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2
SEVEN QC TOOLS
 Check Sheets
 Pareto Diagram
 Cause and Effect Diagram.
 Stratification.
 Scatter Diagram.
 Histogram.
 Graphs and Control Charts.

3
How to Collect Data
1. Have Clear Defined Objectives
• Controlling and monitoring the production process
• Analysis of non-conformance
• Inspection
2. What Is Your Purpose
• Collecting as per strata
• Collecting in Pairs (correlation)
3. Are Measurements Reliable
4. Find Right Ways to Record Data
• Arrangement
• Data sheet

4
Check Sheet
What : An easy to understand form used to answer the
question “ How often are certain events happening?”
Why : Starts the process of translating “opinion” into
“fact
When : Gathering data in order to detect patterns.
Good point to start most problem solving cycles.

5
How :
•Team agrees as to exactly what event is being
observed.
•Decide on the time period during which data will
be collected. This could range from hours to
weeks.
•Design a form that is clear and easy to use
making sure that all columns are clearly labeled
and that there is enough space to enter the data.
•Collect the data making sure that observations/
samples are as representative as possible.
Check Sheet

6
Mark defect by
SN Class Mean Value Tally Marks Total
1 950-955 952.5 IIII 4
2 955-960 957.5 IIII III 8
3 960-965 962.5 IIII IIII IIII 15
4 965-970 967.5 IIII IIII 10
5 970-975 972.5 IIII I 6
Diagram type check sheet Frequency check sheet
Sn Parameter Spec Judgement Remark
1 2 3 4 5
Part No: Process: Machine:
Sample No
Inspection check sheet
Check sheet contd...

7
Pareto Analysis
What: A bar chart that helps to prioritize actions by arranging
elements in descending order of occurrence. Sorts out
the “vital few” from the “trivial many”.
Why :
•To prioritize actions needed to solve complex problems.
•To separate important from non-important causes
contributing to a problem.
When :
•Many factors are impacting a problem.
•Attention needs to be directed only to the few factors that
account for most of the problem.

8
How:
•Define a problem and collect data on the factors that
contribute to it.
•Historical records generally provide sufficient
information.
•Classify the data by type, cost , percent, number of
occurrences, or whatever is appropriate for the
situation.
•Arrange the data in descending order.
Pareto Analysis

9
Contd……. Pareto Analysis
How contd….
•Draw bar graph showing constituent ratio on vertical axis.
•Connect cumulative percentage of each bar graph to obtain
Pareto curve.
D efect D efect Q ty % C um
C ode description R ej C ontribution % age
A D rill B roken 70 46.60% 46.60%
B Serration M ism atch 45 30% 76.60%
C R unout m ore 25 16.60% 93.20%
D D ia U/S 6 4% 97.20%
E D ia O /S 4 2.80% 100%
Total 150
R ejection details of P inion

10
Contd… Pareto
75%
50%
25%
n=150
100%
A B C D E
Defect Code
Nos.

11
Types of Pareto Diagrams
1. Pareto Diagrams by Phenomenon
• Quality: defects, faults, failure, complaints, RW etc.
• Cost: amount of loss, expenses
• Delivery: delay in delivery, stock shortages etc
• Safety: accidents, mistakes, breakdowns etc
2. Pareto Diagrams by Causes
• Operator: shift, group, age, experience, skill etc
• Machine: machines, equipments, tools, instruments etc.
• Material: manufacturer, plant, lot, kind etc
• Process: conditions, orders, arrangements,methods etc.

12
Hints on Making Pareto Diagrams
1. Check various classifications and construct many kinds
of Pareto diagrams
Essence of a problem can be grasped by observing it from
various angles
2. It is undesirable that “others” represents a higher
percentage
A different method of classification should be considered
3. It is best to draw Pareto diagrams by assigning
monetary value
Cost is an important scale of measurement in
management. If financial implications of a problem are not
properly appreciated, the research itself may end up as
ineffective.

13
Hints on Using Pareto Diagrams
1. If an item is expected to be amenable to a simple
solution, it should be tackled right away even if it is of
relatively small importance.
It will serve as an example of efficient problem solving, and
the experience, information and incentives to morale
obtained through this will be of great assets for future
problem solving.
2. Do not fail to make Pareto diagram by causes
After identifying the problem by making a Pareto diagram
by phenomenon, it is necessary to identify the causes in order
to solve the problem. It is therefore vital to make a Pareto
diagram by causes if any improvements are to be effected.

