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7 MOST IMPORTANT TOOLS
FOR CONTINUAL
IMPROVEMENT
7 QC TOOLS
Confederation of Indian Industry
7 MOST IMPORTANT TOOLS
FOR CONTINUAL
IMPROVEMENT
7 QC TOOLS
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Systematic Problem Solvingand Deming Cycle
ACT PLAN
CHECK DO
• Plan :Setup the Objectives and Means• Do :Put the Plan into Practice• Check :Observe the Results and the Process• Act :Standardize if Results are Satisfactory
otherwise Re-plan and Follow the Cycle again
ACT PLAN
CHECK DO
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Improvementactivities
DO improvement
PLAN improvement
CHECK ImprovementresultsD C
P A
Standardization
ACT to standardize orreplan
Focus onvital few
Managementstrategy
Initiateimprovement
The PDCA / SDCA Improvement Cycle
Daily work
ACT to improve thestandard or its use
CHECK the workagainst the standard
KNOW the STANDARD
A S
C DDO the workaccording to thestandard
Focus onvital few
Initiateimprovement
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Basic Steps of Problem Solving
PLANDEFINITION
OBSERVATION
ANALYSIS
DO
CHECK
ACT
ACTION
CHECK
STANDARDISATION
CONCLUSION
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Steps of Problem Solving1. Definition – Identifying and defining the problem2. Observation – Investigating the features of the problem3. Analysis – Finding the root causes4. Actions – Establishing and implementing remedies
(countermeasures)5. Check – Ensuring the effectiveness of remedies6. Standardization – Holding on the gains7. Conclusion – Reviewing the problem solving process and
future plans
1. Definition – Identifying and defining the problem2. Observation – Investigating the features of the problem3. Analysis – Finding the root causes4. Actions – Establishing and implementing remedies
(countermeasures)5. Check – Ensuring the effectiveness of remedies6. Standardization – Holding on the gains7. Conclusion – Reviewing the problem solving process and
future plans
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Problem Solving StepsRecognizeProblem
Form qualityimprovement
teams
EvaluateSolution
Ensureperformance
DefineProblem
Continuousimprovement
ACT
Confederation of Indian Industry
EvaluateSolution
AnalyzeProblem
IdentifyPossibleSolutions
DeterminePossibleCauses
DefineProblem
ImplementSolution
PLAN
DO
CHECK
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Problem Solving Process
Follow Up
SymptomSymptomRecognitionRecognition
FactFinding
ProblemIdentification
Confederation of Indian Industry
Follow UpIdea
Generation
ProblemIdentification
SolutionDevelopment
PlanImplementation
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Benefits of Systematic Problem Solving Process
– It helps avoid jumping to conclusion
– Helps avoid decisions based on opinions andfeeling
– Helps the group in focusing their attention
– It provides a logic for remedies
– Sets a platform to involve all concerned
– Makes implementation simple
– It helps avoid jumping to conclusion
– Helps avoid decisions based on opinions andfeeling
– Helps the group in focusing their attention
– It provides a logic for remedies
– Sets a platform to involve all concerned
– Makes implementation simple
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Summary
– QC story and the Basic Seven StepProblem Solving Process.
– Concept of PDCA and its adaptation toproblem solving in specific work situations.
– QC story and the Basic Seven StepProblem Solving Process.
– Concept of PDCA and its adaptation toproblem solving in specific work situations.
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Technical Analysis and Statistical Analysis• If you see female Japanese assembly line workers without any technical
background whatsoever making suggestions even engineers haven’t been able to
think of, you will ask what makes it possible for those women to acquire their
technical knowledge. The answer is statistical methods.
• We have two methods of analyzing and eliminating trouble in the manufacturing
shop. One is by technological analysis; the other is by statistical analysis. QC
uses statistical methods to analyze and improve the quality of products.
• If you see female Japanese assembly line workers without any technical
background whatsoever making suggestions even engineers haven’t been able to
think of, you will ask what makes it possible for those women to acquire their
technical knowledge. The answer is statistical methods.
• We have two methods of analyzing and eliminating trouble in the manufacturing
shop. One is by technological analysis; the other is by statistical analysis. QC
uses statistical methods to analyze and improve the quality of products.
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Technical Analysis and Statistical AnalysisProblem:
In a color TV factory, a female employee of the Quality Assurance Section found that the
failure rate of TV sets varies though they install same type of TV tuner in all the
models.
Analysis:
She thought that there must be some reason for this difference in failure rate of TV sets.
Therefore, she drew diagrams which showed the relation between the failure rate of
TV sets and the length of the shaft, the temperature of the set, the diameter of the
tuner knob, size of the cabinet and so on.
Conclusion:
At last, she discovered a correlation between the failure rate and the distance from
tuner to speaker; In other words, the failure rate of the turner is quite low when the tuner
is attached far from the speaker. On the other hand, when the tuner is attached near the
speaker, the set doesn’t work well.
Problem:
In a color TV factory, a female employee of the Quality Assurance Section found that the
failure rate of TV sets varies though they install same type of TV tuner in all the
models.
Analysis:
She thought that there must be some reason for this difference in failure rate of TV sets.
Therefore, she drew diagrams which showed the relation between the failure rate of
TV sets and the length of the shaft, the temperature of the set, the diameter of the
tuner knob, size of the cabinet and so on.
Conclusion:
At last, she discovered a correlation between the failure rate and the distance from
tuner to speaker; In other words, the failure rate of the turner is quite low when the tuner
is attached far from the speaker. On the other hand, when the tuner is attached near the
speaker, the set doesn’t work well.
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Technical Analysis and Statistical Analysis (Contd.)
• Such a conclusion would be hard to draw through technical analysis alone. But byaccumulating market data we can discover such a phenomenon. We call this the law oflarge numbers.
• Therefore, you may understand that we have two ways to find out the cause ofdefectives, one is by the use of analysis based on technology and the other isthrough statistics.
• One of QC’s specialties is the use of statistical methods to eliminate trouble in the shop.• In order to find causes for a defect, you don’t need sophisticated technical expertise.
What you need to do is analyze data. And quality control circles have learned to usestatistical tools; this is what makes the circles so successful. Statistical analysis can beused to solve problems not only in manufacturing but also in sales, accounting, personnelmanagement and service.
• Spurred on by this method, QC circles are in demand among various fields includingmanufacturing, construction, financing, restaurants and department stores. The samething may produce varying degrees of results. Companies introducing the method seemto get better results in their work.
• – Source : Hajime Karatsu
• Such a conclusion would be hard to draw through technical analysis alone. But byaccumulating market data we can discover such a phenomenon. We call this the law oflarge numbers.
