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QCC &7 Quality Control Tools
For Problem Solvings
Plan CheckDo Act
MODULE 1
UNDERSTANDINGQC CIRCLE
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Overview
• What are Quality Circles?
• How Do Quality Circles Work?
• How Can They be Used in an Organization?
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What is a Quality Circle?
•Voluntary groups of employees Voluntary groups of employees who work on similar tasks or share who work on similar tasks or share an area of responsibilityan area of responsibility
•They agree to meet on a regular They agree to meet on a regular basis to discuss & solve problems basis to discuss & solve problems related to work.related to work.
•They operate on the principle that They operate on the principle that employee participation in decision-employee participation in decision-making and problem-solving making and problem-solving improves the quality of workimproves the quality of workPlan CheckDo Act
How Do Quality Circles Work?
• Characteristics
• Volunteers
• Set Rules and Priorities
• Decisions made by Consensus
• Use of organized approaches to Problem-Solving
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How Do Quality Circles Work?
• All members of a Circle need to receive training
• Members need to be empowered
• Members need to have the support of Senior Management
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How Can They be Used in an Organization?
• Increase Productivity• Improve Quality• Boost Employee Morale • Increase in employee quality consciousness• Problem prevention becomes habitual• Promotion of employee motivation• Improvement in the human relations• More effective company communication
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How Can They be Used in an Organization?
• More active job involvement• Utilization of problem solving capabilities• Contribution to personnel development• Encouragement of teamwork• Improvement of work environment• Development of safety awareness• Control and improvement of quality• Productivity improvement• Increased job security
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Problems with Quality Circles
• Inadequate Training
• Unsure of Purpose
• Not truly Voluntary
• Lack of Management Interest
• Quality Circles are not really empowered to make decisions.
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MODULE 2
DATA COLLECTION
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CATEGORIES OF DATA
• Primary Data
• Secondary Data
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PRIMARY DATA
The data, which are collected from the units or individual respondents directly for the purpose of certain study or information.
Example:•If an experiment is conducted to know the effect of fertilizer doses on the yield OR the effect of a drug on the patients, the observation taken on each plot or patient constitute the primary data.
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SECONDARY DATAThe data, which had been collected by certain people or agency, and statistically treated.
Now the information contained in it is used again from records, processed and statistically analyzed to extract some information for other purpose.
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SECONDARY DATAExample:
Secondary data is obtained from year books, census report, survey reports, official reports or reported experimental findings.
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ANALYSIS OF DATA
One of the most important objectives is to process the observed data and transform it to a form most suitable for decision making.
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DATA PROCESSING
Before tabulation of primary data, it should be edited for:
• Completeness
• Consistency
• Accuracy
• Homogeneity
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ANALYSIS OF DATA
The measures of central tendency and dispersion are parts of data analysis along with the estimation and testing of hypothesis:
• Mean
• Median
• Mode• Standard deviation
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ANALYSIS OF DATA
The data: 4,5,5,4,8,4,3,7.
• Mean
• Median
• Mode• Standard deviation
• Range
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ANALYSIS OF DATA
The data: 4,5,5,4,8,4,3,7.
• Mean = 4+5+5+4+8+4+3+7
8
Mean = 40/8 = 5
MedianMedian = 3,4,4,4,5,5,7,8 = 3,4,4,4,5,5,7,8 ( Select Two centered Data)( Select Two centered Data)
MedianMedian = ( 4+5)/2 = 4.5 = ( 4+5)/2 = 4.5
Mode = 3,4,4,4,5,5,7,8Mode = 3,4,4,4,5,5,7,8 = 4 = 4 (Most Frequently Occurring Number)(Most Frequently Occurring Number)Plan CheckDo Act
ANALYSIS OF DATA
The data: 4,5,5,4,8,4,3,7.
• Standard deviation = 1.69 (X-Bar – X)2 =
( n – 1)
• Range = Max – Min
= 8 – 3 = 5
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Median =4.5Median =4.5
Mean = 5Mean = 5
Range = 5Range = 5
Mode = 4Mode = 4
STD STD Dev=1.69Dev=1.69
P – Value = 0.1377 Data is NormalP – Value = 0.1377 Data is Normal
This tool is given freeThis tool is given free
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MODULE 3
The Basic 7 Quality Tools
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The Basic 7 Quality Tools.
Ishikawa believed that 90% of all quality problems could be solved through the use of the 7 tools listed below:
• Frequency Diagrams ( Histograms )• Cause and Effect (Ishikawa) Diagrams• Check Sheets• Pareto diagrams• Flowcharts• Scatter Diagrams• Control Charts
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Where did the Basic Seven come from?
Kaoru Ishikawa
• Known for “Democratizing Statistics”
• The Basic Seven Tools made statistical analysis less complicated for the average person
• Good Visual Aids make statistical and quality control more comprehensible.
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Fishbone Diagrams
• No statistics involved
• Maps out a process/problem
• Makes improvement easier
• Looks like a “Fish Skeleton”Plan CheckDo Act
Possible CausesPossible CausesPROBLEMPROBLEM(EFFECT)(EFFECT)
Area AArea A Area BArea B
Area DArea DArea CArea C
11
22
3366
55
4411
22
3366
55
44
11
22
3366
55
44
11
22
3366
55
44
Fishbone DiagramsFishbone Diagrams
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• Step 1 - Identify the ProblemStep 1 - Identify the Problem• Step 2 - Draw “spine” and Step 2 - Draw “spine” and “bones”“bones”• Step 3 - Identify different Step 3 - Identify different areas where problems may arise areas where problems may arise fromfrom• Step 4 - Identify what these Step 4 - Identify what these specific causes could bespecific causes could be• Step 5 – Use the finished Step 5 – Use the finished diagram to brainstorm solutions diagram to brainstorm solutions to the main problems.to the main problems.
