Tqm3 ppt

MG 1401 TOTAL QUALITY MANAGEMENT

3. Statistical Process Control
2010-2011

Statistical Process Control
SPC is an
effective system for
controlling the
process parameters by
comparing it with
standards and take
corrective action if there is any
deviation by employing
statistical methods.

SPC may be used to cover
all uses of
statistical techniques for the
analysis of data that may be
applied in the
control of
product
quality


Statistical techniques
1. The seven tools of quality used by the quality circles
SEVEN QUALITY CONTROL TOOLS
(or) OLD SEVEN TOOLS
2. Control charts
Control charts for Variables ( X and R charts) and
Process Capability
Control charts for Attributes
- Defectives (p and np charts)
- Defects ( c and u charts )
3. Concept of Six Sigma
4. Management tools-
New seven management tools

The Total Statistical Process Control (TSPC) System

The seven tools of Quality- (Old) Q- 7 tools

SEVEN QUALITY CONTROL TOOLS
(or) OLD SEVEN TOOLS

1. Check Lists/ Check sheets
2. (Frequency) Histograms or Bar Graphs
3. Process flow diagrams / Charts
4. Cause and Effect, Fishbone, Ishikawa Diagram
5. Pareto Diagrams
6. Scatter Diagrams / Plots
7. Control Charts

The seven tools of Quality ( Q- 7 tools)
S.No
Tools Problem Solving step
1 Check Lists/ Check How often it is For finding faults
sheets done?
2 (Frequency) What do variations For identifying
Histograms or Bar look like? problems
Graphs
3 Process flow What is done? For understanding
diagrams / Charts the “mess”
4 Cause and Effect, What cause the For generating ideas
Fishbone, Ishikawa problem?
Diagram
5 Pareto Diagrams Which are the big For identifying
problems? problems
6 Scatter Diagrams / What are the For developing
Plots relationships solutions
between factors?
7 Control Charts Which variations to For implementation
control and how?

Check sheets/tally sheet (Data collection sheet)

the intent and
purpose of
collecting data is to either
control the
production process, to see the
relationship between
cause-and-effect, or for the
continuous improvement of those
processes that
produce any
type of defect or
nonconforming product.

Check Sheet –
collecting data to
compile in such a way as to be
easily used, understood and

analyzed automatically.
- as it is being completed, actually becomes
a graphical representation of the data you are collecting,
- thus
you do NOT need any computer software, or spreadsheet
to record the data.
- it can be simply done with pencil and paper!
- is a
data recording form that has been designed to
readily interpret results from the
form itself.
- needs to be designed for the specific data it is to gather.


- used for the collection of
quantitative or
qualitative repetitive data.
- adaptable to
different data gathering situations.
- minimal interpretation of results required.
- easy and quick to use.
- no control for various forms of bias –
exclusion,
interaction,
perception,
operational,
non-response,
estimation.

CHECK SHEET (or)
DEFECT CONCENTRATION DIAGRAM
DESCRIPTION WHEN TO USE
A check sheet is a When
structured, data can be
observed and
prepared form for
collecting and collected repeatedly by the
analyzing data. same person or at the
This is a same location.
generic tool that can be When
adapted for a collecting data on the
frequency or
wide variety of
patterns of
purposes
events, problems,
defects, defect location,

defect causes, etc.
When
collecting data from a

Check sheet
(continuous data use) No.___________
741

PRODUCT ION CHECK SHEET

Product Name_________________________________
Alternator Pulley Date_________________________________
12- 02- 02
Usage________________________________________
Pulley Bolt Torque Factory_______________________________
Church Street
Specification__________________________________
2.2 +/- .5 Section Name__________________________
SI Line
No. of Inspections______________________________
185 Data Collector__________________________
Sam The Man
Total Number__________________________________
185 Group Name___________________________
Lot Number___________________________________
1631 Remarks:_____________________________

Dimensions 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 3.1 3.2

SpecUSL
SpecLSL
40

35

30

25

XXXXX
20
XXXX

XX

XX
XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX
15 X X
XXX

XXX
XX
XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX
10

XXX
XX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX

XXXXX
XXXXX

XXXXX
5 X
XX

XX
0 X X
TOTAL
FREQUENCY 1 2 7 13 10 16 19 17 12 16 20 17 13 8 5 6 2 1

Histogram or Bar Graph
The word histogram is derived from Greek:
- histos 'anything set upright‘
(as the masts of a ship, the bar of a loom, or the vertical bars of
a histogram);
- gramma 'drawing, record, writing'.
A generalization of the histogram is
kernal smoothing techniques.
This will construct a very smooth
probability density function from the supplied data
- is a graphic summary of variation in a set of data.
- it enables us to see
patterns that are
difficult to see in a simple table of numbers.
- can be analyzed to draw conclusions about the data set.
- continuous variable is clustered into categories and the value
of each cluster is plotted to give a series of bars as above.
- without using some form of graphic this kind of
problem can be
difficult to analyze, recognize or identify.