14
Cause & Effect Diagram
What:
•A graphic tool used to represent the relationship between an
effect and the cause that influence it.
Why:
•Identifies various causes affecting a process.
•Helps groups in reaching a common understanding of a
problem.
•Helps reduce incidence of subjective decision making.
When:
•Looking for all potential causes of problem.

15
How:
•Define the problem or effect clearly.
•Generate the potential cause of problem through brain
storming.
•Encourage wild ideas
•‘Quantity’ rather than ‘Quality’ of ideas
•Suspend judgement on ‘Good’ or ‘Bad’
•Ride on another’s idea
•Construct the cause and effect diagram by:
•Place problem statement in a box on right hand side.
•Draw the major cause category boxes on the left hand
side. Commonly used categories are man, machine,
method, material and measurement.

16
•For each cause ask “ Why” and list responses as
branches off the major causes or use ideas from
brainstorming after categorizing into main causes
•Identify likely root cause(s) and circle them.
•Collect data to verify the most likely root causes

Cause and Effect Diagram
Nurses
Many patients
Long waiting
time after
completion of
ultrasonic scan
Methods
Environment
People
Reception
work
Medical charts
hard to tell apart
Many charts to input
Shortage of
numbers
Inexperience
Patients
Two or more booked
in at same time
Record
findings
Charts all
returned together
Handling
Data input
takes time
Calculation
of bill
Charts from all
departments
come together
Test
Rooms
Far away
Busy
Computer
terminal
slow
Reception

18
Hints on Making Cause and Effect
Diagrams
•Identify all the relevant factors through examination
and discussion by many people
•Express the characteristic as concretely as possible
•Make the same number of cause and effect diagrams
as that of characteristics
•Choose a measurable characteristic and factors
•Discover factors amenable to action

19
Hints on Using Cause and Effect
Diagrams
• Assign an importance to each factor objectively on the
basis of data
Examination of factors on the basis of your own skill and
experience is important, but it is dangerous to give importance
to them through subjective perceptions or impressions alone
(would have been solved by now if so). Assigning importance to
factors objectively using data is both more scientific and more
logical.
• Try to improve the cause and effect diagram
continuously while using it
Actually using a cause and effect diagram will help in
seeing those parts which need to be checked, deleted or
modified. This will be useful in solving problems, and at the
same time, will help improve your own skill and to increase your
technological knowledge

20
Pareto Diagrams and Cause and
Effect diagrams-combination
Case Study:
1. Selection of Problems
This is an example illustrating the examination of non-
conformity in a manufacturing process by the use of a
Pareto diagram. When data on non-conformity collected on
two months was classified by non-conforming items, it was
found that dimensional defectives were largest in number,
constituting 48 percent of the total non-conformance. We
therefore tried to reduce the number of non-conformity with
stress on dimensional defectives.

21
Case Study… contd.
150
100
50
100
75
50
25
A B C D E Others
June 1-July 31
A: Dimensional
defectives
B: Pinholes
C: Scratches
D: Cracks
E: Distortion
Pareto Diagram of Non-conformance Items

22
2. Analysis and Countermeasures
All the shop members discussed the causes of the dimensional
variation and constructed a cause and effect diagram. A Pareto diagram
by causes was then made by investigating all the units with dimensional
variation in order to examine to what extent these factors were affecting
the non-conformance. With some items, it was impossible to clarify the
causes of non-conformance, and these were lumped together under the
heading “Unclear”. We discovered from the Pareto diagram that the
occurrence of the defect was greatly affected by the fitting position.
Although the fitting position had been stipulated by the traditional
operational standard, the standard fitting method was not shown. This
led variation in the fitting position, and resulted into dimensional
defectives. The shop members therefore designed a suitable fitting
method, which was further standardized and added to the operational
standards.

23
Fitting Material
Quality of
material
Skills
Health
Training
Spirit
Dimensional
Variation
Methods
Machine
Operation
Stability
Inspection
Working
Order
Setting
Parts & Materials
Dimension
Component
People
Deformation
Illnes
s
Inexperience
Jigs & Tools
Imbalance
Abrasion
Concentration
Attentiveness
Part
Method
Item
Illnes
s Education
Position
Angle
Procedure
Speed
Degree of
tightening
Form
Diameter
Shape
Storage

24
70
50
10
100
75
50
25
W X Y Z
Unclear
Others
June 1-July 31
V: Fitting position
W: Working speed
X: Components
Y: Abrasion of jigs & tools
Z: Shape of parts
Pareto Diagram by causes
V
30
20
60
40
80

25
3. Effects of Improvements
After the improvement was carried out, data
was collected, and a Pareto diagram was made to
compare the results. The following two Pareto
diagrams clearly show that dimensional defectives
were reduced.

