Six Sigma - Variation

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Six Sigma - Variation
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SPC - Module 1 Understanding variation and basic
principles
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• AIM OF SPC COURSE

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

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The History Of SPC

• 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

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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.
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Variation
  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.  
     
------------- 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.  
------------- Signature 1
------------- Signature 2
----------------- Signature 4
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Rank in order of desirability
Customer specification limits are the outside
edge of yellow zone
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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

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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.

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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 RR) Garbage
in, garbage out !
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Attribute Vs. Variable data
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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
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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
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Histogram

• A GRAPHICAL REPRESENTATION OF DATA SHOWING HOW
  THE VALUES ARE DISTRIBUTED BY
• Displaying The Distribution Of Data
• Displaying Process Variability (Spread)
• Identifying Data Concentration

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Histogram

• 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 Excels
Data Analysis Tool pack.
9.1 9.2 9.3 9.4 9.5 9.6
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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

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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

• 19-217
• The Range 17

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The Normal Distribution Curve
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

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Characteristics Of The Normal Curve

• Single peaked
• Bell shaped
• Average is centred
• 50 above below the average
• Extends to infinity (in theory)

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How do we measure variation ?
Variation in a process can be measured by
calculating the standard deviation
The Formula s S(c -c)² n-1
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The Standard Deviation

• 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.
Its quicker than pen paper !
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Normal Distribution Proportion
68.3
-4
-3
-2
-1
0
1
2
3
4
2s

• /- 1 Std Dev 68.3

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Normal Distribution Proportion
95.5
-4
-3
-2
-1
0
1
2
3
4
4s

• /- 2 Std Dev 95.5

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Normal Distribution Proportion
99.74
-4
-3
-2
-1
0
1
2
3
4
6s

• /- 3 Std Dev 99.74

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Control charts
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.
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Different types of variation
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)

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Examples of different types of variation
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

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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
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Objective use of data
In God we trust.
.for everything else show us the data !
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14
12
10
8
6
4
2
Upper spec limit 8. Is this process in control ?
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14
12
UCL
10
8
6
4
2
LCL
Yes , the process is in control but not capable.
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Attribute Vs. Variable data
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Variable Control Chart

• Establishes the values of a single component
  characteristic measured in physical units
• Product Weight (kg)
• Curing Time (hrs)
• Component Length (mm)

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

• Assumptions
• Variable data.
• Normal distribution

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• Decide on operation to be measured

Establish characteristic
Decide on sample frequency
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
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Activity Exercise

• 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.

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UCL x Xbar 2.66 x mRbar LCL x Xbar - 2.66
x mRbar UCL r 3.267 x mRbar
_
mRbar CL
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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
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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
_
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X AND mR CONTROL CHART CALCULATING CONTROL LIMITS
MOVING RANGE CHART
_
mR
_

ENTER mR FIGURES
2.56
mR
INTO CALCULATOR
_
Upper Control
D
X mR
ucl mR
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Limit of mR

x
3.267
2.56
8.36
_
D
X mR
4
AVERAGE CHART
_
X
_

ENTER X FIGURES
32.6

X
INTO CALCULATOR
_
_
Upper Control
(E
mR)
X
ucl X

X
2
Limit of X
2.66
39.4
32.6
_

_

X
2.56
X (E
x mR)
2
_
_
Lower Control
lcl
X
-
mR)
(E
X
X
Limit of X
2

_
25.8
2.56
2.66
32.6
_
X
-
X - (E
x mR)
2
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UCL x Xbar 2.66 x mRbar LCL x Xbar - 2.66
x mRbar UCL r 3.267 x mRbar
_
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Analysing Control Charts

• 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

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Control Chart Analysis
10
16
15
17
13
12
20
4
5
9
11
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• Any Point Outside Control Limits

1
3
2
6
7
8
14
18
18
16
17
20
14
15
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• A Run of 8 Points Above or Below the mean

8
10
13
12
4
6
7
11
1
3
2
5
9

• Any Non-Random Patterns

10
12
11
7
8
9
4
5
6
1
3
2
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Control Chart Analysis
Is there any signs of special cause present ?
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Control Chart Analysis
Is there any signs of special cause present ?
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Control Chart Analysis
Is there any signs of special cause present ?
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Control Chart Analysis
Any special cause here ?
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Control Chart Analysis
What has changed ?
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Control Chart Analysis
What has changed ?
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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 ?.
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• 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

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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
whats changed?, and investigate root causes.
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When to change limits
Re-calculate from here
Changed supplier
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Limits changed to reflect shift in average
What would you do if you changed back to the
original supplier ?
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Control Chart Analysis
New operator
Where would you re-calculate limits ?
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Control Chart Analysis
What would you do here ? Would you change limits ?
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Why is 8 points on one side of the mean
attributed to special cause ?
First lets 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.
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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
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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)
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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