Fishbone DiagramsFishbone Diagrams
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Bad SolderJoints
Machines Manpower
MaterialsMethods
Solder Gun
Size
Heat sink
Power Source
Skill
Training
Physical limits
Terminals
Stripping
TechniqueManual Flux
Solder
Wire Gauge
Fishbone DiagramsFishbone Diagrams
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In the above example, I’ve added some causes and some common categories – know as the 4 “M’s” – Machines, Manpower, Methods and Materials.How do we arrive at the possible causes? The best (and most common) method is brainstorming. This generates a large number of ideas in a short period of time.Once the diagram is complete, then we can continue with the evaluation.We obviously can not tackle all the problems at once because there are too many and besides some will have such small effects that they will not be worth bothering about.
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Bad SolderJoints
Machines Manpower
MaterialsMethods
Solder Gun
Size
Heat sink
Power Source
Skill
Training
Physical limits
Terminals
Stripping
TechniqueManual Flux
Solder
Wire Gauge
Fishbone DiagramsFishbone Diagrams
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On this diagram, three of the causes have been highlighted.
These are thought to be the most important, and the ones to tackle. WHY?
There are a number of ways of choosing the front runners.
We could design a series of experiments to determine the biggest influence, OR
We could use existing data or experience, OR
We could make a judgement purely on opinion
Fishbone Fishbone DiagramsDiagrams
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CAUSE & EFFECT DIAGRAM - Example
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WORKSHOP & PRESENTATION
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WHAT IT IS? Histograms are effective Q.C. tools which are used in the analysis of data. They are used as a check on specific process parameters to determine where the greatest amount of variation occurs in the process, or to determine if process specifications are exceeded.
This statistical method does not prove that a process is in a state of control. Nonetheless, histograms alone have been used to solve many problems in quality control.
HISTOGRAM
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HISTOGRAM ANALYSIS
• How well is the histogram centered?
The centering of the data provides information on the process aim about some mean or nominal value.
• How wide is the histogram?
Looking at histogram width defines the variability of the process about the aim.
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HISTOGRAM ANALYSIS
•What is the shape of the histogram?
Remember that the data is expected to form a normal or bell-shaped curve. Any significant change or anomaly usually indicates that there is something going on in the process which is causing the quality problem.
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NORMAL
Depicted by a bell-shaped curve
• Most frequent measurement appears as center of distribution • Less frequent measurements taper gradually at both ends of distribution Indicates that a process is running normally (only common causes are present).
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BI-MODAL
• Distribution appears to have two peaks • May indicate that data from more than one process are mixed together
Materials may come from two separate vendors Samples may have come from two separate machines. Plan CheckDo Act
CLIFF-TYPE
• Appears to end sharply or abruptly at one end • Indicates possible sorting or inspection of non-conforming parts. Plan CheckDo Act
SAW-TOOTHED
• Also commonly referred to as a comb distribution, appears as an alternating jagged pattern• Often indicates a measuring problem
Improper gage readings Gage not sensitive enough for readings.
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SKEWED
Positively Skewed Negatively Skewed
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Excercise
• Construct an Histogram for the four distribution from the set data “Plot Data”.
• Can you determine the type of distribution from the Histogram?
• Can you determine the bimodal from the Histogram?
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Dist 1Dist 1Dist 2Dist 2
Dist 3Dist 3 Dist 4Dist 4
This tool is given freeThis tool is given free
Measurements of 50 items from process XYZ
147 179 185 125 210
131 137 141 142 166
198 142 205 150 141
190 161 157 165 155
165 155 169 158 150
170 125 177 108 193
178 181 155 186 145
157 135 148 171 124
168 141 151 162 150
145 177 154 137 160
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TALLY CHART
RANGE TALLY NUMBER
100-109 | 1
110-119 0
120-129 | | | 3
130-139 | | | | 4
140-149 | | | | | | | | | 9
150-159 | | | | | | | | | | | 11
160-169 | | | | | | | | 8
170-179 | | | | | | 6
180-189 | | | 3
190-199 | | | 3
200-209 | 1
210-219 | 1
TOTAL 50Plan CheckDo Act
A tally is a simple form of categorising the data so as to let it speak for itself. In the first column, we have the basic categories themselves: 100 – 109, 110 – 119, and so on. In the second column, there is the tally – the actual count of the number of items found in that category. In the third column is the actual number in the category, or the frequency. We now have the data in a form which “speaks” to us. The next obvious step is to display the data on a graph.
HISTOGRAM
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Data
Frequency
200180160140120100
12
10
8
6
4
2
0
Mean 158.4StDev 21.80N 50
Histogram of DataNormal
Data
Frequency
200180160140120100
12
10
8
6
4
2
0
125 185Mean 158.4StDev 21.80N 50
Histogram of DataNormal
If we add the tolerance limits to the graph, we can see that we are going to have a large proportion of rejects from the process. From this it is easy to see how vital the concept of the frequency diagram is to analysing process capabilities
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Compute the
-Mean
-Median
-Standard Deviation
-Range
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Check Sheets Counting and accumulating data
WHAT IS A CHECK SHEETS?