• Therefore, you may understand that we have two ways to find out the cause ofdefectives, one is by the use of analysis based on technology and the other isthrough statistics.
• One of QC’s specialties is the use of statistical methods to eliminate trouble in the shop.• In order to find causes for a defect, you don’t need sophisticated technical expertise.
What you need to do is analyze data. And quality control circles have learned to usestatistical tools; this is what makes the circles so successful. Statistical analysis can beused to solve problems not only in manufacturing but also in sales, accounting, personnelmanagement and service.
• Spurred on by this method, QC circles are in demand among various fields includingmanufacturing, construction, financing, restaurants and department stores. The samething may produce varying degrees of results. Companies introducing the method seemto get better results in their work.
• – Source : Hajime Karatsu
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Quality Improvement: Problem Solving
“Problem solving, the isolation and analysisof a problem and the development of apermanent solution, is an integral part of thequality-improvement process”.– Not hit or miss, but objective and systematic– Not directed at symptoms, but rather at root
causes
Confederation of Indian Industry
“Problem solving, the isolation and analysisof a problem and the development of apermanent solution, is an integral part of thequality-improvement process”.– Not hit or miss, but objective and systematic– Not directed at symptoms, but rather at root
causes
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Why do we need the 7 QC tools?
• Developed By Dr. KAORU ISHIKAWA.
• Total Quality Culture is data driven: data are impersonal; opinions
are not.
• Experience is gained quickest by collecting and analyzing data.
• The 7 QC tools provide common methods of analysis to help
problem solving teams operate effectively.
• It helps in taking decisions faster and objectively as factual
approach to decision making.
Confederation of Indian Industry
• Developed By Dr. KAORU ISHIKAWA.
• Total Quality Culture is data driven: data are impersonal; opinions
are not.
• Experience is gained quickest by collecting and analyzing data.
• The 7 QC tools provide common methods of analysis to help
problem solving teams operate effectively.
• It helps in taking decisions faster and objectively as factual
approach to decision making.
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Why Statistics• It is more economical to assess a sample of
product and use the result to predict the propertiesof the whole lot.
• It leads to predictions with a high degree ofprecision.
Confederation of Indian Industry
STUDY
• It is more economical to assess a sample ofproduct and use the result to predict the propertiesof the whole lot.
• It leads to predictions with a high degree ofprecision.
Base Population Sample Data
InformationJudgment
Taking actions
Population-Sample Model
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STATISTICAL QUALITY CONTROL (SQC)
• When a quality control system uses statisticaltechniques for inspection , testing and analysisto control quality or to conclude whether thequality of product is satisfying the customerneeds or to solve quality problems.
• SQC is systematic as compared to guess-workand avoids personal bias and poor judgments.
Confederation of Indian Industry
• When a quality control system uses statisticaltechniques for inspection , testing and analysisto control quality or to conclude whether thequality of product is satisfying the customerneeds or to solve quality problems.
• SQC is systematic as compared to guess-workand avoids personal bias and poor judgments.
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Benefits of Statistical Quality Control(SQC)
• Efficiency: Rapid and efficient inspection at aminimum cost.
• Reduction of scrap: Tells the causes ofexcessive variation in manufacturing and tellsabout potential non-conformance.
• Adherence to Specification: Specifications canbe accurately predicted and control.
• Increases output: By reduction of wastages,effective utilization of Resources.
• Awareness: Creating awareness in organization.
Confederation of Indian Industry
• Efficiency: Rapid and efficient inspection at aminimum cost.
• Reduction of scrap: Tells the causes ofexcessive variation in manufacturing and tellsabout potential non-conformance.
• Adherence to Specification: Specifications canbe accurately predicted and control.
• Increases output: By reduction of wastages,effective utilization of Resources.
• Awareness: Creating awareness in organization.
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Types of data:Statistical data can be characterized as
VARIABLE DATA and ATTRIBUTE DATA.
1.1 Variable / Continuous Data:Data which can be measurable and can assume anyvalue over some interval.Examples:- Dimension of a part measured- Temperature in degree centigrade.- Weight in Kg.- Time
Confederation of Indian Industry
Statistical data can be characterized as
VARIABLE DATA and ATTRIBUTE DATA.
1.1 Variable / Continuous Data:Data which can be measurable and can assume anyvalue over some interval.Examples:- Dimension of a part measured- Temperature in degree centigrade.- Weight in Kg.- Time
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1.2 Attribute / Discrete Data:Data which can be measurable and can assumeonly certain distinct values (integer values).
Examples:- Defect or not.- Days of the Week / Months of the year.- Performance ranking.- The no. of defective pieces found in a sample.- Cracks in sheets by spots welds etc.
Confederation of Indian Industry
1.2 Attribute / Discrete Data:Data which can be measurable and can assumeonly certain distinct values (integer values).
Examples:- Defect or not.- Days of the Week / Months of the year.- Performance ranking.- The no. of defective pieces found in a sample.- Cracks in sheets by spots welds etc.
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BASIC STATISTICAL CONCEPTSVARIATION
Concept of Variation states that no two items will beperfectly identical even if extreme care is taken tomake them identical in some respect.
Variation is fact of Nature and manufacturingprocesses are no exception to this.
Confederation of Indian Industry
VARIATION
Concept of Variation states that no two items will beperfectly identical even if extreme care is taken tomake them identical in some respect.
Variation is fact of Nature and manufacturingprocesses are no exception to this.
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BASIC STATISTICAL CONCEPTS
Measures of Location / Central Tendency:1. Mean = The sum of the values divided by the
number of values.2. Median = The middle value of a data set when
the data is ordered from smallest to largest3. Mode = The value that occurs most frequently
Mean- Mode = 3(Mean- Median)
Measures of Location / Central Tendency:1. Mean = The sum of the values divided by the
number of values.2. Median = The middle value of a data set when
the data is ordered from smallest to largest3. Mode = The value that occurs most frequently
Mean- Mode = 3(Mean- Median)
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BASIC STATISTICAL CONCEPTS
4. Measures of Spread / Dispersion:The extent to which the data is scattered aboutthe zone of central tendency is known asDispersion or Variation.
Measures of Dispersion or Variability:4.1 Range , R4.2 Variance, V4.3 Standard Deviation,σ or S
4. Measures of Spread / Dispersion:The extent to which the data is scattered aboutthe zone of central tendency is known asDispersion or Variation.
Measures of Dispersion or Variability:4.1 Range , R4.2 Variance, V4.3 Standard Deviation,σ or S
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BASIC STATISTICAL CONCEPTSBASIC STATISTICAL CONCEPTS
4.1 Range, R• Range is the simplest of dispersion in a sample. Itis used in the control chart.
• It is the difference between the largest observedvalue and the smallest observed value.
