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8/9/2019 7 SSGB Amity BSI Stability Control Charts
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Module-7Control Charts
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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 variableand attribute data
Understand the role of control charts within the
DMAIC improvement process
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Control Charts Agenda1. 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
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What is Statistical Process Control?
Statistical Process Control is a method ofmonitoring and detecting changes inprocesses.
SPC uses an advanced form of Time Seriesplots.
SPC provides an easy method of deciding ifa process has changed (in other words, is
the process in-control?).
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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 Xs earnings are $240Million less
than the previous quarter
Should we take action ?
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Leave it alone -it aint broke
Pain &suffering
Pain &suffering
Lower CustomerRequirement
Upper CustomerRequirement
How do we manage data historically?
This Method
Tells you where you are in relation to customers 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)
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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
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Process Control
Process control refersto the evaluation ofprocess stability overtime
Process Capabilityrefers to the
evaluation of how wella process meetsspecifications
LSL USL
0 5 10 15 20 25
Time
UCL
LCL
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Why would a Process be Incapable?There are a number of reasons why aprocess 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
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The specification is incorrect This issue was discussed during the
Customer Focus section of this course
If specifications are not clearly related tocustomer requirements, then it is always agood idea to challenge the specificationbefore attempting to improve the process
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Excessive variationUpper
Specification
Limit
Lower
Specification
LimitTarget
Excessive variation means that we have avariation reduction issue
We will need to understand which process inputsare causing the variation in the process output
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The process is not on targetUpper
Specification
Limit
Lower
Specification
LimitTarget
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!
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Excessive variation and not on targetUpper
Specification
Limit
LowerSpecification
LimitTarget
In this situation we have both excessive variationand a process targeting issue
We will need to understand which process inputsare causing the excessive variation and whichare causing the process to be off-target
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Errors are being madeUpper
Specification
Limit
Lower
Specification
LimitTarget
A situation such as this might indicate that errors arebeing made which result in occasional excursions
outside of the specification
This is often an indication of a mistake proofing issue
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The process is not stable
A situation such as this is an indication that the processis unstable
Whenever this situation is encountered in a DMAICactivity, then the reason(s) for the instability mustbefound and removed before assessing process capability
Upper
Specification
Limit
Lower
Specification
Limit Target
Last week
This week
Next week?
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The process is not stableUpper
Specification
Limit
LowerSpecification
LimitTarget
Last week
This week
Next
week?
Causes of process instability are sometimes referred
to as special causes
Removing these special causes may result in theprocess becoming capable of consistently meeting the
target
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Unstable Process
Special
causes ofvariation arepresent
Time
TotalVariation
Target
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Stable Process
Time
Target
TotalVariation
Only Common
causes ofvariation arepresent
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Capable Process
Time
Spec Limits
CAPABLE
NOT
CAPABLE Process is Stable but
Process is not Capable
Process is Stable andProcess is Capable
Management Action(DMAIC) to reducecommon cause variation
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Control Charts test for Stability(Control Chart of Average)
0 5 10 15 20 25
Time
1.26
1.27
1.28
1.29
1.3
Proce
ssAverage
Upper Control Limit
Lower Control Limit
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Transactional Improvement Process
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify Customer
Requirements
Identify Priorities
Update Project File
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify Customer
Requirements
Identify Priorities