One of the most common form of data collection, the check sheet is a structured form containing a list of things you want to measure, inspect or record. Plan CheckDo Act
WHAT DOES CHECKLIST PREVENT
Forget to inspect
Late inspection
Ineffective inspection
Partial inspection
Not knowing who did the inspection
No record for inspection done
No action for inspection done
Check Sheets
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Process Name: MouldingProduct Name: Widgits
TOTAL3/8{F}
2/8{T}
1/8{W}
31/7{T}
30/7 {M}
Defective part
61811151413TOTAL
7| | || | ||Other
2||Cracks
9|| || | | ||Pinholes
14| | | || | || || | | |Grit
8|| | | || |Fibres
21| | | || | || | | | || | || | | |Mould Cracked
Line Name: Auto1Product Number: 123456
Check Sheets
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Check sheets are used to systematically record data from historical sources or from observations as they happen so that patterns and trends can be clearly detected and shown.Check sheets minimise clerical effort since the operator merely adds a mark to the tally on the prepared sheet rather than writing out a figure.
Check Sheets
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Product: Copper Pipe Date:14th April 2003
Manufacturing Stage: Final insp Inspector’s Name: Sam
Type of Defect: scratch, incomplete, misshapen Lot No: 24
Total No. inspected: 2530 Remarks: All inspected
Type Check Sub-Total
Scratches
Cracks
Incomplete
Misshapen
Others
//// //// //// //// //// //
//// //// //// //// ///
//// //// //// //// //// //// /
////
//// ///
22
19
25
4
7
Grand Total 77
Total Rejects //// //// //// //// //// //// ////
//// //// //// //// //// //// // 54
PARETO DIAGRAM
The 80/20 Principle :Achieving More With Less
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Pareto Discovery• In the late 19th century, an Italian economist by the
name of Vilfredo Pareto undertook a study on the distribution of wealth in Italy.
• Pareto discovered that about 80% of the wealth in Italy was distributed to only 20% of the Italian families.
• In society, 80% of the value of all crimes committed was caused by 20% of the criminals
• In life, most happiness enjoyed by a person occurred during 20% of his lifetime.
• At work, 80% of one’s valuable output occurred in 20% of his time
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The 80/20 Thinking & Analysis
• To engage in 80/20 thinking, we must constantly ask ourselves:
• “What is the 20% that is leading the 80%?”
• “ What are the vital few causes or inputs as opposed to the trivial many ? “
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The 80/20 Principle, as applied to Quality Management
• The pioneer of the 80/20 principle was Joseph Juran :
- the great Quality Management Practitioner - the man behind the global quality revolution
of the late 20th century
• This Romanian-born US Engineer Juran alternately called the “Pareto Principle” or the “80/20 Principle” the so-called “The Rule of the Vital Few and the Trivial Many” – virtually synonymous with the search for high quality products and services.
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Why The 80/20 Principle Is So Important ?
Whether you realize it or not, the 80/20 Principle applies to:
• Your life• Your social world• The place where you work• Your business For each individual and each business, it is
always possible to obtain much more that is of value and avoid what has negative value, with much less input of effort, expense or investment.
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80/20 As Applied To Daily Life
• Only do things we are best at doing and enjoy most• In every important aspect in life, work out where 20% of
effort will lead to 80% of return• Choose your career and employers with care, and if
possible, employ others rather than being employed yourself
• Make the most of the lucky “few streaks” in your life• Strive for excellence in few things, rather than good
performance in many• Calm down, work less and target a limited number of
goals
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80/20 Thinking Is Reflective
The objective of the 80/20 Thinking is to generate actions which will make sharp improvements in your life and that of others
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80/20 Thinking Is Reflective
To be strategic is to concentrate on what is important in the long run, on those few things that can give us a comparative advantage, on what is important to us than others, and to plan and execute the resulting plan with determination and steadfastness.
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80/20 Insights For Individuals• 80 % of achievements and happiness in life,
takes place in 20% of our time• Our lives are profoundly affected for good
and ill, by a few events and a few decisions in our life
• Everyone can achieve something significant. The key is not effort, but finding the right thing to achieve
• There are winners and losers – and always more of the latter. You can be a winner by choosing the right competition, the right team and the right methods to win
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80/20 As It Applies To Business
o That losses (manufactured goods that have to be rejected because of poor quality) do not arise from a large number of causes. Rather the causes are always mal-distributed in such a way that a small percentage of the quality characteristics always contributes a high percentage of the quality loss
o And if you remedy the critical 20% of your quality gaps, you will realize 80% of the benefits.
o The first 80% typically includes the first breakthrough in continuous improvementPlan CheckDo Act
Pareto Diagrams Focus on key problems
• Kadang-kadang sebagian besar masalah disebabkan oleh segelintir sebab. Sebagai contoh, 80% dari downtime disebabkan oleh 20% dari mesin; 80% Revenue berasal dari 20% pelanggan.
• Aturan 80/20 adalah satu cara untuk memprioritaskan usaha supaya tertumpu (fokus) pada apa yang lebih penting.