26
100
50
100
75
50
25
C B A D E Others
Sept. 1-Oct. 31
150
100
50
100
75
50
25
A B C D E Others
June 1-July 31
Total effect
Effect
Comparison of Pareto Diagrams Before and After Improvement

27
Stratification
What: Stratification is a statistical technique of breaking
down values and numbers into meaningful categories or
classification.
Why: To focus on corrective action or identify true causes.
When: To identify the cause of problem if they come from a
particular source.
•To analyze root cause in conjunction with other
techniques like Pareto diagram histogram and graphs.

28
How:
Regroup original data as per the source of data
(eg. Machine wise, shift-wise, model-wise, supplier-wise)
•If required collect data afresh after making the source
from which they come.
• Recreate histogram, Pareto charts and graphs on
classified data
Stratification

29
Stratification ……..contd...
Month Model A Mode B
Apr 10 50
May 8 32
Jun 15 65
Jul 10 50
Aug 8 42
Sep 7 28
0
10
20
30
40
50
60
70
80
90
Apr May Jun Jul Aug Sep
Month
Rej
Nos
Mode B
Model A

30
Stratification ……..contd...
Impurity Amount
V
i
s
c
o
s
i
t
y
After Stratification
Impurity Amount
V
i
s
c
o
s
i
t
y
Before Stratification

31
Scatter Diagram
What:
A tool used to study the possible relationship between
two variables.
Why:
To test for possible causes and effect relationships.
Though it cannot prove that one variable causes the other,
the diagram does make it clear whether a relationship
exists and shows the strength of that relationship.
When:
There is a need to display what happens to one variable
when another one changes in order to test that the two
variables are related.

32
How:
•Collect 50 to 100 paired samples of data believed to be
related.
•Construct a data sheet.
•Draw the horizontal and vertical axis of the diagram.
•Label the axes.
• “Cause”is usually plotted on the horizontal axis and the
“effect” variable on the vertical axis.
• Plot the data on the diagram. If values repeat, circle that
point.
Scatter Diagram

33
Interpretation
D. Possible negative correlation E. Strong Negative correlation
A. Randomly scattered points -
No correlation
B. Possible Positive correlation C. Strong positive correlation
n=15 r=0.06 n=18 r=0.54 n=14 r=0.96
n=22 r=- 0.5 n=18 r=-0.92

34
Some Important Definitions
Mean, x : Sum of the values of the observations divided by
the number of observations.
Variance, s2 : Mean of the squares of deviations of the
observations from their mean
Standard Deviation, s : Positive square root of the
variance

35
Correlation Coefficient
S(xy)
S(xx).S(yy)
r=
S(xx) = (x -x)
i
2
n
i=1
S(yy) = (y -y)
i
2
n
i=1
S(xy) = (x -x) (y –y)
i
n
i=1
i
If r=0 No correlation
If r=1 Very strong correlation
If r=-1 Very strong negative
correlation
If 0<r>1 Possible correlation

36
Significance of ‘r’
If calculated value of r is more than the table
value of r at 1% or 5% significance level at (n-2)
degrees of freedom, then at 99% or 95%
confidence we can say that correlation exists
between two or vice-versa.

37
Notes on Correlation Analysis
1. Coordinate Axes:
Effect of choosing scale of axes
2. Stratification:
Stratify the data and then see the
correlation
3. Range of variables:
Select range of variables carefully as it
affects correlation

38
Notes on Correlation Analysis
4. False Correlation:
According to a certain survey, there was a strong positive correlation
between the consumer price index and the number of incidents of fire. If
so, then, if consumer price index lowers, will there be indeed fewer fire
emergencies? The answer is most likely “No’. In order to reduce the
incidence of fires, we would stress the importance of cleaning-up of
ashtrays and not to discard any trash that would bring upon incendiary. In
this way, when calculating a correlation coefficient between two variables,
it is sometimes found, by chance, there is a high value of correlation
coefficient between the two variables which originally have little or no
cause and effect relationship to each other. This sort of correlation is called
False correlation. Even if the correlation coefficient is high, it does not
necessarily indicate a cause and effect relationship. It is necessary to take
good note of this fact, and to think about its meaning in science and
technology.

