Spc la

Statistical Process Control
SPC
ISO TS 16949:2002 Lead Auditor Course

2
Course Objectives
• By the end of the course the participant
should be able to identify;
1. How to Audit SPC
2. Variables SPC charts
3. Attribute SPC charts
4. When best to apply these charts
5. The difference between Ppk and Cpk
and understand how to calculate these
indexes

3
An
ISO TS 16949
Quality Management System
is based on
Prevention
not
Detection
SPCSPC

4
So what is SPC?
• A tool to detect variation
• It identifies problems, it does not solve problems
•Increases product consistency
•Improves product quality
•Decreases scrap and rework defects
•Increases production output

5
SPC is a proactive tool which assists
in;
• Eliminating waste
• Reducing variation
• Achieving superior quality product
Lower unit cost

6
Types of Variation
• Common cause
– Due to normal wear and tear e.g. tool wear
•Special Cause
•Abnormal situation e.g tool broken

7
Normal Distribution & Standard deviation
• Normal distributions are a family of distributions that have the same general
shape. They are symmetric with scores more concentrated in the middle than in
the tails. Normal distributions are sometimes described as bell shaped. Examples
of normal distributions are below.
Standard Deviation:
Denoted with the
Greek symbol Sigma,
the standard deviation
provides an estimate
of variation. In
mathematical terms, it
is the second moment
about the mean. In
simpler terms, you
might say it is how far
the observations vary
from the mean.
σ

8
• There are two types of SPC charts;
• Variables
– for a variables SPC chart we require variable
“number” data such as;
• Hole dimension (32.45 mm), Thickness (0.55
mm)
• Temperature (32 degrees), Weight (38.98
grams)

9
• Attributes
– for an attributes SPC chart we require attributes
(visual) data such as;
• Short shot (in an injection moulding operation)
• Off color painted spoiler
• Incomplete assembly
• Insufficient weld

10
• VARIABLES SPC CHARTS
The types of variables charts we will be
examining are;
– Average and Range charts (Xbar and R charts)
– Average and Standard Deviation charts (Xbar and
s charts)
– Median charts
– Individual and Moving Range chart ( X-MR)

11
• ATTRIBUTES SPC CHARTS
The types of attributes charts we will be
examining are;
– Proportion nonconforming (p Chart)
– Nonconforming product (np Chart)
– Number of nonconformity's (c Chart)
– Nonconformity's per unit (u Chart)

12
What is Six Sigma
Six Sigma aims for virtually error free business performance.
The Six Sigma standard of 3.4 problems
per million opportunities is a response to
the increasing expectations of customers
and the increased complexity of modern
products.

14
What other global company’s say
• General Electric estimates that the gap between three or four sigma and
Six Sigma was costing them between $8 billion and $12 billion per
year in inefficiencies and lost productivity.

15
The methodology
Design of Experiments

17
Course Objectives
1. Variables SPC charts
3. The difference between Ppk and Cpk
and understand how to calculate these
indexes

18
How to select the correct SPC chart
Variables
Xbar & S Xbar & R I & MR Median
n =10 or more n= 2 to 9 n=1 n= odd number

19
X bar and R chart
• When to use a X bar and R chart
• when there is measured data
• to establish process variation
• when you can obtain a subgroup of constant size i.e.
between 2-9 consecutive pieces
• when pieces are produced under similar conditions
with a short interval between production of pieces

20
• Methodology for the calculation of
parameters for an X bar and R chart
– 1. Determine the subgroup size, typically between 2-9 pieces
– 2. Establish the frequency of taking measurements
– 3. Collect data
– 4. Calculate the average for each subgroup and record results
– 5. Determine the range for each subgroup and record the result
– 6. Plot the average and range onto the chart
– 7. Calculate the Upper and Lower Control Lines
– 8. Interpret the chart
X bar and R chart

21
X bar and R chart
To calculate the control lines we use the
following algorithm
where k iswhere k is
thethe
number ofnumber of
subgroupssubgroups
RA-X=LCLRA+X=UCL
RD=LCLRDUCL
and
k
XXXX
k
RRRR
2x2x
3R4R
n21n21
=
++=+++= 

