7 ssgb-amity-bsi-stability-control charts

1. Module-7
Control Charts

2. 2
Control Charts – Learning Objectives
At the end of this section, delegates will:
• Understand how control charts can show if a
process is stable
• Generate and interpret control charts for variable
and attribute data
• Understand the role of control charts within the
DMAIC improvement process

3. 3
Control Charts – Agenda
1. Introduction to Statistical Process Control, SPC
2. Control Limits
3. Individual and Moving Range Chart
4. Workshop on Control Charts
5. Defective (Binomial) p-Chart
6. Defects (Poisson) u-Chart
7. Workshop on Attribute Control Charts
8. Uses of Control Charts
9. Summary

4. 4
What is Statistical Process Control?
• Statistical Process Control is a method of
monitoring and detecting changes in
processes.
• SPC uses an advanced form of Time Series
plots.
• SPC provides an easy method of deciding if
a process has changed (in other words, is
the process “in-control”?).

5. 5
We Need Ways of Interpreting Data
• Everyday we are flooded by data and we are
forced to make decisions:
• Calls handled decreases by 4%
• UK trade deficit rises by £5 billion
• Company X’s earnings are $240Million less
than the previous quarter
• Should we take action ?

6. 6
How do we manage data historically?
Leave it alone -
it ain’t broke
Pain &
suffering
Pain &
suffering
Lower “Customer”
Requirement
Upper “Customer”
Requirement
This Method
• Tells you where you are in relation to customer’s needs
• It will NOT tell you how you got there or what to do next
• Means that pressure to achieve customer requirements will cause you to:
• Actually Fix The Process
• Sabotage The Process
• Sabotage The Data (Integrity)

7. 7
What do Control Charts detect?
• Control Charts detect changes in a process.
• All processes change slightly, but process control
aims to detect ‘statistically significant’ changes that
are not just random variation.
• Processes can change in several different ways…
• the process average can change
• the process variation can change
• the process may contain one-off events

8. 8
Process Control
• Process control refers
to the evaluation of
process stability over
time
• Process Capability
refers to the
evaluation of how well
a process meets
specifications
0 5 10 15 20 25
Time
LSL USL
UCL
LCL

9. 9
Why would a Process be Incapable?
There are a number of reasons why a
process may not be capable of meeting
specification:
1. The specification is incorrect!
2. Excessive variation
3. The process is not on target
4. A combination of the above
5. Errors are being made
6. The process is not stable

10. 10
The specification is incorrect
• This issue was discussed during the
Customer Focus section of this course
• If specifications are not clearly related to
customer requirements, then it is always a
good idea to challenge the specification
before attempting to improve the process

11. 11
Excessive variation
Upper
Specification
Limit
Lower
Specification
Limit
Target
• Excessive variation means that we have a
variation reduction issue
• We will need to understand which process inputs
are causing the variation in the process output

12. 12 The process is not on target
Upper
Specification
Limit
Lower
Specification
Limit
Target
• In this situation we have a process targeting issue
• We will need to understand which process inputs
are causing the process to be off-target
• This situation is sometimes simple to solve!

13. 13 Excessive variation and not on target
Upper
Specification
Limit
Lower
Specification
Limit
Target
• In this situation we have both excessive variation
and a process targeting issue
• We will need to understand which process inputs
are causing the excessive variation and which
are causing the process to be off-target

14. 14
Errors are being made
Upper
Specification
Limit
Lower
Specification
Limit
Target
• A situation such as this might indicate that errors are
being made which result in occasional excursions
outside of the specification
• This is often an indication of a mistake proofing issue

15. 15
The process is not stable
Upper
Specification
Limit
Lower
Specification
Limit Target
Last week
This week
Next week?
• A situation such as this is an indication that the process
is unstable
• Whenever this situation is encountered in a DMAIC
activity, then the reason(s) for the instability must be
found and removed before assessing process capability

16. 16 The process is not stable
Upper
Specification
Limit
Lower
Specification
Limit
Target
Last week
This week
Next
week?
• Causes of process instability are sometimes referred
to as “special causes”
• Removing these special causes may result in the
process becoming capable of consistently meeting the
target

17. 17
Unstable Process
“Special”
causes of
variation are
present
Total
Variation
Time
Target

18. 18
Stable Process
Time
Target
Total
Variation
Only “Common”
causes of
variation are
present

