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# Six Sigma - Variation - PowerPoint PPT Presentation

Six Sigma - Variation. SPC - Module 1 Understanding variation and basic principles. To enable delegates to better understand variation and be able to create and analyse control charts. AIM OF SPC COURSE. OBJECTIVES. Delegates will be able to:-. Appreciate what variation is

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Understanding variation and basic principles

To enable delegates to better understand variation and be able to create and analyse control charts

AIM OF SPC COURSE

OBJECTIVES

Delegates 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

• 1924 - Walter Shewhart Of Bell Telephones Develops The Control Chart Still Being Used Today

• 1950 - Dr W Edwards Deming Sells SPC To Japan After World War II

• 1965 - Ford Failed To Implement SPC Due To No Management Commitment

• 1985 - Ford Finally Implement SPC

• 1989 - Boeing roll out SPC

• 1992 - BAe Decide To Implement SPC

• 2002 - Airbus UK start SPC in key business areas

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.

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.

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Signature 3

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.

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Signature 1

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Signature 2

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Signature 4

Customer specification limits are the outside edge of yellow zone

• 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

• 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.

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 !

Examples:

Broken or

unbroken?

On or Off?

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

Examples:

Temperature

Weight

Attribute Vs. Variable data

Which type of data ?

Variable

Attribute

ü

Length in millimeters

SMC (standard manufacturing cost)

Number of breakdowns per day

Average daily temperature

Proportion of defective items

Number of spars with concession

Lead time (days)

Mean time between failure

ü

ü

ü

ü

ü

ü

ü

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

A GRAPHICAL REPRESENTATION OF DATA SHOWING HOW THE VALUES ARE DISTRIBUTED BY:

• Displaying The Distribution Of Data

• Displaying Process Variability (Spread)

• Identifying Data Concentration

• Graphic Representation of The Data

• Bar Chart

• Vertical (y) axis shows the frequency of occurrence

• Horizontal (x) axis shows increasing values

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

9.1 9.2 9.3 9.4 9.5 9.6

• Example

• A set of numbers:

• 3,6,9,7,5,9,10,0,4,3

• Total = 56

• Average = 56 = 5.6

10

• 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=17

• The Range = 17

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

Probability of individual values are not uniform

Typical process range

Examples

Weight of component Wing skin thickness

• Single peaked

• Bell shaped

• Average is centred

• 50% above & below the average

• Extends to infinity (in theory)

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

The Formula =s= S(c -c)² n-1

• Use The Following Dataset

• 5,2,9,12,3,19,7,5

• The Formula = s= S(x-x )² n-1

• (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 !

68.3%

0

-4

-3

-2

-1

1

2

3

4

2s

• +/- 1 Std Dev = 68.3%

95.5%

-4

-3

-2

-1

0

1

2

3

4

4s

• +/- 2 Std Dev = 95.5%

99.74%

-4

-3

-2

-1

0

1

2

3

4

6s

• +/- 3 Std Dev = 99.74%

A 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.

Common cause - random 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)

Special cause variation

• 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)

Common cause - random variation

• Temperature

• Humidity

• Standard operating methods

• Measurement systems

• Normal running speed

Special cause variation

• Sudden breakdown of equipment

• Power failure

• Unskilled operator

• Tool breakage

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

In God we trust….

….for everything else show us the data !

12

10

8

6

4

2

Upper spec limit = 8.

Is this process in control ?

12

UCL

10

8

6

4

2

LCL

Yes , the process is in control but not capable.

Examples:

Broken or

unbroken?

On or Off?

Variable data is that which can be physically be measured

Examples:

Temperature

Weight

Attribute Vs. Variable data

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

• Product Weight (kg)

• Curing Time (hrs)

• Component Length (mm)

Individual - Moving Range Charts

(Also known as X-mR or I-mR)

• Assumptions :

• Variable data.