Update Project File
Control Critical xs
Monitor ys
Validate ControlPlan
Identify furtheropportunities
Close Project
15 20 25 30 35
LSL USL
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 DetailedProcess Maps
Identify CriticalProcess Steps (x s)by looking for:
Process Bottlenecks
Rework / Repetition Non-value Added
Steps
Sources of Error /Mistake
Map the IdealProcess
Identify gapsbetween current andideal
START
PROCESSSTEPS
DECISION
STOP
Phase Review
Brainstorm PotentialImprovement Strategies
Select ImprovementStrategy
Plan and ImplementPilot
Verify Improvement
Implement
Countermeasures
Criteria A B C D
Time + s - +
Cost + - + s
Service - + - +
Etc s s - +
15 20 25 30 35
LSL USL
Phase Review
Analyse Improve ControlMeasureDefine
Phase Review
Define
Define Measures (y s)
Check Data Integrity
Determine ProcessStability
Determine ProcessCapability
Set Targets forMeasures
15 20 25 30 35
LSL USL
15 20 25 30 35
LSL USL
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 DetailedProcess Maps
Identify CriticalProcess Steps (x s)by looking for:
Process Bottlenecks
Rework / Repetition Non-value Added
Steps
Sources of Error /Mistake
Map the IdealProcess
Identify gapsbetween current andideal
START
PROCESSSTEPS
DECISION
STOP
Phase Review
Brainstorm PotentialImprovement Strategies
Select ImprovementStrategy
Plan and ImplementPilot
Verify Improvement
Implement
Countermeasures
Criteria A B C D
Time + s - +
Cost + - + s
Service - + - +
Etc s s - +
15 20 25 30 35
LSL USL
Phase Review
Analyse Improve ControlMeasureDefine
Phase Review
Define
Define Measures (y s)
Check Data Integrity
Determine ProcessStability
Determine ProcessCapability
Set Targets forMeasures
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Role of Control ChartsMeasure 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 (xs) in order to
reduce variability in process outputs (ys)
used to monitor process outputs (ys) on an ongoing basis to
ensure that the process remains in control
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Control ChartsVariable
Data
NoSubgroups
Subgroupsn = 2-9
Subgroupsn > 9
Individuals &Moving Range
Chart
X Bar & RChart
X Bar & sChart
AttributeData
Defect Data(Poisson)
Defective Data(Binomial)
VaryingSubgroup
Size
ConstantSubgroup
Size
VaryingSubgroup
Size
ConstantSubgroup
Size
u Chart c Chart p Chart np Chart
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What do Control Charts tell us?
Is the process stable? Should we be taking action?
Are there any special causes? What is the average process output? What is the variability?
0 5 10 15 20 25
Subgroup
1.26
1.27
1.28
1.29
1.3
X-bar
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Control Limits
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Total Variation
TotalVariation
Within SubgroupVariation
Between SubgroupVariation
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Control Limits Use Within SubgroupVariation
The total variation and Within Subgroup variation arethe same only if the process is stable
The Within Subgroup variation is an estimate of what
the total variation would be if the process werestable
The Within Subgroup variation is used to calculatethe control limits since these limits represent the
range of values expected for a stable process
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Controls Limits
Controls limits are always:
Average 3 Standard DeviationsWhere the average and standard deviation are the
average and standard deviation of whatever data
is plotted:
99.7%99.7%99.7%99.7%
4444 3333 2222 1111 +1+1+1+1 +2+2+2+2 +3+3+3+3 +4+4+4+40
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Control LimitsUpper Control Limit
Lower Control Limit
Control Limits are statistical boundaries which tell us whether ornot the process is stable
Based on the normal distribution, 99.7% of the points plot withinthe control limits if the process is stable
The chance of a point outside the control limits, falsely indicatingthe process is unstable, is only 0.3% or 1 in 370
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Individuals Control Chart
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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
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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:
1.128
R
d
R
2
Within ==
When using R the standard deviation is estimated by:
0.954
R~
d
R~
4
Within ==
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Table of Constants for ImR chartsSample size d 2 d 3 d 4 D 3 D 4 D 5 D 6 E 2 E 5
2
3
456
7
8
9
10
0.853
0.888
0.8800.8640.848
0.833
0.820
0.808
0.797
0.954
1.588
1.9782.2572.472
2.645
2.791
2.915
3.024
3.267
2.574
2.2822.1142.004
1.924
1.864
1.816
1.777
2.970
3.078
3.865
2.744
2.376
0
0
00 2.179
0.209
1.075
1.029
0.9921.809 0.975
0
0.055
0.119
0.168
2.054
1.967
1.901
1.850
1.128
1.693
2.0592.3262.534
2.704
2.847
0
0
000
0.076
0.136
0.184
0.223
2.660
1.772
1.4571.2901.184
1.109
1.054
1.010
3.145
1.889
1.5171.3291.214
1.134
We would generally calculate the differences betweenconsecutive samples, which corresponds to a samplesize of 2 in this table.Minitab will calculate the control chart limits for us!