19. 19
Capable Process
Time
Spec Limits
CAPABLE
NOT
CAPABLE Process is Stable but
Process is not Capable
Process is Stable and
Process is Capable
Management Action
(DMAIC) to reduce
common cause variation

20. 20
Control Charts test for Stability
(Control Chart of Average)
0 5 10 15 20 25
Time
1.3
1.29
1.28
1.27
1.26
Process Average
Upper Control Limit
Lower Control Limit

21. 21 Transactional Improvement Process
Analyse Define
Measure Improve Control
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify Customer
Requirements
Identify Priorities
Update Project File
Control Critical x ’s
Monitor y’s
Validate Control
Plan
Identify further
opportunities
Close Project
LSL USL
15 20 25 30 35
Phase Review
1 5 10 15 20
10.2
10.0
9.8
9.6
Upper Control Limit
Lower Control Limit
y
Phase Review
Develop Detailed
Process Maps
START
PROCESS
STEPS
DECISION
STOP
Identify Critical
Process Steps (x’s)
by looking for:
– Process Bottlenecks
– Rework / Repetition
– Non-value Added
Steps
– Sources of Error /
Mistake
Map the Ideal
Process
Identify gaps
between current and
ideal
Phase Review
Brainstorm Potential
Improvement Strategies
Select Improvement
Strategy
Criteria A B C D
Time + s - +
Cost + - + s
Service - + - +
Etc s s - +
Plan and Implement
Pilot
Verify Improvement
LSL USL
15 20 25 30 35
Implement
Countermeasures
Phase Review
Phase Review
Define Measures (y’s)
Check Data Integrity
Determine Process
Stability
Determine Process
Capability
Set Targets for
Measures

22. 22
Role of Control Charts
Measure Phase:
• used during capability studies to assess process stability
Improve Phase:
• used to establish if the modified, improved process is stable
Control Phase
• used to control critical process input variables (x’s) in order to
reduce variability in process outputs (y’s)
• used to monitor process outputs (y’s) on an ongoing basis to
ensure that the process remains in control

23. 23
Control Charts
Variable
Data
No
Subgroups
Subgroups
n = 2-9
Subgroups
n 9
Individuals
Moving Range
Chart
X Bar R
Chart
X Bar s
Chart
Attribute
Data
Defect Data
(Poisson)
Defective Data
(Binomial)
Varying
Subgroup
Size
Constant
Subgroup
Size
Varying
Subgroup
Size
Constant
Subgroup
Size
u Chart c Chart p Chart np Chart

24. 24
What do Control Charts tell us?
0 5 10 15 20 25
Subgroup
1.3
1.29
1.28
1.27
1.26
X-bar
• Is the process stable?
• Should we be taking action?
• Are there any special causes?
• What is the average process output?
• What is the variability?

25. Control Limits

26. 26
Total Variation
Total
Variation
Within Subgroup
Variation
Between Subgroup
Variation

27. 27
Control Limits Use Within Subgroup
Variation
• The total variation and Within Subgroup variation are
the same only if the process is stable
• The Within Subgroup variation is an estimate of what
the total variation would be if the process were
stable
• The Within Subgroup variation is used to calculate
the control limits since these limits represent the
range of values expected for a stable process

28. 28
Controls Limits
• Controls limits are always:
Average ± 3 Standard Deviations
Where the average and standard deviation are the
average and standard deviation of whatever data
is plotted:
−4s −3s −2s −1s 0 +1s +2s +3s +4s
99.7%

29. 29
Control Limits
Upper Control Limit
Lower Control Limit
• Control Limits are statistical boundaries which tell us whether or
not the process is stable
• Based on the normal distribution, 99.7% of the points plot within
the control limits if the process is stable
• The chance of a point outside the control limits, falsely indicating
the process is unstable, is only 0.3% or 1 in 370

30. Individuals Control Chart

31. 31
Individuals Control Chart
• Used when only a single observation per time period
(subgroup):
Monthly reporting data:
• On-time shipments, In-process Inventory, Complaints, etc.
Rare events
Sales
Stock Price
Inventory Levels
Customer Response Time
Lost Time Accidents
Complaints
Anything that can be measured and varies

32. 32
Within Subgroup Variation
• The best estimate is obtained by taking the differences between
consecutive samples i.e. the Moving Range (MR).
• We can use the the average MR, R, or the median MR, R
• When using R the Short Term standard deviation is estimated by:
R
1.128
R
d
2
Within
= =
˜
• When using R˜ the standard deviation is estimated by:
~
R
0.954
~
R
d
4
Within
= =

