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?