Range, R= XHigh- XLow
4.1 Range, R• Range is the simplest of dispersion in a sample. Itis used in the control chart.
• It is the difference between the largest observedvalue and the smallest observed value.
Range, R= XHigh- XLow
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BASIC STATISTICAL CONCEPTS
Variability
• Deviation = distance between observations andthe mean (or average)
Observations10
9887
averages 8.4
Deviations10 - 8.4 = 1.69 – 8.4 = 0.6
8 – 8.4 = -0.48 – 8.4 = -0.47 – 8.4 = -1.4
0.0
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BASIC STATISTICAL CONCEPTS4.2 Variance, V• Average distance between observations andthe mean squared• Square of the standard deviation.
Observations Deviations Squared DeviationsObservations
10
9
8
8
7
averages 8.4
Deviations
10 - 8.4 = 1.6
9 – 8.4 = 0.6
8 – 8.4 = -0.4
8 – 8.4 = -0.4
7 – 8.4 = -1.4
0.0
Squared Deviations
2.56
0.36
0.16
0.16
1.96
1.0 Variance
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BASIC STATISTICAL CONCEPTS
4.3 Standard deviation, σ or SSquare root of variance.
Example
Variance Standard Deviation
1.0 1.0
0.24 0.4898979
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Symbols and Formulae
Sample Size
Mean
Range
N = The total number of values
X = XN
R = Max - Min
Confederation of Indian Industry
Range
Variance
Standard Deviation
R = Max - Min
V = (X – X)2
N - 1
S = V
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Seven Quality Control Tools
Check-sheet
Pareto
Histogram
Control Chart
Cause and Effect diagram
Scatter Plot
Stratification
Confederation of Indian Industry
Check-sheet
Pareto
Histogram
Control Chart
Cause and Effect diagram
Scatter Plot
Stratification
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The function of a check sheet is to present
information in an efficient, graphical format.
For problem solving, data is to be captured.
Check list is a tool to capture the parameter.
Check-sheet is a tool to capture data as per
check list.
1. CHECKSHEET
Confederation of Indian Industry
The function of a check sheet is to present
information in an efficient, graphical format.
For problem solving, data is to be captured.
Check list is a tool to capture the parameter.
Check-sheet is a tool to capture data as per
check list.
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CHECKSHEET
Shift wiseShift wiseD
efec
t Typ
eD
efec
t Typ
e
Type
Type
--11Ty
peTy
pe--22
ShiftShift--AA ShiftShift--BB ShiftShift--CC ShiftShift--GG
Confederation of Indian Industry
Def
ect T
ype
Def
ect T
ype
Type
Type
--22Ty
peTy
pe--33
Type
Type
--44
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CHECKSHEET
Confederation of Indian Industry
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CHECKSHEET
Confederation of Indian Industry
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18
12
33
TotalSat
2 / 6
III
I
Fri
2 / 5
III
II
IIII
Thu
2 / 4
II
II
Wed
2 / 3
I
IIII
Tue.
2 / 2
II
IIII
Mon.
2 / 1
Dirt in distance sensor
Exterior scratches
Loose screws
To 6 Feb. 1992No. 3 assembly lineProcess name
Miki Tanaka
Form 1 Feb. 1992
Recordedby:
Date
--------
LN1238LN1239LN1240
Measuring instrument
Lot number
100% visual operation
CS20-5D
Measuring method
Date / dayDefect
Product name
18
12
33
TotalSat
2 / 6
III
I
Fri
2 / 5
III
II
IIII
Thu
2 / 4
II
II
Wed
2 / 3
I
IIII
Tue.
2 / 2
II
IIII
Mon.
2 / 1
Dirt in distance sensor
Exterior scratches
Loose screws
To 6 Feb. 1992No. 3 assembly lineProcess name
Miki Tanaka
Form 1 Feb. 1992
Recordedby:
Date
--------
LN1238LN1239LN1240
Measuring instrument
Lot number
100% visual operation
CS20-5D
Measuring method
Date / dayDefect
Product name
• Make boxes for filling in the required items • Decide on methods of stratification. • Fill in data• Indicate items to be checked
Table 1: Check sheet for “defects in camera assembly process”
IIIIIIII
IIIIIIIIIIIIIIIIIIIIIIII IIIIIIII IIIIIIII
IIIIIIII
Check Sheets: To take down data simply and prevent inspection omission
Confederation of Indian Industry
4.5%
91
2
3
3
5
10
5
18
16
I
I
17
I
II
III
20
II
III
I
II
20
II
I
II
I
2037 Percent age defects
18
III
IIII
II
Number inspected
Bonding defect
Operating defect
Gap defect
Part lost
Exterior dirt
Total
Soldering defect
Exterior scratches
4.5%
91
2
3
3
5
10
5
18
16
I
I
17
I
II
III
20
II
III
I
II
20
II
I
II
I
2037 Percent age defects
18
III
IIII
II
Number inspected
Bonding defect
Operating defect
Gap defect
Part lost
Exterior dirt
Total
Soldering defect
Exterior scratches IIIIIIII IIIIIIII
IIIIIIII
• Add totals • Make a scratch of the product to be inspected.• Decide on items to be checked.• Every time a defect occurs, fill in a mark of number a
corresponding location.
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2. PARETO CHART
• Vilfredo Pareto (1848-1923), An Italian economist– 20% of the population has 80% of the wealth
• Juran used the term “vital few, trivial many”. Henoted that 20% of the quality problems caused80% of the dollar loss.
• Pareto charts are extremely useful because theycan be used to identify those factors that have thegreatest cumulative effect on the system, and thusscreen out the less significant factors in ananalysis.
Confederation of Indian Industry
• Vilfredo Pareto (1848-1923), An Italian economist– 20% of the population has 80% of the wealth
• Juran used the term “vital few, trivial many”. Henoted that 20% of the quality problems caused80% of the dollar loss.
• Pareto charts are extremely useful because theycan be used to identify those factors that have thegreatest cumulative effect on the system, and thusscreen out the less significant factors in ananalysis.
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PARETO CHART• Pareto Diagram allows the user to focus attention
on a few important factors in a process.
• They are created by plotting the cumulativefrequencies of the relative frequency data(event count data), in descending order.
• When this is done, the most essential factors forthe analysis are graphical presentation and in anorderly format.
Confederation of Indian Industry
• Pareto Diagram allows the user to focus attentionon a few important factors in a process.
• They are created by plotting the cumulativefrequencies of the relative frequency data(event count data), in descending order.
• When this is done, the most essential factors forthe analysis are graphical presentation and in anorderly format.