33. 33
Table of Constants for ImR charts
Sample size d 2 d 3 d 4 D 3 D 4 D 5 D 6 E 2 E 5
2
3
4
5
6
7
8
9
10
0.853
0.888
0.880
0.864
0.848
0.833
0.820
0.808
0.797
0.954
1.588
1.978
2.257
2.472
2.645
2.791
2.915
3.024
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
2.970
3.078
0
3.865
0
2.744
0
2.376
0 2.179
0.209
1.075
1.029
1.809 0.975 0.992
0
0.055
0.119
0.168
2.054
1.967
1.901
1.850
1.128
1.693
2.059
2.326
2.534
2.704
2.847
0
0
0
0
0
0.076
0.136
0.184
0.223
2.660
1.772
1.457
1.290
1.184
1.109
1.054
1.010
3.145
1.889
1.517
1.329
1.214
1.134
We would generally calculate the differences between
consecutive samples, which corresponds to a “sample
size” of 2 in this table.
Minitab will calculate the control chart limits for us!

34. 34
Control Limits
The controls limits for the average, based on R are:
X 3 X 3 2
X E R X 2.66R
R
± = ± = ± = ± = ±
1.128
X 3
R
d
2
Within
The controls limits for the range, based on R are:
LCL = D R = 0 × R =
0
Range 3
UCL = D R =
3.267R
Range 4

35. 35
Control Limits
3.145 X R ~
X E
R ~
R ~
X 3 X 3 5
± = ± = ± = ± = ±
0.953
X 3
R ~
d
4
Within
~
The controls limits for the average, based on R are:
~
The controls limits for the range, based on R are:
~
~
LCL = D
R = 0 × R =
0 Range 5
3.865 R ~
UCL D
R ~
= =
Range 6

36. 36
¯ ˜
R Versus R
• Some of the differences may be contaminated by
shifts in the mean (special Causes).
• R, the median MR, is more robust to this
contamination so is generally preferred.
• When many of the differences are zero, it might
be necessary to use R instead.
• A conversion factor can be developed:
R ~
182 . 1 R ~
= s =
1.128
0.954
R ~
R
0.954
R
1.128
within
= × = ×
~

37. 37
Call Out Time
Sample Number Call Out Time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
5.35
3.28
1.07
1.06
4.29
3.23
5.40
6.42
3.25
8.55
4.26
7.48
5.35
2.14
4.24
6.44
3.21
9.66
4.28
5.33

38. 38
Call Out Time
Sample Number Call out Time
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Difference
5.35
3.28
1.07
1.06
4.29
3.23
5.40
6.42
3.25
8.55
4.26
7.48
5.35
2.14
4.24
6.44
3.21
9.66
4.28
5.33
2.07
2.21
0.01
3.23
1.06
2.07
1.02
5.30
4.29
3.22
2.13
3.21
2.10
2.20
3.23
6.45
5.38
1.05
2.21
4.71 2.82
Average Average Difference
Ordered
0.01
1.02
1.05
1.06
2.07
2.07
2.10
2.13
2.20
2.21
2.21
3.21
3.22
3.23
3.23
4.29
5.30
5.38
6.45
Median

39. 39 Individuals chart - Minitab
Open Worksheet: Call Out Time
StatControl ChartsVariables Charts for IndividualsI-MR
Select Variable: Call Out Time
Click “I-MR” Options
Click “Estimate” – select “Median moving range”
Click “Tests” - select “1 point 3 standard deviations from center line”

40. 40
IMR Chart – Minitab (using R)
Observation
Individual Value
2 4 6 8 10 12 14 16 18 20
12
8
4
0
UC L=11.66
_
X=4.71
LC L=-2.24
Observation
Moving Range
2 4 6 8 10 12 14 16 18 20
8
6
4
2
0
UC L=8.538
__
MR=2.613
LC L=0
I-MR Chart of Call out Time
˜
21 . 2 R ~
Median
=
~
R
= R × 1 . 182 =
2 . 613

41. 41
Lognormal and other non –
normal data
• When dealing with lognormal and other non-normal data
we need to be cautious.
• X-bar and Range charts will be acceptable for most non-normal
data with a sub-group size of 5 or larger.
• I-MR charts may give false indications of instability.