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Control LimitsThe controls limits for the average, based on R are:
R2.66XREX1.128
R3XdR3X3X 2
2
Within ====
The controls limits for the range, based on R are:
R3.267RDUCL
0R0RDLCL
4Range
3Range
==
===
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Control Limits
R~3.145XR~EX0.953
R
~
3XdR
~
3X3X 54
Within ====
~The controls limits for the average, based on R are:
The controls limits for the range, based on R are:~
R~
3.865R~
DUCL
0R~
0R~
DLCL
6Range
5Range
==
===
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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 thiscontamination so is generally preferred.
When many of the differences are zero, it mightbe necessary to use R instead.
A conversion factor can be developed:
182.1R~
954.0
128.1R~
R
954.0
R~
128.1
Rwithin
========
========
~
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Call Out TimeSample Number Call Out Time
1
2
3
4
5
6
7
8
9
10
1112
13
14
15
16
1718
19
20
5.35
3.28
1.07
1.06
4.29
3.23
5.40
6.42
3.25
8.55
4.267.48
5.35
2.14
4.24
6.44
3.219.66
4.28
5.33
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Call Out TimeSample Number Call out Time
1
2
3
4
56
7
8
9
10
11
12
1314
15
16
17
18
19
20
Difference
5.35
3.28
1.07
1.06
4.293.23
5.40
6.42
3.25
8.55
4.26
7.48
5.352.14
4.24
6.44
3.21
9.66
4.28
5.33
2.07
2.21
0.01
3.231.06
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
1.062.07
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
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Individuals chart - MinitabOpen Worksheet: Call Out Time
Stat>Control Charts>Variables Charts for Individuals>I-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
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IMR Chart Minitab (using R)
Observation
Individual
Value
2018161412108642
12
8
4
0
_X=4.71
UC L=11.66
LCL=-2.24
Observation
MovingRange
2018161412108642
8
6
4
2
0
__MR=2.613
UC L=8.538
LC L=0
I-MR Chart of Call out Time
613.2182.1R~
R
21.2R~
Median
========
====
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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.
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Workshop Individuals Control ChartOpen 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
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Attribute Control Charts
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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 fromvarying (or fixed) subgroup sizes
The data opposite shows the numberof defective orders from randomsamples taken over 10 working days
The subgroups should be large
enough to contain 5 or more defectiveitems
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 11110 8 105
45
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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 classifiedas 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 bepossible 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%)
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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 0.0042824 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
n
)p-(1p3-p3pLCL,
n
)p-(1p3p3pUCL
n
)p-(1p0.091,
1013
92
n
npp
pp ==+=+=
====
47
P Ch Mi i b
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P Chart - Minitab
Open Worksheet P Chart
Stat>Control Charts>Attributes Charts>P
Variable: DefectivesSubgroups in: Subgroup Size Click P Chart Options
Click Tests select 1 point > 3 standard deviations from center line
Sample
Proportion
10987654321
0.20
0.15
0.10
0.05
0.00
_P=0.0908
UCL=0.1749
LCL=0.0067
P Chart of Defectives
Tests performed with unequal sample sizes
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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 onthe number of defects from varying
subgroup sizes (number of units).