22
X bar and R chart
values for D4, D3 and A2
n 2 3 4 5 6 7 8 9 10
D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78
D3 - - - - - 0.08 0.14 0.18 0.22
A2 1.88 1.02 0.73 0.58 0.48 0.42 0.37 0.34 0.31

23
X bar and R chart
• Exercise
– Using the data in Appendix 1, calculate the
UCL and LCL for the average and range of
the data.
– Plot the data onto the charts and identify
any out of control conditions

24
Average and standard deviation chart X
bar and s chart
• When to use a X bar and s chart
• when there is measured data recorded on a real time
basis or when operators are proficient is using a
calculator
• when you require a more efficient indicator of
process variability
• when you can obtain a subgroup of constant size with
a larger sampling size than for Xbar and R charts,
n=10 or more
• when pieces are produced under similar conditions
with a short interval between production of pieces

25
X bar and s chart
• Methodology for the calculation of X
bar and s chart
– 1. Determine the subgroup size, typically 10 or more
– 3. Collect data
– 4. Calculate the average for each subgroup and record
results
– 5. Calculate the standard deviation for each subgroup
and record the result
– 6. Plot the average and standard deviation onto the chart
– 7. Interpret the chart

26
X bar and s chart
following algorithm where n is
the number
of parts in
the
subgroup
and k is the
number of
subgroups
sA-X=LCLsA+X=UCL
sB=LCLsBUCL
K
S
K
XXX
1n
s
n
XXXX
3x3x
3s4s
Kk21
n21
=
+++=+++=
−+++= ∑


21
s
2)(
SSX
XXi
-
=

27
X bar and s chart
values for B4, B3 and A3
n 2 3 4 5 6 7 8 9 10
B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72
B3 - - - - 0.03 0.12 0.19 0.24 0.28
A3 2.66 1.95 1.63 1.43 1.29 1.18 1.1 1.03 0.98

28
X bar and s chart
• Exercise
– Using the data in Appendix 2 calculate the
UCL and LCL for the average and
standard deviation of the data.

29
Median charts
• When to use a Median chart
• 1. When there is measured data recorded
• 2. When you require an easy method of process
control. This can be a good method to begin
training operators
• 3. When you can obtain a subgroup of constant
size - for convenience ensure subgroup size is odd
not even, typically 5
• 4. When pieces are produced under similar
conditions with a short interval between
production of pieces

30
Median charts
• Methodology for the calculation of Median
charts
– 1. Determine the subgroup size, typically 5, ensure it is an
odd number
– 3. Collect data
– 4. Determine the median (middle number) for each subgroup
and record results
– 5. Determine the range for each subgroup and record the
result
– 6. Plot the median and range onto the chart