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Part Cum % Annual Cost Annual Cum Cum % Inv.# Of Total Usage Per Cost Ann. Cost Of Total Class
1 10% 5000 98.00$ 490,000$ 490,000$ 49% A2 20% 395000 0.79$ 312,050$ 802,050$ 80% A3 30% 10000 8.25$ 82,500$ 884,550$ 88% B4 40% 75000 0.87$ 65,250$ 949,800$ 95% B5 50% 5000 2.00$ 10,000$ 959,800$ 96% B6 60% 1000 9.75$ 9,750$ 969,550$ 97% C7 70% 125000 0.07$ 8,750$ 978,300$ 98% C8 80% 30000 0.26$ 7,800$ 986,100$ 99% C9 90% 250000 0.03$ 7,500$ 993,600$ 99% C
10 100% 600 10.70$ 6,420$ 1,000,020$ 100% C
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Pareto Diagrams Focus on key problems
Fault No.
A. DRY JOINT
B. MISSED COMPONENT
C. REVERSED COMPONENT
D. ARCING
E. OPEN CIRCUIT
F. OTHER
2
5
8
4
1
3
TOTAL 23
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Fault No.
C. REVERSED COMPONENT
B. MISSED COMPONENT
D. ARCING
F. OTHER
A. DRY JOINT
E. OPEN CIRCUIT
8
5
4
3
2
1
TOTAL 23
Pareto Diagrams Focus on key problems
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This tool is given freeThis tool is given freePlan CheckDo Act
88
REVERSEDREVERSEDCOMPONENTCOMPONENT
55
MISSED MISSED COMPONENTCOMPONENT
44
ARCINGARCING
33
OTHEROTHER22
DRY JOINTDRY JOINT 11OPEN CIRCUITOPEN CIRCUIT
BBCC DD FF AA EE
Pareto Diagrams Focus on key problems
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Fault No. COST TOTAL COST
C. REVERSED COMPONENT
B. MISSED COMPONENT
D. ARCING
F. OTHER
A. DRY JOINT
E. OPEN CIRCUIT
8
5
4
3
2
1
2
2
5
1
4
6
16
10
20
3
8
6
TOTAL 23 - 63
Pareto Diagrams Focus on key problems
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Fault No. COST TOTAL COST
D. ARCING
C. REVERSED COMPONENT
B. MISSED COMPONENT
A. DRY JOINT
E. OPEN CIRCUIT
F. OTHER
4
8
5
2
1
3
5
2
2
4
6
1
20
16
10
8
6
3
TOTAL 23 - 63
Pareto Diagrams Focus on key problems
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This tool is given freeThis tool is given free
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£20
ARCING
£16
REVERSEDCOMPONENT
£10
MISSED COMPONENT
£8
DRY JOINT
£6
OPEN CIRCUIT£3
OTHER
CD B A E F
Pareto Diagrams Focus on key problems
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Flowcharts Picturing the process
• Overview
• Detailed look at flowcharting
• Real world examples
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Flowcharts Picturing the process
Overview of Flowcharts
• What is a flowchart?
• How are they useful?
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Flowcharts Picturing the process
What is a flowchart?
• Process Flow Diagram
• A diagram illustrating the activities of a process
• One of Ishikawa’s seven basic tools of quality
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Flowcharts Picturing the process
Brief History
• No originator, or “father” of flowcharts
• Forms of flowcharts have always been used
• Give us insight into historical processesPlan CheckDo Act
Flowcharts - Picturing the processFlowchart Symbols
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Start/EndThe terminator symbol marks the starting or ending point of the system. It usually contains the word "Start" or "End."
Action or ProcessA box can represent a single step ("add two cups of of flour"), or and entire sub-process ("make bread") within a larger process.
Flowcharts Picturing the process
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DocumentA printed document or report.
DecisionA decision or branching point. Lines representing different decisions emerge from different points of the diamond.
Flowcharts Picturing the process
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Flowcharts Picturing the process
Input/OutputRepresents material or information entering or leaving the system, such as customer order (input) or a product (output).
ConnectorIndicates that the flow continues where a matching symbol (containing the same letter) has been placed.Plan CheckDo Act
Flowcharts Picturing the process
Flow LineLines indicate the sequence of steps and the direction of flow.
DelayIndicates a delay in the process.
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Flowcharts Picturing the process
MergeIndicates a step where two or more sub-lists or sub-processes become one.
SubroutineIndicates a sequence of actions that perform a specific task embedded within a larger process. This sequence of actions could be described in more detail on a separate flowchart.
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Flowcharts Picturing the process
Manual LoopIndicates a sequence of commands that will continue to repeat until stopped manually.
Data storageIndicates a step where data gets stored.
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Flowcharts Picturing the process
How are they useful?
• Create visual maps of a process• Help with planning a project• Quality improvement tool
– Identify processes that need improvement
– Identify unnecessary/ problem steps in a process
– Good communication toolPlan CheckDo Act
Common Rules of Flowcharts
• Indicate and label all elements of the project
• Sequence of events is clear
• No gaps or dead ends
• Must be logical to the user
• Use correct symbols
Flowcharts Picturing the process
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Real World Use of Flowcharts
• Production – Manufacturing– Used to identify critical path
• Accounting– Help visualize money flow
• Services– Restaurants– Real estate
Flowcharts Picturing the process
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Flowcharts Picturing the process
Real World (cont’d)
• Education– Curriculum flowcharts– Student flow through process
• Hospitals– Patient flow– Medical processes
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Summary :• Valuable and unique quality improvement tool• Simple and effective way of visualizing and
understanding a process• Entire organization has an effect on the
flowchart • Everyone involved can take part in improving
the process
Flowcharts Picturing the process
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Scatter Diagrams Measuring relationships between variables
WHAT IS IT?• Shows relationship between 2 characteristic values
HOW DOES IT RELATE?• Number of working years and the salary!
