SPC Training by D&H Engineers

SPC - Module 1
Understanding variation and basic principles
S
P
C

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

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

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 counted
Examples:
On or
Off?
Variable (continuous) data is that which can be
physically be measured on a continuous scale
Examples:
Temperature
Weight
Broken or
unbroken?
Attribute Vs. Variable data

Which type of data ?
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
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

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

Histogram
• Graphic Representation
of The Data
• Bar Chart
• Vertical (y) axis shows
the frequency of
occurrence
• Horizontal (x) axis shows
increasing values
0
1
2
3
4
5
6
7
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=17
The 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 component Wing 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 = σ= Σ(χ −χ)²
n-1

The Standard Deviation
oUse The Following Dataset
o5,2,9,12,3,19,7,5
oThe Formula = σ= Σ(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
2σ

95.5%
+/- 2 Std Dev =
95.5%
-4 -3 -2 -1 0 1 2 3 4
4σ

99.74%
+/- 3 Std Dev =
99.74%
-4 -3 -2 -1 0 1 2 3 4
6σ

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.

Different types of variation
Common 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 variation
Common 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 ?
2
4
6
8
10
12
14

Yes , the process is in control but not
capable.
2
4
6
8
10
12
14
UCL
LCL

Attribute data is that which can be counted
Examples:
On or
Off?
Variable data is that which can be physically be
measured
Examples:
Temperature
Weight
Broken or
unbroken?

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 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.

UCL x = Xbar + 2.66 x mRbar
LCL x = Xbar - 2.66 x mRbar
UCL r = 3.267 x mRbar
22
24
26
28
30
32
34
36
38
40
42
44
0
1
2
3
4
5
6
7
8
9
10
_
Date
Time
X
mR -----
Process Control Chart (iX-mR) Dept. 019 Sampling Frequency 100%
Characteristic Length Chart No two Specification Limit 30mm +/- 6mm
Xbar = UCL= LCL=
mRbar = CL =

UCL x =Xbar+ 2.66 xmR bar
LCL x =Xbar- 2.66 xmR bar
UCL r = 3.267 xmR bar
22
24
26
28
30
32
34
36
38
40
42
44
0
1
2
3
4
5
6
7
8
9
10
_
Date
Time
X 38 39 36
mR ----- 1 3
Xbar = UCL= LCL=
mR bar = CL=
X
X
X
X
X

UCL x =Xbar+ 2.66 xmR bar
LCL x =Xbar- 2.66 xmR bar
UCL r = 3.267 xmR bar
22
24
26
28
30
32
34
36
38
40
42
44
0
1
2
3
4
5
6
7
8
9
10
_
Date
Time
X 38 39 36
mR ----- 1 3
Xbar = UCL= LCL=
mR bar = CL=

MOVING RANGE CHART
AVERAGE CHART
_
mR =
ENTER mR FIGURES
INTO CALCULATOR
Upper Control
Limit of mR =
_
D4 X mR
=
_
D4 X mR
=
_
X =
ENTER X FIGURES
INTO CALCULATOR
=
_
X
ucl X+ (E2
_
X
ucl mR
lcl XmR)
_
X
X
+ =
=
x
-
-
X
X
X
Lower Control
Limit of X =
_
X - (E2 x mR)
Upper Control
Limit of X =
_
X + (E2 x mR)
mR)
(E2
_
mR
X AND mR CONTROL CHART CALCULATING CONTROL
LIMITS
_
_
_
_

Table of Constants
for Control Charts
X and R Charts Charts for Individuals
Chart for
Averages
_
(X)
Charts for
Individuals
(X)Chart for Ranges (R)
Factors for
Control
Limits
Factors for
Control
Limits
Divisors for
Estimate of
Standard
Deviation
Factors for
Control
Limits
Subgroup
Size
A
2
d
2
D
3
E
2
D
4
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 Control
Limit of mR =
_
D4X mR
=
_
D4 X mR
=
_
X =
ENTER X FIGURES
INTO CALCULATOR
=
_
X
ucl X+ (E2
_
X
ucl mR
lcl XmR)
_
X
X
+ =
=
x
-
-
X
X
X
Lower Control
Limit of X =
_
X - (E2 x mR)
Upper Control
Limit 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

UCL x = Xbar + 2.66 x mRbar
LCL x = Xbar - 2.66 x mRbar
UCL r = 3.267 x mRbar
22
24
26
28
30
32
34
36
38
40
42
44
0
1
2
3
4
5
6
7
8
9
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 27
mR ----- 1 3 2 4 3 3 4 2 2 3 2 3 4 1 4 1 1 3 3 6 1 0 3
Xbar = 32.6 UCL= 40.2 LCL= 26.7
mR bar = 2.56 CL= 8.38

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

Control Chart Analysis
– Any Point Outside Control
Limits
– A Run of 8 Points Above or
Below the mean
– Any Non-Random Patterns
1 3
4
2
5
6 7 8
9
10
13
14
12
15
16
17
18
1119
20
1 3
4
25
6 7
8
9
1013
14
12
15
16 17
18
11
1 3
4
2
5 6
7 8 9
10 1211
19
20

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
Moving Range
0
1
2
3
4
5
6
Range
UCL
Rbar
Is there any signs of special cause present ?

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
Moving Range
0
1
2
3
4
5
6
Range
UCL
R bar

Individuals
0
2
4
6
8
10
12
14
X bar
UCL
LCL
Data
Moving Range
0
1
2
3
4
Range
UCL
R bar

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
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 bar
UCL
LCL
Data
Moving Range
0
1
2
3
4
5
Range
UCL
R bar
What has changed ?

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
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 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.

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
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
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
Moving Range
0
1
2
3
4
Range
UCL
R bar
What would you do if you changed back
to the original supplier ?

Individuals
0
2
4
6
8
10
12
14
16
X bar
UCL
LCL
Data
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 bar
UCL
LCL
Data
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

More Related Content

What's hot

Viewers also liked

Similar to SPC Training by D&H Engineers

Recently uploaded

SPC Training by D&H Engineers

Editor's Notes