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PARETO CHART
Per
cent
from
eac
h ca
use
30
40
50
60
70 (64)
Confederation of Indian Industry
Per
cent
from
eac
h ca
use
Causes of poor quality
0
10
20(10) (6)
(3) (2) (2)
(13)
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Confederation of Indian Industry
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Example
S. No. Defect No. of Defects
1 Weld Missing 26
2 Dent 11
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3 Ovality 21
4 Fitment NG 16
5 Other 6
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Example
S. No. Type of Defect No. of Defects1 Weld Missing 26
3 Ovality 21
4 Fitment NG 16
Step 1: Arrange data in decreasing order
Confederation of Indian Industry
4 Fitment NG 16
2 Dent 11
5 Other 6
Step 2 : Summation of individual frequencies.
26+21+16+11+6 = 80
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Example
S# Type of Defect No. ofDefects
Cumulativefreq. % of Cumulative freq.
1 Weld Missing 26 26 26/80=33%
3 Ovality 21 47 (26+21)/80=59%
Step 3: Calculate cumulative percentage
Confederation of Indian Industry
4 Fitment NG 16 63 (26+21+16)/80=79%
2 Dent 11 74 (26+21+16+11)/80=93%
5 Other 6 80 (26+21+16+11+6)/80=100%
Total Sum 80
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26
21
16
79 93100
60
80
100
20
25
30
Perc
enta
ges
Num
bers
Pareto Chart
Step 4 : Draw Chart
Confederation of Indian Industry
16
11
633
59
0
20
40
60
0
5
10
15
Weld Missing Ovality Fittment NG Dent Other
Perc
enta
ges
Num
bers
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EXERCISE
Confederation of Indian Industry
EXERCISE
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S.No Defect type No’s
1 Cracks 298
ExerciseMake Pareto Chart for the data given below.
Product : Spanner
Production Per day : 25000
Confederation of Indian Industry
1 Cracks 298
2 Scaling 1266
3 Unfilled – Cavity 435
4 Grinding NG 684
5 Plating NG 1372
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Exercise
13721266
65.1
81.992.7
100
60.070.080.090.0100.0
1000
1200
1400
1600
Perc
enta
ge (%
)
No
of D
efec
ts
Pareto Analysis
Confederation of Indian Industry
684
435298
33.8
65.1
0.010.020.030.040.050.060.0
0
200
400
600
800
1000
Plating NG Scaling Grinding NG Unfilled – Cavity Cracks
Perc
enta
ge (%
)
No
of D
efec
ts
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3. HISTOGRAM
• A histogram is a graphical summary of variationin a set of data.
• Histogram is a visual tool for presentingvariable data. It organises data to describe theprocess performance.
• The pictorial nature of the histogram enables usto see patterns that are difficult to see in a tableof numbers.
Confederation of Indian Industry
• A histogram is a graphical summary of variationin a set of data.
• Histogram is a visual tool for presentingvariable data. It organises data to describe theprocess performance.
• The pictorial nature of the histogram enables usto see patterns that are difficult to see in a tableof numbers.
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Key Concept of Histogram
• Data always have variation
• Variation have pattern
• Patterns can be seen easily when summarized
pictorially.
Confederation of Indian Industry
• Data always have variation
• Variation have pattern
• Patterns can be seen easily when summarized
pictorially.
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• Location of mean of the process
• Spread of the process
• Shape of the process
While studying histogramlook for its
Confederation of Indian Industry
• Location of mean of the process
• Spread of the process
• Shape of the process
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Calculations for Histogram
535053515050504534849535148493554949504949552534848535050511
XlXs54321
Confederation of Indian Industry
5349514953514910535050535050519544950495049548524850485251517525050505251506514751475150495535053515050504
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Calculations for Histogram Smallest Value, S= 47
Largest Value, L = 55
Range, R = L-S = 8
No. of cells= 1 + 3.22 log10(50) = 7
Calculated cell width (C.W.)= R / No. of cells=1.14
Rounded off Cell width= 1
Confederation of Indian Industry
Smallest Value, S= 47
Largest Value, L = 55
Range, R = L-S = 8
No. of cells= 1 + 3.22 log10(50) = 7
Calculated cell width (C.W.)= R / No. of cells=1.14
Rounded off Cell width= 1
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Calculations for Histogram
Starting value, A= 47
LCB (Lower Class Boundary)= A-(C.W. / 2)= 47-1/2= 46.5
UCB (Upper Class Boundary)= LCB + C.W.= 46.5+1= 47.5
Confederation of Indian Industry
Starting value, A= 47
LCB (Lower Class Boundary)= A-(C.W. / 2)= 47-1/2= 46.5
UCB (Upper Class Boundary)= LCB + C.W.= 46.5+1= 47.5
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Plotting Histogram
165050.549.5
104949.548.5
3III4848.547.5
1I4747.546.5
FreqTally MarkTally MarkMid valueUpperLower
Confederation of Indian Industry
15555.554.5
15454.553.5
55353.552.5
25252.551.5
115151.550.5
165050.549.5
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Confederation of Indian Industry
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2025303540
Histogram
Confederation of Indian Industry
0
5101520
1 2 6 13 10 16 19 17 12 16 20 17 13 5 6 2 1
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Types of Histogram
General Type Comb Type Positively Skew Type
Confederation of Indian Industry
General Type Comb Type Positively Skew Type
Left-handPrecipice Type
Plateau Type Twin Peak Type
Isolated PeakType
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NORMAL CURVE• If the number of observations are increasedconsiderably, then the no. of cells increases and thewidth of the cell become smaller and smaller.The series of steps that constitutes the top line of thehistogram will then approach a smooth curve. Sucha curve is called Frequency curve.• The frequency curves may be of different shapes.• The most important of these curve as far as SQC isconcerned is the NORMAL CURVE.• It is symmetrical about its mean value and has Bellshape.
Confederation of Indian Industry
• If the number of observations are increasedconsiderably, then the no. of cells increases and thewidth of the cell become smaller and smaller.The series of steps that constitutes the top line of thehistogram will then approach a smooth curve. Sucha curve is called Frequency curve.• The frequency curves may be of different shapes.• The most important of these curve as far as SQC isconcerned is the NORMAL CURVE.• It is symmetrical about its mean value and has Bellshape.
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“Normal” bell shaped curve
Confederation of Indian Industry
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“Normal” bell shaped curve
Confederation of Indian Industry
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Manufacturing Outcome: Central Tendency
Falling balls hit these pinsand go either left or right
Ball part way through rowof pins
Confederation of Indian Industry
Ball part way through rowof pins
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5. CAUSE AND EFFECT DIAGRAM
• Show the relationships between a problemand its possible causes.
• Developed by Kaoru Ishikawa (1953)• Also known as …
– Fishbone diagrams– Ishikawa diagrams
Confederation of Indian Industry
• Show the relationships between a problemand its possible causes.
