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:
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.

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
Customer specification limits are the outside edge of yellow zone
Why do we need to improve our processes….
By improving processes we can….
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 counted
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:
Note : To produce histograms quickly use Excel’s Data Analysis Tool pack.
9.1 9.2 9.3 9.4 9.5 9.6
10
The Sample Range is the largest value minus the smallest value
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
Characteristics Of The Normal Curve
Variation in a process can be measured by calculating the ‘standard deviation’
The Formula =s= S(c c)² n1
i
Note : In excel you can use the STDEV function. It’s quicker than pen & paper !
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
Special cause variation
Examples of different types of variation
Common cause  random variation
Special cause variation
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
Attribute data is that which can be counted
Examples:
Broken or
unbroken?
On or Off?
Variable data is that which can be physically be measured
Examples:
Temperature
Weight
Attribute Vs. Variable data
Individual  Moving Range Charts
(Also known as XmR or ImR)
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
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
_
X AND mR CONTROL CHART CALCULATING CONTROL LIMITS
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
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
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
Shake Down
16
10
15
17
12
13
20
9
11
4
5
19
14
6
7
1
3
2
18
8
18
16
17
20
15
14
19
13
12
8
10
11
6
4
7
1
9
5
2
3
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 ?….
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.
What would you do if you changed back to the original supplier ?
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%
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