• The plating time and the plating thickness!
• Dimensions before and after assembly!
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Scatter Diagrams Measuring relationships between
variables
When Scatter Diagram are preparedcheck the following:•Is there any correlation?
• Are there any abnormally plotted points?
• Is there a need for stratification?
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Scatter Diagrams Measuring relationships between variables
Example Exercise :The rise in temperature in the motor coil of an electric shaver needs to be controlled so it does not exceed 500C.
The data shown in the next slide is the results of a survey carried out to find out the relationship between the coil temperature (X) and the surface temperature of the motor case (Y).
Collect more then 30 pairs of data to show relationship
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Scatter Diagrams No X Y No X Y No X Y No X Y
1 30.6 15.9 17 37.0 23.2 33 39.5 24.5 49 43.8 26.3
2 33.0 20.0 18 37.1 21.5 34 40.0 22.0 50 44.5 26.8
3 33.2 17.7 19 37.2 22.4 35 40.3 23.0
4 33.5 19.0 20 37.5 20.1 36 40.4 20.9
5 34.2 22.5 21 37.5 23.3 37 40.5 21.3
6 34.3 19.9 22 37.8 21.8 38 40.5 29.9
7 34.7 20.9 23 37.8 23.0 39 40.6 25.7
8 35.6 20.3 24 38.3 23.3 40 41.0 23.7
9 35.6 22.9 25 38.6 22.9 41 41.2 24.4
10 35.7 19.7 26 38.7 24.5 42 41.3 22.2
11 35.7 21.9 27 38.8 20.7 43 41.3 25.7
12 35.9 23.7 28 38.8 21.5 44 41.8 26.8
13 36.0 18.9 29 38.9 23.1 45 42.0 25.0
14 36.2 21.2 30 39.2 23.1 46 42.1 23.1
15 36.3 20.5 31 39.3 23.3 47 42.8 26.6
16 36.4 22.3 32 39.5 22.0 48 42.9 25.5
Scatter Diagrams Measuring relationships between variables
X-Bar = 38.308 and Y-Bar = 22.608 Gradient, m = 0.645
Y = mX + C , C = Y – mX
C = 22.608 – (0.645*38.308)
C = 22.61– 24.71
C = - 2.1
The Regression Equation is Y = 0.645X – 2.101
m = m = ∑xy – n(x-Bar)(y-Bar)∑xy – n(x-Bar)(y-Bar) ∑ ∑x² -n(x-Bar)²x² -n(x-Bar)²
r = r = ______n∑xy - ∑x∑y______ = .771 ______n∑xy - ∑x∑y______ = .771 √ √[n∑x² - (∑x)²][n∑y² - (∑y)²][n∑x² - (∑x)²][n∑y² - (∑y)²]
See Scatter See Scatter plot Data file.plot Data file.
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Scatter Diagrams Measuring relationships between variables
Regression
Parameter Est value St dev t studentProb(>|t|)
b0 -2.11 2.96 -0.720.48
b1 0.65 0.08 8.390.00
Residual St dev 1.64y = b0 + b1.x1
R2 0.59
R2(adj) 0.59
F 70.42
Prob(>F) 0.00
Y = -2.11 + 0.65X
R2 = 0.59
P-Value = 0
There is a CorrelationPlan CheckDo Act
Scatter Diagrams Measuring relationships between variables
X
Y
464442403836343230
30.0
27.5
25.0
22.5
20.0
17.5
15.0
S 1.64175R-Sq 59.5%R-Sq(adj) 58.6%
Fitted Line PlotY = - 2.114 + 0.6453 X
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Scatter Diagrams Measuring relationships between variables
There is a positive correlation between X and Y.
But how good is the correlation???
The value of r = 0.7711
The Regression Model is 59.59 % accurate.Plan CheckDo Act
Scatter Diagrams Measuring relationships between variables
3.5
4
4.5
5
150 400 650
An increasAn increase in y may dependupon an increase in x.
PositivPositive Correlation
3.5
4
4.5
5
150 400 650
Negative Correlation
An decrease in y may dependupon an increase in x.
3.5
4
4.5
5
150 400 650
No Correlation
There is no demonstrated connection between x and y.
3.5
4
4.5
5
150 400 650
Positive Correlation?
If X is increased, y may also increase.
3.5
4
4.5
5
150 400 650
Negative Correlation?
If X is increased, y maydecrease.
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Control Charts Identifying Sources Of Variations
•Control charts are used to monitor, control and improve process performance by focussing on its variation and its cause.•The control chart can be thought of as a target. The average line is the bull's-eye and the control limits are the extremes of the target. •Control charts are used by taking periodic measurements or observations of products or processes. These results are compared with calculated control limits, and if the limits are exceeded action is taken (and recorded) to bring the process “back into control”.
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About This Module…
Six Sigma, A Quest for Process PerfectionMeet Goals and Attack Variation
Control charts portray process performance andseparate causes of variation:
• Random• Assignable
Control Chart Systems are:• A proven technique for improving productivity• Effective in defect prevention• Prevent unnecessary process adjustments• Provide diagnostic information• Provide information about process capability
\DataFile\Attribut mtw\DataFile\Variable.mtw
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1. Control charts are a powerful tool to hold the gains.