• Developed by Kaoru Ishikawa (1953)• Also known as …
– Fishbone diagrams– Ishikawa diagrams
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Cause and Effect Diagram• Used to associate multiple possible causes with a
single effect.
• Given a particular effect, the diagram isconstructed to identify and organize possiblecauses for it.
• The primary branch represents the effect (thequality characteristic that is intended to beimproved and controlled) and is typically labelledon the right side of the diagram.
Confederation of Indian Industry
• Used to associate multiple possible causes with asingle effect.
• Given a particular effect, the diagram isconstructed to identify and organize possiblecauses for it.
• The primary branch represents the effect (thequality characteristic that is intended to beimproved and controlled) and is typically labelledon the right side of the diagram.
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Cause and Effect Diagram
• Each major branch of the diagram corresponds toa major cause (or class of causes) that directlyrelates to the effect.
• Minor branches correspond to more detailedcausal factors.
• This type of diagram is useful in any analysis, as itillustrates the relationship between cause andeffect in a rational manner.
Confederation of Indian Industry
• Each major branch of the diagram corresponds toa major cause (or class of causes) that directlyrelates to the effect.
• Minor branches correspond to more detailedcausal factors.
• This type of diagram is useful in any analysis, as itillustrates the relationship between cause andeffect in a rational manner.
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Cause and Effect skeleton
QualityProblem
Materials Procedures
Confederation of Indian Industry
QualityProblem
EquipmentPeople
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QualityProblem
MachinesMeasurement Human
Faulty testing equipment
Incorrect specifications
Improper methods
Poor supervision
Lack of concentration
Inadequate training
Out of adjustment
Tooling problems
Old / worn
Fishbone Diagram
Confederation of Indian Industry
QualityProblem
ProcessEnvironment Materials
Defective from vendor
Not to specifications
Material-handling problems
Deficienciesin productdesign
Ineffective qualitymanagement
Poor processdesign
Inaccuratetemperaturecontrol
Dust andDirt
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Fishbone Diagram
Confederation of Indian Industry
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Cause and effect diagrams• Advantages
– making the diagram is educational in itself– diagram demonstrates knowledge of problem
solving team– diagram results in active searches for causes– diagram is a guide for data collection
Confederation of Indian Industry
• Advantages– making the diagram is educational in itself– diagram demonstrates knowledge of problem
solving team– diagram results in active searches for causes– diagram is a guide for data collection
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Cause and effect diagrams
To construct the skeleton, remember:• For manufacturing - the 4 M’sman, method, machine, material
• For service applicationsequipment, policies, procedures, people
Confederation of Indian Industry
To construct the skeleton, remember:• For manufacturing - the 4 M’sman, method, machine, material
• For service applicationsequipment, policies, procedures, people
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Typical causes for non conformance/defects
Machine factors
• Inadequate process capability
• Incorrectly designed tooling
• Worn tools, jigs or dies
• Poor maintenance
• Equipment effected by environmental factors such as heat,
humidity etc.
Confederation of Indian Industry
• Inadequate process capability
• Incorrectly designed tooling
• Worn tools, jigs or dies
• Poor maintenance
• Equipment effected by environmental factors such as heat,
humidity etc.
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Typical causes for non conformance/defects
Material factors
• Use of untested materials
• Mix-up of materials
• Substandard material accepted on concession because of non-
availability of correct material
• Inconsistency in specifications on the part of vendors
Confederation of Indian Industry
• Use of untested materials
• Mix-up of materials
• Substandard material accepted on concession because of non-
availability of correct material
• Inconsistency in specifications on the part of vendors
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Typical causes for non conformance/defects
Men factors
• Incorrect knowledge of setting up machines
• Careless operator and inadequate supervision
• Undue rush by the operator to achieve quality targets
• Lack of understanding of drawing instructions relating to a process
• Operator does not possess requisite skill for operating machines
Confederation of Indian Industry
• Incorrect knowledge of setting up machines
• Careless operator and inadequate supervision
• Undue rush by the operator to achieve quality targets
• Lack of understanding of drawing instructions relating to a process
• Operator does not possess requisite skill for operating machines
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Typical causes for non conformance/defects
Method factors
• Inadequate process controls
• Non availability of proper test equipments
• Test equipment out of calibration
• Vague inspection/ testing instructions
• Inspectors do not possess the necessary skill
Confederation of Indian Industry
• Inadequate process controls
• Non availability of proper test equipments
• Test equipment out of calibration
• Vague inspection/ testing instructions
• Inspectors do not possess the necessary skill
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PAPER / BOTTOM PANELFITMENT
EXCESSIVESEEPAGE
LOW SHOT WEIGHT TAPE MISSING
SIDE WALL TEMP
VOIDS
MENMETHOD
Cause & Effect diagram
Example
Confederation of Indian Industry
CHEMICALTEMPIMPROPER POL/CP MIXING
POURING HOLEMISMATCH
DAMAGED PESHEETS.
VOIDS
MATERIAL
CHEMICALPRESSUREIMPROPER P/I RATIO
M/C ALARMS
MACHINE
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Cause & Effect diagram
Exercise
Confederation of Indian Industry
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6. SCATTER PLOT
• Scatter diagrams are graphical tools that attemptto show the influence that one variable has onanother.
• A scatter diagram shows the relationship betweenindependent variable (cause) and dependentvariable (effect).
Confederation of Indian Industry
• Scatter diagrams are graphical tools that attemptto show the influence that one variable has onanother.
• A scatter diagram shows the relationship betweenindependent variable (cause) and dependentvariable (effect).
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Characteristics of Independent Variable• It should be measurable on a continuous
scale.
• It should have a logical relationship with thedependent variable.
• Changes in level of independent variableshould cause changes in level of dependentvariable.
Confederation of Indian Industry
• It should be measurable on a continuousscale.
• It should have a logical relationship with thedependent variable.
• Changes in level of independent variableshould cause changes in level of dependentvariable.