31
Median charts
following algorithm
A-=LCLA+=UCL
D=LCLDUCL
k
RRR
k
XXX
2X2X
3R4R
kk21
R
~
R
~
RR
R
~~~~
lueLowest va-alueHighest v
value(middle)Median
~
~~
21
XX
X
R
X
=
+++=+++=
=
=

Where k is theWhere k is the
number ofnumber of
subgroupssubgroups

32
Median charts
values for B4, B3 and A3
n 2 3 4 5 6 7 8 9 10
D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78
D3 - - - - - 0.08 0.14 0.18 0.22
A2 1.88 1.19 0.8 0.69 0.55 0.51 0.43 0.41 0.36

33
Median charts
• Exercise
– Using the data in Appendix 3
calculate the UCL and LCL for the
median chart
– Plot the data onto the charts and
identify any out of control conditions

34
Individuals and moving range chart
(X-MR)
• When to use a X-MR chart
• when there is measured data recorded
• when process control is required for individual
readings e.g. a destructive type test which cannot
be repeated frequently because of cost or other

35
Individuals and moving range
chart
• Methodology for the calculation of X-MR
chart
– 1. Establish the frequency of taking
measurements
– 2. Obtain individual readings
– 3. Collect data
– 4. Record the individual reading on the chart
– 5. Determine the moving range from successive
pairs of reading

36
chart
Example of calculating control lines for
individuals and moving range charts (X-MR)
where k is thewhere k is the
number ofnumber of
readingsreadings
RE-X=LCLRE+X=UCL
RD=LCLRDUCL
and
k
XXXX
1-k
RRRR
2x2X
3MR4MR
21K21 k
=
++=+++= 

37
chart
n 2 3 4 5 6 7 8 9 10
D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78
D3 - - - - - 0.08 0.14 0.18 0.22
E2 2.66 1.77 1.46 1.29 1.18 1.11 1.05 1.01 0.98

38
chart
• Exercise
UCL and LCL for the X-MR chart

39
Process Capability Studies
What is
Ppk
and what is
Cpk

40
• Definition of Ppk
Preliminary Process Capability Study
from 25 or more subgroups
QS 9000 requires Ppk to be greater that or
equal to 1.67

41
• Calculation of PpK
1
2)(
−
−
=
∑
n
XXi
s
SS
MIN
Z
Ppk
LSL-X
Z,
X-USL
Z
)Z,Z(Zmin,
3
min
LSLUSL
LSLUSL
==
==

42
• Definition of Cpk
Ongoing Process Capability Study
for a stable process
PPAP requires CpK to be greater that or
equal to 1.67, if between 1.33 and 1.67
must review with customer

43
Ongoing Capability Studies
• Calculation of CpK n d2
2 1.128
3 1.693
4 2.059
5 2.326
6 2.534
7 2.704
8 2.847
9 2.97
10 3.078
11 3.173
12 3.258
13 3.336
14 3.407
15 3.472
2
R
LSL-X
Z,
2
R
X-USL
Z
)Z,Z(Zmin,
3
min
LSLUSL
LSLUSL
dd
MIN
Z
Cpk
==
==

44
Standard Deviation Correction factors
n c4
15 0.9823
16 0.9835
17 0.9845
18 0.9854
19 0.9862
20 0.9869
21 0.9876
22 0.9882
23 0.9887
24 0.9892
25 0.9896
30 0.9914
35 0.9927
40 0.9936
45 0.9943
50 0.9949
4C
S
Scorrected =
To obtain an accurate calculation of
the standard deviation, at least 60
data points are required. If less than
60 are available use the following
error correction factors

45
Capability study assumptions
1. Data is normally distributed
2. Process is in statistical control
Question: Why is the PpK requirement
higher than the Cpk requirement???

47
Course Objectives
1. Attribute SPC charts

48
How to select the correct SPC chart
Attributes
P chart Np chart U chart C chart
Count parts
N = fixed or
varied
Count parts
N = fixed
Count occurrences
N = varies
Count occurrences
N = fixed

49
Proportion of Units -Nonconforming
p charts
• When to use a p chart
• when data is of attribute type (an attribute
that can be counted)
• when you wish to determine the proportion of
nonconforming products in a group being
inspected
• from samples of equal or unequal size

50
p charts
• Methodology for the calculation of p
charts
– Determine the subgroup size typically >50 units
– Establish the frequency of inspection
– Collate data - Determine the number of
nonconforming products from that subgroup
– Record the number of parts defective onto p-chart
– Determine the proportion defective i.e number
defective/number in subgroup
– Plot this onto the p-chart

51
p charts
• Example of calculating control lines for
p-charts
Note: nNote: n11pp11 etc..etc..
are the numberare the number
ofof
nonconformingnonconforming
productsproducts
detected and ndetected and n11,,
nn22 etc are theetc are the
correspondingcorresponding
sample sizessample sizes