2. How control charts discriminate between common cause and assignable cause variation.
3. Why control charts must be designed to fit the data type and the control purpose.
What We Will Learn.
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Uses of Control Charts1) Attain a state of statistical control:
• All subgroup averages and ranges within control limits - no assignable causes of variation present
2) Monitor a process
3) Determine process capability
What happens after an out-of-control situation occurs at the core of a successful SPC program?
Juran’s Quality Control Handbook, 4th edition, page 24.7
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General Conceptsw = some characteristic of interest
= mean of each sample
Sw = standard deviation of w
Upper Control Limit
Centerline =
Lower Control Limit
Therefore 99.73% of points will be within the control limits unless there is an assignable cause
WX
3 wUCL X S
3 wLCL X S X
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Components of a Control Chart
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Sample Number
Sam
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Co
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U Chart for Defects
U=1.930
UCL=3.794
LCL=0.06613
Upper Control Limit
Lower Control Limit
Center Line
How many points do we need to set the initial
control limits?
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Control Chart Selection TreeType of data
Count or Classification
Discrete
Fixed or variable
opportunity?
Count
C Chart
Fixed
U Chart
Variable Fixed or variable
opportunity?
Attribute
NP Chart
Fixed
P Chart
Variable
Subgroup >1?
Variable
IMR Chart
No
X Bar and Ror
X Bar and S
Yes
Supplement with EWMA if
CTQ is sensitive to
small process shifts
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DefinitionsNon-conformance (defect)
A single instance of a failure to meet some requirement
Non-conforming Unit (defective)A single item containing one or more non-conformance
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Types of Attribute Control Charts
*Juran’s Quality Control Handbook, Fourth Edition
c chart: Number of non-conformances in a sample
Use & effectiveness: • All subgroups are the same size • Effective when the number of non-conformances possible
on a unit is large, but the percentage of any single non-conformance is small
Example:• Surface irregularities, flaws, pinholes on continuous or
extensive products such as yarn, wire, paper, textiles or other sheeted materials. The chance of a non-conformance occurring at any one spot is small, but the overall opportunity for non-conformance may be great.*
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Types of Attribute Control Chartsu chart: Defects Per Unit (DPU)
Use & effectiveness: Use when several independent (required) non-conformities may occur in one unit, document, etc.
• Samples not required to be the same sizeExample:
Complex assembly or document; electronic assembly, purchase order, bill of material, etc.
np chart: Number Non-conforming Use & effectiveness:
Use when direct count of the number of non-conforming in a subgroup is desired.
• All subgroup sizes must be the same (Juran 24.22).
p chart: Fraction or Proportion Non-conformingUse & effectiveness:
Use to describe a single quality characteristic or two or more characteristics considered collectively.
• Samples not required to be the same size
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c (Count of Defects) Chart Formulae
Center Line c
c3cLCL
c3cUCL
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LCL uu
n 3
Center Line u
UCL uu
n 3
u (Defects per Unit) Chart Formulae
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np Number Nonconforming Chart Formulae
UCL = n p + 3 n p (1 - p)
CL = n p
Plot the number of nonconforming not the percentage of nonconforming. Variable sample sizes are OK.
LCL = n p - 3 n p (1 - p)
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LCL pp p
n
3
1( )
UCL pp p
n
3
1( )
Center line = p
To estimate p ( ) measure 20 - 25 samples calculate the average proportion defective. Use this as a trial p until more data is available. Variable sample sizes are OK.
p
P (Proportion Defective) Chart Formulae
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C Chart ExampleFile= /Datafiles/Attribut.mtwStat>Control Charts>Attribute Charts>C Chart
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Sample
Sam
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Cou
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_C=20.7
UCL=34.35
LCL=7.05
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C Chart of C Chart Data
Worksheet: Attribut.MTW
The C Chart
Data points 6 and 15 were the result of errors. Replace them with asterisks to indicate missing data then replot.Plan CheckDo Act
The New Chart
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Sample
Sam
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Cou
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_C=19.58
UCL=32.86
LCL=6.31
C Chart of C Chart Data
Worksheet: Attribut.MTW
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The U Chart
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The U Chart
Note: the control limits changed as the sample size changed.
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Sample
Sam
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Count Per
Unit
_U=0.763
UCL=1.439
LCL=0.086
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U Chart of Defects found
Worksheet: Attribut.MTWTests performed with unequal sample sizes
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The NP Chart
NP charts should be used only when the subgroup size is uniform.
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The NP Chart
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Sam
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Count
__NP=19.17
UCL=30.98
LCL=7.36
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NP Chart of Batch 1
Worksheet: Attribut.MTWNote: The session window describes the special causes identified on the chart.
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The P Chart
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The P Chart
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Sample
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_P=0.0955
UCL=0.1885
LCL=0.0026
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P Chart of Defectives
Worksheet: Attribut.MTWTests performed with unequal sample sizes
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Control Charts for Variable Data
Much more sensitive than charts for attribute data charts
• X bar and R• X bar and s
Critical decisionsSample size - the width of the control limits is inversely
proportional to the sample size for any multiple of s
Subgroups - chances of differences due to assignable causes within subgroups should be minimized (same operator, shift, head, material etc.)