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Typical Relationship We Normally Liketo Study
Independent Variable Dependent Variable
• Moisture contents Elongation of thread
• Wax purity Hardness of lipstick
• Roller Pressure Paper thickness
• Charge weight Range of bullet
• Number of users Response time
Confederation of Indian Industry
Independent Variable Dependent Variable
• Moisture contents Elongation of thread
• Wax purity Hardness of lipstick
• Roller Pressure Paper thickness
• Charge weight Range of bullet
• Number of users Response time
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Leng
th o
f bar
Typical RelationshipY
Confederation of Indian Industry
Pull Speed
Leng
th o
f bar
X
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Sta
min
aTypical
RelationshipY
Confederation of Indian Industry
Life (Age)
Sta
min
a
X
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Table - Humidity Vs VoltageVoltageHumidity %
V1 V2 V3 V4 V5102030405060708090100
40464549515454575960
43434345475152555758
41464348505151545657
42464449515255585958
40444346495353585758
Confederation of Indian Industry
VoltageHumidity %V1 V2 V3 V4 V5
102030405060708090100
40464549515454575960
43434345475152555758
41464348505151545657
42464449515255585958
40444346495353585758
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Scatter Plot60
4045
50
55
Volta
ge
Confederation of Indian Industry
10 5020 6030 70 80 90 100
40
Humidity
Volta
ge
35
40
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7. STRATIFICATION• It is the process of segregating or regrouping the
data on the basis of certain characteristics ( e.g.machine wise, operator wise etc.) for identifyingthe influence factors (i.e. identifying contributorycauses to the problems being handled)
• Data on Customer Complaints may besegregated by
a) Nature of Complaints: defective products,Delayed delivery etc.
b) Department Responsible: Production, Design,Quality etc.
Confederation of Indian Industry
• It is the process of segregating or regrouping thedata on the basis of certain characteristics ( e.g.machine wise, operator wise etc.) for identifyingthe influence factors (i.e. identifying contributorycauses to the problems being handled)
• Data on Customer Complaints may besegregated by
a) Nature of Complaints: defective products,Delayed delivery etc.
b) Department Responsible: Production, Design,Quality etc.
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Benefits of Stratification• Separate Data into groups.
• Draw meaningful and correct inferences from
the data.
• Diagnose and Localize problems i.e. establish
clear relationship between cause and effect.
• Identify the influencing factors, thereby making it
easier to solve the problems.
Confederation of Indian Industry
• Separate Data into groups.
• Draw meaningful and correct inferences from
the data.
• Diagnose and Localize problems i.e. establish
clear relationship between cause and effect.
• Identify the influencing factors, thereby making it
easier to solve the problems.
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1025
1550
51015202530
A B C D
% D
efec
tives
Suppliers
% Defectives Stratified supplierwise
Confederation of Indian Industry
Suppliers
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1030 25 15 20
010203040
% A
ccid
ents
% Accidents Stratified Shopwise
Confederation of Indian Industry
Shops
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• Fundamental tool of statistical process control.
• It indicates the stability of the process.
• It helps determine whether a process is in controlor if a special cause exists to change the processmean or variance.
Control Chart
Confederation of Indian Industry
• Fundamental tool of statistical process control.
• It indicates the stability of the process.
• It helps determine whether a process is in controlor if a special cause exists to change the processmean or variance.
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In all production processes, we need to monitor the extent
to which our products meet specifications.
In the most general terms, there are two "enemies" of
product quality:
• deviations from target specifications, and
• excessive variability around target specifications.
Control Chart
Purpose
Confederation of Indian Industry
In all production processes, we need to monitor the extent
to which our products meet specifications.
In the most general terms, there are two "enemies" of
product quality:
• deviations from target specifications, and
• excessive variability around target specifications.
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Why Control Chart ?
To find out,
• Any change in location of process average ?
• Any change in the spread of the process ?
• Any change in shape?
• To identify if special cause variation exists.
Confederation of Indian Industry
To find out,
• Any change in location of process average ?
• Any change in the spread of the process ?
• Any change in shape?
• To identify if special cause variation exists.
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Significance of Control Chart ?
The quality of a product manufactured in a process isinevitably accompanied by dispersion. Various Causes ofsuch dispersion exist and they can be classified into thefollowing two types.
1. Chance / Random cause:
Dispersion by chance is natural and unavoidable i.e.inevitably occurs in a process, even if the operation iscarried out using standardized raw materials and methods.
It is impossible to avoid the Random cause variation.
Significance of Control Chart ?
The quality of a product manufactured in a process isinevitably accompanied by dispersion. Various Causes ofsuch dispersion exist and they can be classified into thefollowing two types.
1. Chance / Random cause:
Dispersion by chance is natural and unavoidable i.e.inevitably occurs in a process, even if the operation iscarried out using standardized raw materials and methods.
It is impossible to avoid the Random cause variation.
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Control Chart2. Assignable / Special cause:
Dispersion from an assignable cause is unusual andmeaningful in that it is avoidable and cannot beoverlooked.Example: Neglecting various standards or application ofimproper standards.
In order to control a process it is necessary to eliminateassignable causes and take action to prevent theirrecurrence, while tolerating dispersion by chance /random cause.
2. Assignable / Special cause:
Dispersion from an assignable cause is unusual andmeaningful in that it is avoidable and cannot beoverlooked.Example: Neglecting various standards or application ofimproper standards.
In order to control a process it is necessary to eliminateassignable causes and take action to prevent theirrecurrence, while tolerating dispersion by chance /random cause.
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A control chart was first used in 1924 by W.A. Shewhart,who belonged to the Bell Telephone Laboratories, with aview to classifying an abnormal process by distinguishingvariations due to chance from those due to assignablecauses.
Example of Control Chart
Upper controlLimit
Central line
Lower controlLimit
Control chart for controlled state
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To make a control chart it is necessary to classify theprocess by type of raw materials, machine and line andfurther to classify these data into small groups such as timeor shift.
There are various types of control chart, according to thecharacteristic values or purpose. However, in any type ofcontrol chart the control limits are calculated by the formula :(average value) ± 3 x (standard deviation)Therefore such a chart is called a three sigma control chart.
Control chart for uncontrolled state
To make a control chart it is necessary to classify theprocess by type of raw materials, machine and line andfurther to classify these data into small groups such as timeor shift.
There are various types of control chart, according to thecharacteristic values or purpose. However, in any type ofcontrol chart the control limits are calculated by the formula :(average value) ± 3 x (standard deviation)Therefore such a chart is called a three sigma control chart.
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• The bounds of the control chart are marked byupper and lower control limits that are calculatedby applying statistical formulas to data from theprocess.
• Data points that fall outside these boundsrepresent variations due to special causes, whichcan typically be found and eliminated.
• On the other hand, improvements in commoncause variation require fundamental changes in theprocess.
Confederation of Indian Industry
• The bounds of the control chart are marked byupper and lower control limits that are calculatedby applying statistical formulas to data from theprocess.
• Data points that fall outside these boundsrepresent variations due to special causes, whichcan typically be found and eliminated.
• On the other hand, improvements in commoncause variation require fundamental changes in theprocess.