39
Regression Analysis
Estimating the exact relationship between
dependent and independent variables
Line of best fit joining data
points on a scatter diagram is a
regression line having equation
y=a+bx
where y is dependent
variable, x is independent
variable, a is a constant and b is
regression coefficient
y
x

40
Regression Analysis
Calculations:
1. Calculate x and y
2. Calculate S(xx) and S(xy)
3. Calculate b
b=S(xy)/S(xx)
4. Calculate a
a=y-b x
Then, equation of line is y=a+bx
Note: For both Correlation and Regression
Analysis, draw scatter diagram first

41
Histogram
What: A bar chart that displays the variation within the
process. Also called a frequency distribution because the
frequency of occurrence of any given value is represented by
the height of the bars.
Why:
•Allows one to quickly visualize what’s going on within a
large amount of data.
•Provides clues to causes of problems.
•Maybe be used to show the relationship between the
engineering tolerance and the capabilities of the process.

42
When:
•Capability studies are being performed.
•Analyzing the quality of incoming material.
•Understanding population at a glance
How:
•Collect measurements(variable data)from a process or key
characteristic.
•Thirty or more measurements are preferred.
•Construct check sheet to record the data.
•Find the range by subtracting the smallest measurements
from the largest.
•Using this guide determine the proper number of class
intervals.
Histogram

43
Histogram…...
How…….contd..
Observations No. of classes(K)
25 to 50 5 to 8
51 to 100 6 to 11
101 to 250 9 to 13
251 and over 11 to 15
K=R/h +1 (R = Range)
Select h such that K is between 5~8 or …..
•Construct a frequency table by properly making class
boundaries. Tally the number of observations found in each
class.

44
•Taking the class interval on horizontal axis, draw the
height of the bar corresponding to frequencies in interval
on the vertical axis.
Class Class limits Tally Number of observations
1 0.51 to 5.50 IIII IIII 10
2 5.51 to 10.50 IIII IIII IIII IIII 20
3 10.51 to 15.50 IIII IIII IIII IIII IIII 25
4 15.51 to 20.50 IIII IIII IIII IIII 20
5 20.51 25.50 IIII IIII IIII 15
6 25.51 to 30 .50 IIII IIII 10
Histogram…...
How…….contd..

45
0.5 5.5 10.5 15.5 20.5 25.5 30.5
5
10
15
20
5
25
Histogram…...
How…….contd..

46
Types of Histogram
General Type Comb Type Positively Skew Type
Left-hand
Precipice Type
Plateau Type Twin Peak Type
Isolated Peak
Type

READING HISTOGRAMS
A. General Type
Shape symmetrical (Bell shaped). If your vendor has less variability but
centre is shifting you can help him to do right setting.
B. Bimodal or Twin Peak Type
Two Distributions with widely different mean values mixed.
C. Comb Type Multimodel
Number of units of data included in class varies from class to class.
Rounding off. Incorrect least count of measurement system
D. Positive Skew
Occurs when lower limit is controlled either theoretically or by
specification value or when values lower than certain value do not occur
E. Left Hand Precipice Type
100% screening has been done because of low process capability or when
positive skewness becomes more extreme. (Check your vendor if in receipt
supply having such pattern)
F. Plateau Type
Mixture of several distributions having different mean values, or 100%
screening on both sides

EXERCISE
Given below are 100 observations taken in microns of the surface finish of 100 machined
tubes.
24 33 19 19 21
24 24 12 20 27
28 15 23 23 21
23 27 27 27 25
24 27 31 16 20
23 27 24 27 30
27 15 16 17 22
27 24 19 31 23
29 31 24 21 22
24 32 20 27 20
19 15 19 22 29
19 27 27 19 27
31 17 21 20 20
12 23 27 24 25
29 19 23 21 31
15 23 27 24 24
23 16 27 20 21
15 32 23 27 24
34 23 19 22 30
25 24 20 16 27
Prepare Frequency table, plot histogram.
Calculate mean and standard deviation

49
Normal Distribution
x
f(x)
•Frequency is the highest in the middle and becomes gradually lower towards the tail.
•It is symmetrical
It is denoted by N (s