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X and R Control Chart Formulae & Constants
2
4
3
X Control Limits =X ± A R
R Upper Control Limit = D R
R Lower Control Limit = D R
SampleSize
A2 D3 D4 d2
2 1.880 - 3.267 1.1283 1.023 - 2.574 1.6934 .729 - 2.282 2.0595 .577 - 2.114 2.3266 .483 - 2.004 2.5347 .419 .076 1.924 2.7048 .373 .136 1.864 2.8479 .337 .184 1.816 2.970
10 .308 .223 1.777 3.078
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X and s Chart Formulae & Constants 1
4
3
X Control Limits = X ± A s
s Upper Control Limit = B s
s Lower Control Limit = B s
N A1 B3 B4
2 2.121 0 3.267
3 1.732 0 2.568
4 1.500 0 2.089
5 1.342 0 2.089
6 1.225 .030 1.970
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Creating an X-bar and R Chart
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An X-Bar and R Chart
Sample
Sam
ple
Mean
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40
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38
__X=40.000
UCL=41.294
LCL=38.706
Sample
Sam
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Range
45403530252015105
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3.0
1.5
0.0
_R=2.243
UCL=4.743
LCL=0
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Xbar-R Chart of measure1, ..., measure5
Worksheet: Variable.MTW
The numbers show violations of the assumption of control. The nature of the violation is given in the session window.
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StatGuide Interprets the Tests
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Rules of Standard Deviation“where the data is?”
UCL
LCL
99-99.9%
90-98%
60-75%1 Sigma
1 Sigma
2 Sigma
2 Sigma
3 Sigma
3 Sigma
A
A
B
B
C
C
Time
Me
as
ure
d V
aria
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% of Data
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Test 1
Test 2 One or more points beyond the 3 limit
2 out of 3 pts > 2 std Dev from the center line (same side)
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Test 4
Test 3
4 out of 5 pts > 1 Std Dev from the center line (same side)
8 pts in a row > 1 Std Dev from the center line (either side)
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One or more points beyond the 3 limit
8 pts in a row > 1 Std Dev from the center line (either side)
Test for special causes (pattern)( For Range Chart )
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Cycle Pattern
* The cycle pattern repeats continuously.* This is an indication of special causes
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* Trend is identified with - Points moving in one direction ( up or down )- Points does not change direction continuously.
Trends are easily noticeable
Trends occurs when more than six points continuously moves upwards or downwards.
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Mixture
Points falling near the UCL or LCL crossing the center line.
Mixture pattern contains 2 different types of patterns on the same chart….one falling on the UCL and the other on the LCL.
Mixture pattern occurs when 8 points continuously fall on both side of the centerline without any point on Zone C.
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Systematic
Continuously points are alternating …up, down, up, down without changes.
Points not necessarily alternating only, as long it is moving up anddown, it is termed systematic.
Systematic pattern is occuring as long as 14 points continuously is alternating up and down.
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Hugging at centerline
All the points distribution comparing with the width between UCLand LCL : Points are distributed at the centerline. No points at UCL and LCL
Hugging shows:- There is special causes existing or the process has changed.- Sampling method is not good- Two population existing (Bimodal)
Hugging happens if more than 15 points are distributed in Zone C.
Shewhart’s concept of variation “Every process has variation; some process exhibits
controlled variation , while others exhibits uncontrolled variation ” - (Walter Shewhart)
• Controlled variation exhibits patterned variation characteristic which is stable and consistent against time.
• Uncontrolled variation exhibits inconsistent variationwhich changes against time. This type of variation is not consistent and not stable.
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Causes of Variation
Controlled Variation = Common CausesControlled Variation = Common Causes
We will call any unknown random cause of variation a chance cause or a common cause, the terms are synonymous and will be used as such. If the influence of any particular chance cause is very small, and if the number of chance causes of variation are very large and relatively constant, we have a situation where the variation is predictable within limits. You can see from the definition above, that a system such as this qualifies as a controlled system. Where Dr. Shewhart used the term chance cause, Dr. W. Edwards Deming coined the term common cause to describe the same phenomenon.
Uncontrolled Variation = Special CausesUncontrolled Variation = Special Causes
At times, the variation is caused by a source of variation that is not part of the constant system. These sources of variation were called assignable causes by Shewhart, special causes of variation by Dr. Deming. Experience indicates that special causes of variation can usually be found without undue difficulty, leading to a process that is less variable.
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Common causes Vs Special CausesSpecial Causes
Common causes
BreakthroughImprovement
To achieve our goal, which will we concentrate, common causes or special causes?
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Intuitive SPC -Case Study 1~The factory scrap level is at a year low of 2%
~Manager presents an award to the plant
~Ceremony in the cafeteria:Pizza and refreshment for all!
~Everyone should be proud of what you have accomplished
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Manager wantsto take backthe award
Manager wantsto take backthe award
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Intuitive SPC -Case Study 1~Three consecutive months of scrap increases
~Manager wishes he could take back the award.
~Instead of holding the gains, scrap went right back up
~Manager decides:"This group just needs tough management
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Scrap is highest this year. Action needed!!!
Scrap is highest this year. Action needed!!!
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Intuitive SPC -Case Study 1~ Scrap rises to a value of 2.6%
~ Manager decides to take action.
~ A "special meeting" is called to solve this problem once and for all.
~ After a sound lecture on the importance of scrap, the manager leaves. Employees aren't sure what to do.
~ Besides, they have other metrics which have more importance. So they do nothing.
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Year 1 Year 2
Manager Conclude: Tough management style gets results
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Intuitive SPC -Case Study 1~Manager has seen reduced scrap levels since the end
of last year. "Things are looking - up!"