42. 42
Workshop – Individuals Control Chart
Open Minitab worksheet: PAYMENT TIMES.MTW
Use Minitab to create:
• Individuals and Moving Range chart
• Use the Median with a moving range of 2
• Assess the stability of the process
• What would you want to do next?
• Prepare a short report of your findings

43. Attribute Control Charts

44. 44
Control Charts for Defective Items (Binomial)
• A p-Chart is used to track the
proportion defective
• The p-Chart is constructed using data
on the number of defectives from
varying (or fixed) subgroup sizes
• The data opposite shows the number
of defective orders from random
samples taken over 10 working days
• The subgroups should be large
enough to contain 5 or more defective
items
Sample
Number
Defectives
(np)
Subgroup
Size
1 8 96
2 12 104
3 13 99
4 8 100
5 7 103
6 13 110
7 6 97
8 7 88
9 10 111
10 8 105

45. 45
Control Charts for Defective Items (Binomial)
• The p-chart must satisfy the requirements for the Binomial
Distribution. The particular requirements affecting the p-chart are:
1. Each unit (e.g., transaction, invoice, …) can only be classified
as pass or fail
2. If one unit (e.g., transaction, invoice, …) fails, then the chance
of the next unit failing is not affected
• If the Binomial distribution is not appropriate then it may be
possible to use the Individuals control chart already discussed
• Since we are charting defective items this chart should not be
used when the number of defectives is zero or there are a large
number of zeros (80-90%)

46. 46 P Chart Construction
Sample
Number
Defectives
(np)
Subgroup
Size (n)
Proportion
Defective
(p)
Average
Proportion
Defective
(pbar) 3 Sigma UCL(p) LCL(p)
1 8 96 0.083 0.091 0.088062 0.179062 0.002938
2 12 104 0.115 0.091 0.084608 0.175608 0.006392
3 13 99 0.131 0.091 0.086718 0.177718 0.004282
4 8 100 0.08 0.091 0.086283 0.177283 0.004717
5 7 103 0.068 0.091 0.085017 0.176017 0.005983
6 13 110 0.118 0.091 0.082268 0.173268 0.008732
7 6 97 0.062 0.091 0.087607 0.178607 0.003393
8 7 88 0.08 0.091 0.091978 0.182978 -0.00098
9 10 111 0.091 0.091 0.081896 0.172896 0.009104
10 8 105 0.076 0.091 0.084204 0.175204 0.006796
Total 92 1013
p(1-p)
n
p(1-p)
, LCL p 3 p-3
= = = =
p(1-p)
n
92
np
UCL p 3 p 3
n
0.091,
1013
n
p
p = + = + p = − =

47. 47 P Chart - Minitab
P Chart of Defectives
1 2 3 4 5 6 7 8 9 10
Sample
Proportion
0.20
0.15
0.10
0.05
0.00
UCL=0.1749
_
P=0.0908
LCL=0.0067
Tests performed with unequal sample sizes
Open Worksheet P Chart
StatControl ChartsAttributes ChartsP
Variable: Defectives
Subgroups in: “Subgroup Size” Click “P Chart – Options”
Click “Tests” – select “1 point 3 standard deviations from center line”

48. 48
Control Charts for Defects (Poisson)
• A u Chart is used to track the number of
defects per unit (e.g., transaction,
invoice, …).
• The u chart is constructed using data on
the number of defects from varying
subgroup sizes (number of units).
• The data opposite shows the number of
defects in the given number of invoices
sampled randomly from 10 weeks of
invoicing.
Sample
Number
Defects
c
Invoices
n
1 7 40
2 4 45
3 8 33
4 5 40
5 3 39
6 8 46
7 5 27
8 7 45
9 9 38
10 4 39

49. 49
Control Charts for Defects (Poisson)
• Since the u-chart is based on the Poisson
Distribution, the data should be tested to see if it fits
the Poisson distribution (e.g., some “count data”
such as complaints and late shipments may not fit
the Poisson distribution)
• If the Poisson distribution does not fit then it may be
possible to use the Individuals control chart already
discussed
• Since we are charting defects, this chart should not
be used when the number of defects is zero or there
are a large number of zeros (80-90%)

50. 50
U Chart - Construction
Sample
Number
Defects
c
Invoices
n
DPU
u u bar LCL(u) UCL(u)
1 7 40 0.175 0.153 0 0.34
2 4 45 0.089 0.153 0 0.328
3 8 33 0.242 0.153 0 0.307
4 5 40 0.125 0.153 0 0.339
5 3 39 0.077 0.153 0 0.341
6 8 46 0.174 0.153 0 0.326
7 5 27 0.185 0.153 0 0.378
8 7 45 0.156 0.153 0 0.327
9 9 38 0.237 0.153 0 0.343
10 4 39 0.103 0.153 0 0.341
Total 60 392 0.153
u
n
0.153, u
= = = =
u
, LCL u 3 u 3
n
60
392
c
n
u
UCL u 3 u 3
= + s = + = − s
= −
u u