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18
15
21
24
Num
ber o
f def
ects
UCL = 23.35
x = 12.67
Control Chart
Confederation of Indian Industry
12
6
3
9
2 4 6 8 10 12 14 16Sample number
Num
ber o
f def
ects
LCL = 1.99
x = 12.67
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Control LimitsUpper Control Limit
Target
3 x sd of means
Confederation of Indian Industry
1 2 3 4 5 6 7Sample Number
Lower Control Limit
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Control Charts
Variables Attributes
Types of Control Charts
Confederation of Indian Industry
p Chartnp ChartC Chartu Chart
Variables Attributes
– R Chart– s Chart
XX
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o Defect prevention andprocess improvement
o More expensive toconstruct and maintain
o Can tell reasons forprocess behavior
o Smaller n (1 to 10)needed
o Defect detectiono Cheaper to construct
and maintaino Cannot tell cause of
defecto Need large n (>100)o A screening device to
initiate variables controlcharting
Variable Control Charts Attribute Control Charts
Confederation of Indian Industry
o Defect prevention andprocess improvement
o More expensive toconstruct and maintain
o Can tell reasons forprocess behavior
o Smaller n (1 to 10)needed
o Defect detectiono Cheaper to construct
and maintaino Cannot tell cause of
defecto Need large n (>100)o A screening device to
initiate variables controlcharting
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DATA TYPE
Start
SampleSize, n
MeasurableVariables Data
X-bar MRChart
n = 1 Defectivesor
Defects?
CountableAttributes Data
Constant‘n’
Yes
Defects
No
Selecting a Control Chart
Confederation of Indian Industry
X-bar MRChart
Range orS.D
X-bar -R Chart
Range,if n<10 Constant
‘n’Yes
np or pChart
Constant‘n’
c (or) uChart
Yes
Defectives
No
pChart
X-bar -s Chart
S.D,if n>10
uChart
No
n > 1
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Types of Charts
Variable control charts are :-
• X bar – R Chart
• Run Chart
Attribute control Charts are :-
• P Chart
• C chart
• U Chart
Confederation of Indian Industry
Variable control charts are :-
• X bar – R Chart
• Run Chart
Attribute control Charts are :-
• P Chart
• C chart
• U Chart
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Types of Charts
Variable control charts are :-
• X bar – R Chart
• Run Chart
Confederation of Indian Industry
Variable control charts are :-
• X bar – R Chart
• Run Chart
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X bar – R Chart
•Shows both the mean value ( X ), and the range ( R ).
•The Xbar portion shows any changes in the mean value of
the process, while the R portion shows any changes in the
dispersion of the process.
•This chart is particularly useful in that it shows changes in
mean value and dispersion of the process at the same time,
making it a very effective method for checking abnormalities
within the process
Confederation of Indian Industry
•Shows both the mean value ( X ), and the range ( R ).
•The Xbar portion shows any changes in the mean value of
the process, while the R portion shows any changes in the
dispersion of the process.
•This chart is particularly useful in that it shows changes in
mean value and dispersion of the process at the same time,
making it a very effective method for checking abnormalities
within the process
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Formula’s Used
X bar – R Chart
Center Line = X
X bar Chart
Confederation of Indian Industry
Center Line = R
R Chart
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X bar – R Chart
SNO. 1 2 3 4 5 6 7 8 9 10
1 65.84 65.88 65.86 65.86 65.9 65.84 65.88 65.88 65.92 65.92
2 65.88 65.86 65.88 65.88 65.84 65.9 65.9 65.9 65.9 65.88
3 65.82 65.9 65.86 65.88 65.86 65.86 65.9 65.86 65.92 65.88
4 65.9 65.84 65.84 65.84 65.88 65.88 65.86 65.82 65.88 65.86
5 65.88 65.86 65.9 65.86 65.86 65.86 65.88 65.84 65.88 65.84
Average X 65.864 65.868 65.868 65.864 65.868 65.868 65.884 65.86 65.9 65.876
Range 0.08 0.06 0.06 0.04 0.06 0.06 0.04 0.08 0.04 0.08
Example
SPECIFIC: 65.8±0.2
PART NAME: SPACER FRAME CROSS MEMBER
Confederation of Indian Industry
SNO. 1 2 3 4 5 6 7 8 9 10
1 65.84 65.88 65.86 65.86 65.9 65.84 65.88 65.88 65.92 65.92
2 65.88 65.86 65.88 65.88 65.84 65.9 65.9 65.9 65.9 65.88
3 65.82 65.9 65.86 65.88 65.86 65.86 65.9 65.86 65.92 65.88
4 65.9 65.84 65.84 65.84 65.88 65.88 65.86 65.82 65.88 65.86
5 65.88 65.86 65.9 65.86 65.86 65.86 65.88 65.84 65.88 65.84
Average X 65.864 65.868 65.868 65.864 65.868 65.868 65.884 65.86 65.9 65.876
Range 0.08 0.06 0.06 0.04 0.06 0.06 0.04 0.08 0.04 0.08
(x)
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X bar – R Chart
X = Average (Average X) = Average X
=658.72/10 = 65.872
R = Average (Range)
=0.6/10 = 0.06
Confederation of Indian Industry
R = Average (Range)
=0.6/10 = 0.06
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X bar – R Chart
Center Line = X
For X bar ChartUCL = 65.872 + 0.590x0.06
= 65.907
X =65.872
LCL = 65.872 - 0.590x0.06= 65.836
Confederation of Indian Industry
Center Line = R
R Chart
LCL = 65.872 - 0.590x0.06= 65.836
UCL = 0.06x2.110 = 0.1266
LCL = 0.06x0 = 0
R = 0.06
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Size of Sub-group X-Chart R Chart R Chart R Chart
n A2 D3 D4 d22 1.880 - 3.267 1.128
Coefficients for X bar R Charts
Confederation of Indian Industry
2 1.880 - 3.267 1.1283 1.023 - 2.575 1.6934 0.729 - 2.282 2.0595 0.590 - 2.110 2.3266 0.483 - 2.004 2.534
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65.88
65.89
65.9
65.91
65.92
X ba
r
UCL = 65.905
X = 65.872
X bar Chart
Confederation of Indian Industry
65.83
65.84
65.85
65.86
65.87
0 1 2 3 4 5 6 7 8 9 10
X ba
r
LCL = 65.836
X = 65.872
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UCL = 0.126
R = 0.06
R Chart
0.08
0.1
0.12
0.14
Ran
ge
Confederation of Indian Industry
LCL = 0
R = 0.06
0
0.02
0.04
0.06
0.08
0 1 2 3 4 5 6 7 8 9 10
Ran
ge
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X bar – R ChartExercise
PART NAME: PIPE COMP. STRG. HEAD-KTEA
SPECIFIC: 8+0 /-0.2
SNO. 1 2 3 4 5 6 7 8 9 10
1 7.9 7.98 8 8.1 7.85 7.84 7.91 7.98 7.85 7.84
2 7.84 7.84 7.84 7.94 7.97 7.94 7.94 7.98 7.84 7.94
3 7.96 7.94 7.88 7.82 7.88 8.1 7.85 7.84 7.91 7.98
4 7.84 7.84 7.94 7.97 7.94 7.84 7.91 7.98 7.85 7.84
5 7.94 7.97 7.94 7.94 7.98 8.1 7.85 7.84 7.91 7.98
Confederation of Indian Industry
SNO. 1 2 3 4 5 6 7 8 9 10
1 7.9 7.98 8 8.1 7.85 7.84 7.91 7.98 7.85 7.84
2 7.84 7.84 7.84 7.94 7.97 7.94 7.94 7.98 7.84 7.94
3 7.96 7.94 7.88 7.82 7.88 8.1 7.85 7.84 7.91 7.98
4 7.84 7.84 7.94 7.97 7.94 7.84 7.91 7.98 7.85 7.84
5 7.94 7.97 7.94 7.94 7.98 8.1 7.85 7.84 7.91 7.98
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Attribute Charts:
• p Chart Fraction Defective
• c Chart No. of Defects in a fixed sized Product
• u Chart No. of Defects in a varying sized product
Attribute Charts:
• p Chart Fraction Defective
• c Chart No. of Defects in a fixed sized Product
• u Chart No. of Defects in a varying sized product
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p Chart
Control charts dealing with the proportion or fraction
of defective product are called p chart (for proportion).