(Although nothing had been done to change the system)
~His takeaway: "A tough management style gets results"
In this excercise, what’s your opinion withregards to the Manager’s action?
Is the Manager’s action valid?
Is the Manager’s action fruitful?
Kalau dilihat mengunakan control chart,bagaimana rupanya?
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Intuitive SPC -Case Study 1
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Year 1 Year 2
Control Chart shows the VOP
LCL
UCL
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Manager: "Hey, I made my decision based on data - How can I go wrong ?"
Black Belt: "Your decisions were made from observing high and low points as signals. When in reality, it was all noise.
Look at the data, there was no significant change in the
process."
Pokerchip Excercise
(1) Take sample from process Pokerchip once an hour, total sample is 5 each time. Obtain data from Normal distribution with mean = 100 and stdev = 10.
(2) Continue collecting sample until 15 samples are obtained.
(3) Enter data into XBar-R Chart dan estimate: - Mean Sample Xbar-Bar - Range Sample Rbar - Stdev Sample X bar
(4) Save data into file Pokerchip.excel.
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This Tool Is Given FreeThis Tool Is Given Free
This Tool Is Given FreeThis Tool Is Given Free
This Tool Is Given FreeThis Tool Is Given Free
n 5 x-bar-bar 98.98 R-bar 22.23 s-bar 8.976
UCL 111.8 UCL 47.02 UCL 18.75
LCL 86.16 LCL 0 LCL 0
Pokerchip Excercise
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Excercise:
• Open file ‘Tensile_Strength’.
• Plot Xbar / R chart for Strength.
• An Engineer who has 10 years experience inthe process says he face no problem with the process.
Do you belief what he is saying?Analyze the control chart that has been plotted.
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252321191715131197531
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Sample
Sam
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Mean
__X=55.093UCL=55.803
LCL=54.382
252321191715131197531
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Sample
Sam
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Range
_R=1.232
UCL=2.605
LCL=0
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Xbar-R Chart of Strength
Tensile Strength X-Bar R Chart
Does the process has problems?Is the process in-control?Plan CheckDo Act
Control Chart for Batch process• Range chart shows variation within batch.
• However, X bar R chart is not suitable. X bar chart only uses variation within batch for determining control limit. This assumption when variation between batch can be ignored (negligible).
•Generally, variation between batach is greater than variation within batch.
• For batch process, the type of control chart is IMR-R chart; where every mean sample is expected an individual value.
Batch 1 Batch 2 Batch 3
X-Bar, R X-Bar, R X-Bar, RPlan CheckDo Act
I-MR-R ChartsI-Chart
CL = XUCL = X + 2.66 MRLCL = X – 2.66 MR
MR ChartCL = MRUCL = D4 MRLCL = D3 MR
Range ChartCL = RUCL = D4 RLCL = D3 R
(D4 dan D3 when n=2,because MR is range between2 continuous measurement)
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I-MR-R Chart Output
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Subg
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Mea
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_X=55.09
UCL=61.61
LCL=48.57
252321191715131197531
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MR
of
Subg
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Mea
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__MR=2.452
UCL=8.010
LCL=0
252321191715131197531
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Sample
Sam
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Ran
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_R=1.232
UCL=2.605
LCL=02
1
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I-MR-R/ S (Between/ Within) Chart of Strength
Batch mean
Batch-to-Batchvariation
Variation withinBatch
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Comparison between Xbar chart dan I-MRchart for mean sample
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Sample
Sam
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Mean
__X=55.093
UCL=56.361
LCL=53.825
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Sample
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Range
_R=2.198
UCL=4.647
LCL=0
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Xbar-R Chart of Strength
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Subg
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Mea
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_X=55.09
UCL=61.61
LCL=48.57
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MR o
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ean
__MR=2.452
UCL=8.010
LCL=0
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Sample
Sam
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Ran
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_R=1.232
UCL=2.605
LCL=02
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I-MR-R/ S (Between/ Within) Chart of Strength
Control limit only depictsvariation within batch.Subgroup Mean
Control limitdepictsvariation between and within batch
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CONTROL CHART FOR INDIVIDUAL DATA.
• Sometimes, we are forced to use one measurement only (compared with taking one sample containing more than one measurement). (Jumlah sample n = 1)
This happens when,
- measurement is expensiveExample : Test destroying the product (destructive test)
- Measurement obtained from standard sources.Example : pH measurement for chemical mixture
Based on total Sample n = 1Based on total Sample n = 1
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Sample X MR 1 4 ... 2 4 ... 0 3 3.3 ... 0.7 4 4.7 ... 1.4 5 5.3 ... 0.6
I – MR Control Charts
I CHART
Centre Line = X
Upper Control Limit = X + 2.66 MR
Lower Control Limit = X - 2.66 MR
MR CHART
Centre Line = MR
Upper Control Limit = 3.27 MR
Lower Control Limit = NonePlan CheckDo Act
X Chart
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1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73
Batch Number
X V
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Pokerchip
UCL X
LCL X
Data Mean
Print Chart Return To Data Entry Screen
This Tool is Given FreeThis Tool is Given Free
Moving Range Control Chart
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Batch Number
MR
Val
ue Moving Range
UCL MR
LCL MR
MR Mean
Print Chart Return To Data Entry Screen
This Tool is Given FreeThis Tool is Given Free
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