51. 51 U Chart - Minitab
U Chart of Defects
1 2 3 4 5 6 7 8 9 10
Sample
Sample Count Per Unit
0.4
0.3
0.2
0.1
0.0
UCL=0.3410
_
U=0.1531
LCL=0
Tests performed with unequal sample sizes
Open Worksheet: U Chart
StatControl ChartsAttributes ChartsU
Variable: Defects Subgroups in: “Units”
Click “U Chart Options”
Click “Tests” – select “1 point 3 standard deviations from center line”

52. 52
Workshop - Attributes Control Chart
• Using the packets of sweets provided (assume
that each packet has been taken from a different
batch of production over the last few days):
Randomly select 20 sweets from each packet
Inspect the sweets for two types of defect-
• Badly mis-shaped/damaged sweet
• Missing or poorly printed logo
• Using Minitab, assess the stability of the process
• Prepare a short report of your findings

53. Uses of Control Charts

54. 54
Control Charts
Variable
Data
No
Subgroups
Subgroups
n = 2-9
Subgroups
n 9
Individuals
Moving Range
Chart
X Bar R
Chart
X Bar s
Chart
Attribute
Data
Defect Data
(Poisson)
Defective Data
(Binomial)
Varying
Subgroup
Size
Constant
Subgroup
Size
Varying
Subgroup
Size
Constant
Subgroup
Size
u Chart c Chart p Chart np Chart

55. 55
Improvement
• Control charts are one of many variation reduction
tools
• Controls charts detect change of the output variable
(y)
• The output changes because a critical input variable
(x) has changed
• Control charts provide clues that can help to identify
these critical inputs (x’s)

56. 56
Clues to Discovering Critical x’s
• When did the change occur?
• What patterns are emerging?
Shifts
• Gradual or Sudden?
Trends
• Increasing or Decreasing?
Unusual patterns or cycles?

57. 57
Identification of Critical x’s
• To determine the critical x, i.e., the input causing
the shift, we need to consider:
Delayed detection
Multiple inputs causing shifts
Lack of information on inputs
• We can also use screening experiments, scatter
diagrams, … to determine critical x’s

58. 58
Transmission of Variation, y = f(x)
• Control charts can help to discover critical x’s that
are causing the process to shift
• Tighter control of these critical x’s will make the
process more stable
O
U
T
P
U
T
Relationship Between
Input and Output
Variation of Input
INPUT
Transmitted
Variation

59. 59 Transactional Improvement Process
Analyse Define
Measure Improve Control
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify Customer
Requirements
Identify Priorities
Update Project File
Control Critical x ’s
Monitor y’s
Validate Control
Plan
Identify further
opportunities
Close Project
LSL USL
15 20 25 30 35
Phase Review
1 5 10 15 20
10.2
10.0
9.8
9.6
Upper Control Limit
Lower Control Limit
y
Phase Review
Develop Detailed
Process Maps
START
PROCESS
STEPS
DECISION
STOP
Identify Critical
Process Steps (x’s)
by looking for:
– Process Bottlenecks
– Rework / Repetition
– Non-value Added
Steps
– Sources of Error /
Mistake
Map the Ideal
Process
Identify gaps
between current and
ideal
Phase Review
Brainstorm Potential
Improvement Strategies
Select Improvement
Strategy
Criteria A B C D
Time + s - +
Cost + - + s
Service - + - +
Etc s s - +
Plan and Implement
Pilot
Verify Improvement
LSL USL
15 20 25 30 35
Implement
Countermeasures
Phase Review
Phase Review
Define Measures (y’s)
Check Data Integrity
Determine Process
Stability
Determine Process
Capability
Set Targets for
Measures

60. 60
Control Charts - Summary
• Charts can be constructed for variable or attribute data
• I-MR Charts should always be considered for attribute data
• Control Charts are used during capability studies to
determine process stability
• Real-Time control charts are used to detect shifts so that
causes of shifts can be identified and eliminated
• Should be used to control critical x’s (process input
variables) in order to reduce variability in process outputs
(y’s).
• Used to monitor y’s on an ongoing basis to ensure that the
process remains in control.