Note: If the LCL is ever calculated to be a negative number, the LCL should then default to a zeroNote: If the LCL is ever calculated to be a negative number, the LCL should then default to a zero
n
pp
pLCLp
n
pp
pUCLp
)1(
3
)1(
3
n+n+n
pn++pn+pn
=p
p-ingnonconformproportionaveragetheDetermine
k21
kk2211
−
×−=
−
×+=



52
p charts
• Class Exercise
UCL and LCL for the p chart

53
Number of Nonconforming products
np charts
• When to use a np chart
• when it is more important that you know the
number of nonconforming products in a
group being inspected
• when sample sizes are of equal size

54
np charts
• Methodology for the calculation of np charts
– Determine the subgroup size typically >50 units
– Collate data - Determine the number of
nonconforming products from that subgroup
– Record the number of parts defective onto np-chart
– Plot this data onto the np-chart

55
np charts
np-charts
Where k isWhere k is
the numberthe number
of subgroupsof subgroups
and n is theand n is the
sample sizesample size
in each ofin each of
thosethose
subgroups.subgroups.
)1(3
)1(3
np++np+np
=pn
pn-ingnonconformnumberaveragetheDetermine
k
k21
n
pn
pnpnLCLnp
n
pn
pnpnUCLnp
−×−=
−×+=


56
np charts
• Class Exercise
UCL and LCL for the np chart

57
Number of Nonconformity's
c charts
• When to use a c chart
• when the nonconformity's are distributed
throughout a product e.g. number of defects
on a painted part, number of flaws in a
assembly operation
• when nonconformity's can be found from
multiple sources or attributed to multiple
sources

58
c charts
• Methodology for the calculation of c charts
– Ensure inspection sample sizes are equal e.g.
number of parts, specified area or volume
– Determine the number of nonconformity's
found in that sample
– Record the number of nonconformity's onto c-
chart
– Plot this data onto the c-chart

59
c charts
c-charts
Where k is the numberWhere k is the number
of subgroups.of subgroups.
c3c
c3c
k
k++2+1
=c
citiesnonconformofnumberaveragetheDetermine
ccc
×−=
×+=
LCLc
UCLc


60
c charts
• Class Exercise
UCL and LCL for the c chart

61
Number of Nonconformity's per unit
u Chart
• When to use a u-chart
• when data is of attribute type (an attribute that can
be counted)
• when the number of nonconformity's are
distributed throughout a product (e.g. number of
defects on a painted part, number of flaws in a
assembly operation) given varying sample sizes
• when nonconformity's can be found from multiple
sources or attributed to multiple sources

62
u Chart
• Methodology for the calculation of u
charts
– Define what will be inspected
– Determine the number of nonconformity's found
in that sample
– Divide the number of nonconformity's found by
the sample size
– Record the proportion of nonconformity's onto the
u chart
– Plot this data onto the u-chart

63
u Chart
• Example of calculating control lines for u-charts
Where c1, c2Where c1, c2
etc are numberetc are number
ofof
nonconformity'nonconformity'
s per unit ands per unit and
n1, n2 etc isn1, n2 etc is
thethe
correspondingcorresponding
sample sizesample size
n
u
3u
n
u
3u
nk+n2+n1
k++2+1
=u
uunitperitiesnonconformaveragetheDetermine
uuu
×−=
×+=
+
LCLu
UCLu



64
u Chart
• Class Exercise
– Using the data in Appendix 8
calculate the UCL and LCL for the u
chart
– Plot the data onto the charts and
identify any out of control conditions

65
Auditing SPC
1. Are special characteristics being measured using
SPC/Cpk?
2. Is their a link from the customer’s designated
special characteristics to what the organisation is
monitoring?
3. What is the acceptance criteria the organisation is
using?
4. How does the organisation determine which SPC
chart to use
5. What training has been provided to people using
SPC charts
6. Is the organisation able to interpret control charts?

66
Auditing SPC
7. Check calculation of a sample of SPC charts
8. Does the organisation know what to do when there is
an adverse trend or point go outside of the control
lines
9. How often does the organisation recalculate control
lines? And do they follow this process?
10. Does the sample size/frequency in the Control Plan
or other coincide with what the organisation is in
fact checking?
11. Is the IMTE calibrated?

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