Control charts dealing with the proportion or fraction
of defective product are called p chart (for proportion).
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p ChartFormula’s Used
‘p’ is the fraction defective in a lot or population
‘n’ is the number of lot
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p ChartExample
S.No. Date Total QuantityProduced
Defective Qty.
1 1st Jan 07 990 87
2 2nd Jan 07 1000 93
3 3rd Jan 07 1110 1893 3rd Jan 07 1110 189
4 4th Jan 07 980 126
5 5th Jan 07 1000 109
6 6th Jan 07 1100 102
7 8th Jan 07 910 145
8 9th Jan 07 1080 90
9 10th Jan 07 985 81
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p ChartStep 1: Calculate Fraction Defective
S.No Date Total QuantityProduced
Defective Qty. Fraction Defective
1 1st Jan 07 990 87 87/990 =0.088
2 2nd Jan 07 1000 93 93/1000 =0.093
3 3rd Jan 07 1110 189 189/1110 =0.1703 3rd Jan 07 1110 189 189/1110 =0.170
4 4th Jan 07 980 126 126/980 =0.129
5 5th Jan 07 1000 109 109/1000 =0.109
6 6th Jan 07 1100 102 102/1100 =0.093
7 8th Jan 07 910 145 145/910 =0.159
8 9th Jan 07 1080 90 90/1080 =0.083
9 10th Jan 07 985 81 81/985 =0.82
Total 9155 1022 1.006
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p ChartStep 2: Calculate UCL & LCL
P = 1.006 / 9 =0.112
UCL = 0.112 + 3 0.112(1-0.112)/9 = 0.422UCL = 0.112 + 3 0.112(1-0.112)/9 = 0.422
LCL = 0.112 – 3 0.112(1-0.112)/9 = - 0.203
= 0
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p ChartStep 3: Draw Chart
0.250
0.300
0.350
0.400
0.450
Frac
tion
Def
ecti
ve
UCL = 0.422
0.000
0.050
0.100
0.150
0.200
0.250
Frac
tion
Def
ecti
ve
LCL = 0
P = 0.112
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c Chart
C Chart is used where each item inspected may have
several nonconformities and each nonconformity is counted,
and sample size is constant.
C Chart is used where each item inspected may have
several nonconformities and each nonconformity is counted,
and sample size is constant.
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c ChartFormula’s Used
Center line c = c /n
UCL = c + 3 * c
LCL = c - 3 * c
Where ‘c’ is the number of nonconformities in each sample
‘n’ is the number of lot
LCL = c - 3 * c
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c ChartExample
Lot Number Number of pinholes
1 8
2 9
3 5
4 8
Lot Number Number of pinholes
11 6
12 4
13 7
14 64 8
5 5
6 9
7 9
8 11
9 8
10 7
14 6
15 14
16 6
17 4
18 11
19 7
20 8
Total 152
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c ChartStep 1: Calculate UCL & LCL
Center line c = c /n
UCL = c + 3 * c
c = 152/20 = 7.6
UCL = 7.6 + 3 * 7.6 = 15.85UCL = c + 3 * c
LCL = c - 3 * c
UCL = 7.6 + 3 * 7.6 = 15.85
LCL = 7.6 - 3 * 7.6 = -0.65
= 0
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c ChartStep 2: Draw Chart
1012141618
No.
of P
inho
les
UCL = 15.85
02468
10
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
No.
of P
inho
les
c = 7.6
LCL = 0
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u Chart
A u-chart is an attributes control chart used with data
collected in subgroups of varying sizes
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u ChartFormula’s Used
Center line u = u /n
UCL = u + 3 * u /N
LCL = u - 3 * u /N
Where ‘u’ is the number of nonconformities in each sample
‘n’ is the number of items in the sample
‘N’ is the average sample size
LCL = u - 3 * u /N
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u ChartExample
S. No. No. of parts Inspected Number of Nonconformities
1 200 5
2 80 7
3 100 3
4 300 154 300 15
5 120 4
6 90 6
7 250 10
8 50 1
9 100 6
10 70 2
Total 1360 59
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u Chart
S. No. No. of parts Inspected( A )
Number of Nonconformities( B )
U = B/A
1 200 5 0.025
2 80 7 0.088
3 100 3 0.030
4 300 15 0.050
5 120 4 0.033
Step 1: Calculate u
5 120 4 0.033
6 90 6 0.067
7 250 10 0.040
8 50 1 0.020
9 100 6 0.060
10 70 2 0.029
Total 1360 59
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u ChartStep 2: Calculate UCL & LCL
Center line u = u /n
UCL = u + 3 * u /N
N = 1360 / 10 = 136
u = 59/1360 = 0.043
UCL = 0.043 + 3 0.043/136 = 0.097UCL = u + 3 * u /N
LCL = u - 3 * u /N
UCL = 0.043 + 3 0.043/136 = 0.097
LCL = 0.043 - 3 0.043/136 = -0.011
= 0
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u ChartStep 3: Draw Chart
0.06
0.08
0.1
0.12
u
UCL = 0.097
0
0.02
0.04
0.06
0 1 2 3 4 5 6 7 8 9 10
u
u = 0.043
LCL = 0
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Thank You!Thank You!