 : The centre of the distribution (the mean)
s : The spread of the distribution(the standard deviation)
To obtain a probability in a normal distribution, we standardize by transforming x to a
variable, u= x-
s , We then have a standard measure u, which is distributed as the
standard normal distribution N(0, 12
). The normal distribution table gives probabilities in the
standard normal distribution.
s :- 68.3% of area
2s :- 95.4% of area
3s :- 99.7% of area

50
Process Capability Index
After Histogram shows that it follows normal distribution, a study of
process capability is often undertaken. This is to find out whether the process
can meet specifications or not
Both-sided specifications (SU and SL)
CP = SU - SL/6s
One-sided specification (SU or SL)
CP = SU - x /3s
Evaluation of process:
1) 1.33  CP Satisfiable enough
2) 1.00  CP  1.33 Adequate
3) CP  1.00 Inadequate

DIFFERENCE BETWEEN Cp & Cpk
1. Cp is a ratio of tolerance and six sigma.
It does not talk about process setting. This can be
appreciated that even if variability is small & setting is
out we will have Cp very high. This is therefore not an
effective indicator.
Even though process setting may be totally out, Cp value
could be well above 1.33. Therefore, Cp can be best
described as process potential index.
2. Cpk takes care of setting as well as
variation. Therefore Cpk describes the actual condition

52
Graphs
Graphs are among the simplest and best techniques to analyze and
display data for easy communication.
Various types of graphs generally used are shown below which are
self explanatory.
Y e a r R e j C o s t
1 9 9 6 5 0
1 9 9 7 4 5
1 9 9 8 7 0
0
2 0
4 0
6 0
8 0
1 9 9 6 1 9 9 7 1 9 9 8
Y e a r
R
e
j
.
c
o
s
t
M onth Rej
A pr 0.2
M ay 0.6
Jun 0.2
Jul 0.2
A ug 0.15
S ep 0.2
0
0.2
0.4
0.6
0.8
Apr May Jun Jul Aug Sep
Month
Rejection
%age
Rej
Bar chart Trend chart

53
OTHERS
5.56%
RBS STRG.
ASSY.
10.83%
R&P ASSY.
17.62%
POW ER
STRG.
4.92%
AXLE ASSY.
28.67%
PROP.SHAFT
ASSY.
6.15%
COLUMN
ASSY.
26.25
Pie-chart
Graphs…contd

54
Control Charts
What: A control chart is a line graph used to display
variation on time ordered fashion. A centerline and control
limits are placed on the graph to help analyze the pattern of
the data.
Why:
•To separate common causes from special causes of
variation.
•To help assign causes of variation.
When : Measuring control characteristics.
Where: At the earliest possible point in the manufacturing
process.

55
How :
•Define process parameter to be measured.
•Define wherein the process the control characteristics will
be measured.
•Select where control chart is to be used.
•Determine sample size and frequency.
•Take measurements.
•Plot measurements on graph.
•Connect dots.
•After 20 plot points calculate center-line and control limits.
•Analyze pattern for special cause of variation.
Control Charts

56
Control Charts……contd..
•Chance Cause
•Assignable Cause
•Upper Control Limit
•Lower Control Limit
•Upper Specification Limit
•Lower Specification Limit

57
x – R Chart:
30
50
40
20
0
60
40
20
x
R
UCL ( x + A2R )
LCL ( x - A2R )
x
R
UCL ( D4 R )
LCL ( D3 R )

58
Coefficients for x-R Charts
Size of Sub-group X-Chart R Chart R Chart R Chart
n A2 D3 D4 d2
2 1.880 - 3.267 1.128
3 1.023 - 2.575 1.693
4 0.729 - 2.282 2.059
5 0.577 - 2.115 2.326
6 0.483 - 2.004 2.534

59
Other Charts:
pn Chart Number of Defective
p Chart Fraction Defective
c Chart No. of Defects on a
fixed sized Product
u Chart No. of Defects on a
varying sized product

60
How to Read Control Charts
1. Out of Control Limits: Points outside the limits
2. Run: Continuously on one side of center line
• Seven-Point length of run is abnormal
• 10 Out of 11 consecutive points on one side
3. Trend: Continuous upward or downward curve

61
How to Read Control Charts
4. Approach to the Control Limits
• Two out of three points occur outside of 2-sigma
limits is abnormal
5. Approach to the Center Line
• When most of the points are within central 1.5-sigma
lines, this is also abnormal. It indicates mixing odd
data in sub-groups
6. Periodicity
• When the curve repeatedly shows an up and down
trend for almost same interval, this is also abnormal

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