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Statistical Process Control for suppliersTRANSCRIPT
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
Statistical Process Control
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
Statistical Process Control
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.
8
Statistical Process Control
• 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
Statistical Process Control
• 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
Statistical Process Control
• 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
Statistical Process Control
• 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.
13
What is Six Sigma
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
SPC
Variables
17
Course Objectives
• By the end of the course the participant should be able to identify;
1. Variables SPC charts
2. When best to apply these 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 is where k is the the number of number of subgroupssubgroups
RA-X=LCL RA+X=UCL
RD=LCL RD UCL
and
kXXXX
kRRRR
2x2x
3R4R
n21n21
22
X bar and R chart values for D4, D3 and A2
n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22A2 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
– 2. Establish the frequency of taking measurements
– 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
To calculate the control lines we use the following algorithm
where n is the number of parts in the subgroup and k is the number of subgroups
sA-X=LCL sA+X=UCL
sB=LCL sBUCL
KS
KXXX
1nsn
XXXX
3x3x
3s4s
Kk21
n21
21s
2)(
SSX
XXi
-=
27
X bar and s chartvalues for B4, B3 and A3
n 2 3 4 5 6 7 8 9 10B4 3.27 2.57 2.27 2.09 1.97 1.88 1.82 1.76 1.72B3 - - - - 0.03 0.12 0.19 0.24 0.28A3 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.
– Plot the data onto the charts and identify any out of control conditions
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– 2. Establish the frequency of taking measurements– 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
To calculate the control lines we use the following algorithm
A-=LCL A+=UCL
D=LCL DUCL
kRRR
kXXX
2X2X
3R4R
kk21
R~
R~
RR
R ~~~~
lue Lowest va- alue Highest v value(middle) Median
~
~~
21
XX
X
RX
Where k is the Where k is the number of number of subgroupssubgroups
32
Median charts values for B4, B3 and A3
n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22A2 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
Individuals and moving range chartExample of calculating control lines for
individuals and moving range charts (X-MR)
where k is the where k is the number of number of readingsreadings
RE-X=LCL RE+X=UCL
RD=LCL RD UCL
and
kXXXX
1-kRRRR
2x2X
3MR4MR
21K21 k
37
Individuals and moving range chart
n 2 3 4 5 6 7 8 9 10D4 3.27 2.57 2.28 2.11 2 1.92 1.86 1.82 1.78D3 - - - - - 0.08 0.14 0.18 0.22E2 2.66 1.77 1.46 1.29 1.18 1.11 1.05 1.01 0.98
38
Individuals and moving range chart• Exercise
– Using the data in Appendix 4 calculate the UCL and LCL for the X-MR chart
– Plot the data onto the charts and identify any out of control conditions
39
Process Capability Studies
What is
Ppk
and what is
Cpk
40
Process Capability Studies
• Definition of PpkPreliminary Process Capability Study
from 25 or more subgroups
QS 9000 requires Ppk to be greater that or equal to 1.67
41
Process Capability Studies
• Calculation of PpK
1
2)(
n
XXis
SS
MINZ
Ppk
LSL-X Z ,
X - USL Z
)Z,Z(Zmin ,3
min
LSLUSL
LSLUSL
42
Process Capability Studies
• Definition of CpkOngoing 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 d22 1.1283 1.6934 2.0595 2.3266 2.5347 2.7048 2.8479 2.9710 3.07811 3.17312 3.25813 3.33614 3.40715 3.472
2R
LSL-X Z ,
2R
X - USL Z
)Z,Z(Zmin ,3
min
LSLUSL
LSLUSL
dd
MINZ
Cpk
44
Standard Deviation Correction factors
n c415 0.982316 0.983517 0.984518 0.985419 0.986220 0.986921 0.987622 0.988223 0.988724 0.989225 0.989630 0.991435 0.992740 0.993645 0.994350 0.9949
4C
SScorrected
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???
SPC
Attributes
47
Course Objectives
• By the end of the course the participant should be able to identify;
1. Attribute SPC charts
2. When best to apply these 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 -Nonconformingp 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 number are the number of of nonconforming nonconforming products products detected and ndetected and n11, , nn22 etc are the etc are the corresponding corresponding 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
pppLCLp
n
pppUCLp
)1(3
)1(3
n+n+n
pn++pn+pn=p
p - ingnonconform proportion average theDetermine
k21
kk2211
52
p charts
• Class Exercise– Using the data in Appendix 5 calculate the
UCL and LCL for the p chart– Plot the data onto the charts and identify
any out of control conditions
53
Number of Nonconforming productsnp charts
• When to use a np chart• when data is of attribute type (an attribute
that can be counted)• 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
– Establish the frequency of inspection
– 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
• Example of calculating control lines for np-charts
Where k is Where k is the number the number of subgroups of subgroups and n is the and n is the sample size sample size in each of in each of those those subgroups.subgroups.
)1(3
)1(3
np++np+np=pn
pn - ingnonconformnumber average theDetermine
kk21
n
pnpnpnLCLnp
n
pnpnpnUCLnp
56
np charts
• Class Exercise– Using the data in Appendix 7 calculate the
UCL and LCL for the np chart– Plot the data onto the charts and identify
any out of control conditions
57
Number of Nonconformity's c charts• When to use a c chart• when data is of attribute type (an attribute
that can be counted)• 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
– Establish the frequency of inspection– 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
• Example of calculating control lines for c-charts
Where k is the number Where k is the number of subgroups.of subgroups.
c3c
c3c
k
k++2+1 =c
c itiesnonconform ofnumber average theDetermine
ccc
LCLc
UCLc
60
c charts
• Class Exercise– Using the data in Appendix 7 calculate the
UCL and LCL for the c chart– Plot the data onto the charts and identify
any out of control conditions
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
Number of Nonconformity's per unit u Chart
• Methodology for the calculation of u charts– Define what will be inspected– Establish the frequency of inspection– 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
Number of Nonconformity's per unit u Chart
• Example of calculating control lines for u-charts
Where c1, c2 Where c1, c2 etc are number etc are number of of nonconformity'nonconformity's per unit and s per unit and n1, n2 etc is n1, n2 etc is the the corresponding corresponding sample sizesample size
n
u3u
n
u3u
nk+n2+n1
k++2+1 =u
uunit per itiesnonconform average theDetermine
uuu
LCLu
UCLu
64
Number of Nonconformity's per unit 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?