The data opposite shows the number ofdefects in the given number of invoicessampled 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 3 396 8 46
7 5 27
8 7 45
9 9 38
10 4 39
49
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Control Charts for Defects (Poisson)
Since the u-chart is based on the PoissonDistribution, the data should be tested to see if it fitsthe Poisson distribution (e.g., some count datasuch as complaints and late shipments may not fitthe Poisson distribution)
If the Poisson distribution does not fit then it may be
possible to use the Individuals control chart alreadydiscussed
Since we are charting defects, this chart should notbe used when the number of defects is zero or thereare a large number of zeros (80-90%)
50
C C
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U Chart - ConstructionSampleNumber
Defectsc
Invoicesn
DPUu 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 0.341Total 60 392 0.153
n
u3u3uLCL,
n
u3u3uUCL
u0.153,392
60
n
cu
uu ========++++====++++====
================
51
U Chart Minitab
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U Chart - Minitab
Open Worksheet: U Chart
Stat>Control Charts>Attributes Charts>U
Variable: Defects Subgroups in: UnitsClick U Chart Options
Click Tests select 1 point > 3 standard deviations from center line
Sample
SampleCountPerUnit
10987654321
0.4
0.3
0.2
0.1
0.0
_U=0.1531
UCL=0.3410
LCL=0
U Chart of Defects
Tests performed with unequal sample sizes
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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
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Uses of Control Charts
54
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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
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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 (xs)
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Clues to Discovering Critical xs When did the change occur?
What patterns are emerging? Shifts
Gradual or Sudden?
Trends Increasing or Decreasing?
Unusual patterns or cycles?
57
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Identification of Critical xs 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 xs
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Transmission of Variation, y = f(x) Control charts can help to discover critical xs that
are causing the process to shift
Tighter control of these critical xs will make the
process more stable
OUTPUT
INPUT
Relationship BetweenInput and Output
Variation of Input
TransmittedVariation
59
Transactional Improvement Process
8/9/2019 7 SSGB Amity BSI Stability Control Charts
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Transactional Improvement Process
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify CustomerRequirements
Identify Priorities
Update Project File
Select Project
Define Project
Objective
Form the Team
Map the Process
Identify CustomerRequirements
Identify Priorities
Update Project File
Control Critical xs
Monitor ys
Validate ControlPlan
Identify furtheropportunities
Close Project
15 20 25 30 35
LSL USL
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 DetailedProcess Maps
Identify CriticalProcess Steps (x s)by looking for:
Process Bottlenecks
Rework / Repetition
Non-value AddedSteps
Sources of Error /Mistake
Map the IdealProcess
Identify gaps
between current andideal
START
PROCESSSTEPS
DECISION
STOP
Phase Review
Brainstorm PotentialImprovement Strategies
Select ImprovementStrategy
Plan and ImplementPilot
Verify Improvement
ImplementCountermeasures
Criteria A B C DTime + s - +
Cost + - + s
Service - + - +
Etc s s - +
15 20 25 30 35
LSL USL
Phase Review
Analyse Improve ControlMeasureDefine
Phase Review
Define
Define Measures (y s)
Check Data Integrity
Determine ProcessStability
Determine ProcessCapability
Set Targets forMeasures
15 20 25 30 35
LSL USL
15 20 25 30 35
LSL USL
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 DetailedProcess Maps
Identify CriticalProcess Steps (x s)by looking for:
Process Bottlenecks
Rework / Repetition
Non-value AddedSteps
Sources of Error /Mistake
Map the IdealProcess
Identify gaps
between current andideal
START
PROCESSSTEPS
DECISION
STOP
Phase Review
Brainstorm PotentialImprovement Strategies
Select ImprovementStrategy
Plan and ImplementPilot
Verify Improvement
ImplementCountermeasures
Criteria A B C DTime + s - +
Cost + - + s
Service - + - +
Etc s s - +
15 20 25 30 35
LSL USL
Phase Review
Analyse Improve ControlMeasureDefine
Phase Review
Define
Define Measures (y s)
Check Data Integrity
Determine ProcessStability
Determine ProcessCapability
Set Targets forMeasures
60
8/9/2019 7 SSGB Amity BSI Stability Control Charts
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 xs (process input
variables) in order to reduce variability in process outputs
(ys).
Used to monitor ys on an ongoing basis to ensure that theprocess remains in control.