• Normal distribution

Decide on sample frequency

Decide on operation to be measured

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

• Groups 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 straws

• Characteristic: Length

• Sample frequency: 100%

• Cut by eye, 1 straw at a time to an estimated 30mm

• Measure the straws in the order that they are cut

• Record the information on a chart (remember to input data and update chart as you go)

• One person records, one person cuts

• No communication between the operator and tester.

UCL x = Xbar + 2.66 x mRbar

LCL x = Xbar - 2.66 x mRbar

UCL r = 3.267 x mRbar

_

mRbar = CL =

Dept. 019

Sampling Frequency 100%

Characteristic Length

Chart No two

Specification Limit 30mm +/- 6mm

Xbar =

UCL=

LCL=

44

42

40

38

36

34

32

30

28

26

24

22

mR bar =

CL=

10

9

8

7

6

5

4

3

2

1

0

Date

Time

X

38

39

36

mR

-----

1

3

UCL x =

X

+ 2.66 x

mR

bar

bar

LCL x =

X

- 2.66 x

mR

bar

bar

UCL r = 3.267 x

mR

bar

X

X

X

_

X

X

Dept. 019

Sampling Frequency 100%

Characteristic Length

Chart No two

Specification Limit 30mm +/- 6mm

Xbar =

UCL=

LCL=

44

42

40

38

36

34

32

30

28

26

24

22

mR bar =

CL=

10

9

8

7

6

5

4

3

2

1

0

Date

Time

X

38

39

36

mR

-----

1

3

UCL x =

X

+ 2.66 x

mR

bar

bar

LCL x =

X

- 2.66 x

mR

bar

bar

UCL r = 3.267 x

mR

bar

_

MOVING RANGE CHART

_

mR

_

=

ENTER mR FIGURES

mR =

INTO CALCULATOR

_

Upper Control

D

X mR

ucl mR

4

Limit of mR =

=

x

_

D

X mR

4

AVERAGE CHART

_

X

_

=

ENTER X FIGURES

=

X

INTO CALCULATOR

_

_

Upper Control

(E

mR)

X

+

X

ucl X

2

Limit of X =

_

_

=

+

X

X + (E

x mR)

2

_

_

Lower Control

-

lcl

X

mR)

(E

X

X

Limit of X =

2

=

_

_

X

-

X - (E

x mR)

2

MOVING RANGE CHART

_

mR

_

=

ENTER mR FIGURES

2.56

mR =

INTO CALCULATOR

_

Upper Control

D

X mR

ucl mR

4

Limit of mR =

=

3.267

x

2.56

8.36

_

D

X mR

4

AVERAGE CHART

_

X

_

=

ENTER X FIGURES

32.6

=

X

INTO CALCULATOR

_

_

Upper Control

(E

mR)

X

+

X

ucl X

2

Limit of X =

32.6

2.66

39.4

_

_

=

+

X

2.56

X + (E

x mR)

2

_

_

Lower Control

-

lcl

X

mR)

(E

X

X

Limit of X =

2

=

_

_

32.6

2.66

2.56

25.8

X

-

X - (E

x mR)

2

UCL x = Xbar + 2.66 x mRbar

LCL x = Xbar - 2.66 x mRbar

UCL r = 3.267 x mRbar

_

Shake 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

16

10

15

17

12

13

20

9

11

4

5

19

• Any Point Outside Control Limits

14

6

7

1

3

2

18

8

18

16

17

20

15

14

19

• A Run of 8 Points Above or Below the mean

13

12

8

10

11

6

4

7

1

9

5

2

3

• Any Non-Random Patterns

10

11

12

7

8

9

4

5

6

1

2

3

Is there any signs of special cause present ?

Is there any signs of special cause present ?

Is there any signs of special cause present ?

Any special cause here ?

What has changed ?

What has changed ?

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 limits

When 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.

Re-calculate from here

Changed supplier

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

New operator

Where would you re-calculate limits ?

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.

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

0.26% (from normal theory)!

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

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 special cause ?

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….? special cause ?

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