7 8 910 1211

1920


Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

01

234

56

Range

UCL

R bar

Is there any signs of special cause present ?


Individuals

0

2

4

6

8

10

12

14

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar

Is there any signs of special cause present ?

Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar


Any special cause here ?

Individuals

0

2

4

6

8

10

12

14

X barUCLLCLData

Moving Range

0

1

2

3

4

5

Range

UCL

R bar


What has changed ?

Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar


What has changed ?

Now make a change to the process

Is the process in control ?

Is there a better way of meeting your customers’ needs ?

Modify the process to try to reduce variation and make production more on target.

Plot the data on the chart.

What should you do to the limits ?….

NOTE : Not all data is normally distributed

•Variable control charts limits are based on normal theory.•If the distribution is non-normal the theory falls down•If your data is not normally distributed consult an expert in statistical analysis for advice

Calculating Control limitsWhen calculating limits remove any special causes

that you know the reason for.

Only recalculate limits when a change is made to the process.

Ask “what’s changed?”, and investigate root causes.

Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar

When to change limits

Changed supplier

Re-calculate from here

Limits changed to reflect shift in average…Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar

What would you do if you changed back to the original supplier ?

Individuals

024

6

8

1012

14

16

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar


Where would you re-calculate limits ?

New operator


Individuals

0

2

4

6

8

10

12

14

X barUCLLCLData

Moving Range

0

1

2

3

4

Range

UCL

R bar

What would you do here ?

Would you change limits ?

Why is 8 points on one side of the mean attributed to special cause ?

First let’s consider why we set the upper and lower control limits at +/- 3SD.

99.74% of the data falls within 3SD of the mean.

How often will we be wrong when we judge data outside control limits to be special cause variation ?

0.26% (from normal theory)!

Why is 8 points on one side of the mean attributed to special cause ?

If we are satisfied with being wrong 0.26% of the time for one test, it makes sense have a similar level of risk for the other tests for special cause !

What is the probability of a point falling below the mean on a control chart?

50%What is the probability of another point falling below the mean?

50% x 50% = 25%And so on…….

50% x 50% x 50% x 50% x 50% x 50% x 50% x 50% = 0.39%

Other types of chart

Depending on the process you are measuring you may need to use the following charts :

C chart : for count data where sample size remains constant.U chart : for count data where sample size changes

nP chart : for proportion data where sample size remains constant

P chart : for proportion data where sample size changes

X bar R chart : when samples are taken in batches of production (sample size remains constant)

So what to do next….?1) Check that the data you are gathering is variable data where possible.2) Ensure that it is recorded in a legible manner and in time order. Ensure everyone records it in the same way. 3) Ensure that other factors are recorded to aid the problem solving process. For example if you are measuring parts off several machines you may need to either use several different data collection sheets, or record the machine number against each reading taken.4) Consider process inputs that could affect the outputs of the process. Some of these could be recorded against output data collection. (Or we could use SPC to control them also).5) Maintain process logs to aid analysis.6) Make sure everyone understands the part they play in process improvement

SPC Training by D&H Engineers

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