Histogram
In statistics, a
histogram is a
graphical display of tabulated
frequencies.
It shows what proportion of cases fall into
each of several categories.
A histogram differs from a bar chart in that it is the
area of the bar that denotes the
value,
not the height, a
crucial distinction when the categories are
not of uniform width
The categories are usually specified as
non-overlapping intervals of some variable.
The categories (bars) must be adjacent.

Histogram or Bar Graph
•
H or B

Histogram

Grouping a set of measurements into a Histogram

Histogram shapes

Low with gaps Isolated-peaked

High with
few bars Cog-toothed (or comb)

Skewed
(this is positive;
negative skew Plateau
has tail to right)

Exponential Edge-peaked

missing
bars

Dual-peaked
(bimodal) Truncated

Bar chart

Using the Bar Chart in problem-solving

Numbers into bars

.

Pie chart

Band Chart

Flow Charts

• Pictures,
• symbols or
• text coupled with lines,
• arrows on lines show direction of flow.
• enables modeling of processes;
• problems/opportunities and decision points etc.
• develops a common understanding of a process by those
involved.
• no particular standardization of symbology,
• so communication to a different audience may require
considerable time and explanation.

.

Basic Flowchart elements

Decisions in Flowcharts

.

Continuing Flowcharts across pages

Delay symbol
Sub processes

Cause & Effect diagram
Cause and Effect ,
Fishbone,
Ishikawa Diagram

- is the brainchild of
Kaoru Ishikawa, who pioneered
quality management processes in the
Kawasaki shipyards, and in the process
became one of the
founding fathers of DR. KAORU ISHIKAWA (1915–1989)
modern management.
Disciple of Juran & Feigenbaum.
TQC in Japan, SPC,
- is used to Cause &Effect Diagram, QC.

explore all the potential or
real causes (or inputs) that result in a
single effect (or output).

(also called Ishikawa or fishbone chart )

DESCRIPTION WHEN TO USE
- identifies - When identifying
many possible causes possible causes for a
for an problem.
effect or - especially when a
problem. team’s thinking tends to
-can be used to fall into
structure a ruts
brainstorming
session.
- immediately sorts
ideas into DR. KAORU ISHIKAWA (1915–1989)
useful categories.
Disciple of Juran & Feigenbaum.
TQC in Japan, SPC,
Cause &Effect Diagram, QC.

Causes are arranged according to their level of
importance or detail, resulting in a
depiction of relationships and
hierarchy of events.
- This can help you search for
root causes,
identify areas where there may be
problems, and
compare the
DR. KAORU ISHIKAWA (1915–1989)
relative importance of
different causes. Disciple of Juran & Feigenbaum.
TQC in Japan, SPC,
- Causes in a Cause &Effect Diagram, QC.
cause & effect diagram are frequently arranged into
four major categories.
While these categories can be anything, you
will often see:
• manpower, methods, materials, and machinery
(recommended for manufacturing)
• equipment, policies, procedures, and people
(recommended for administration and service).


• is a method for analyzing process dispersion.
• purpose is to relate causes and effects.
• three basic types:
1. Dispersion analysis,
2. Process classification and
3. Cause enumeration.
Effect = problem to be resolved, opportunity to be grasped,
result to be achieved.
• excellent for capturing team brainstorming output and for
filling in from the 'wide picture'.
• helps organize and relate factors, providing a sequential view.
• deals with time direction but not quantity.
• can become very complex.
• can be difficult to identify or
demonstrate interrelationships.


This fishbone diagram was drawn by a manufacturing team to try
to understand the source of periodic iron contamination.
The team used the six generic headings to prompt ideas.
Layers of branches show thorough thinking about the causes of the problem.

(Standard )

Pareto diagrams

• Pareto diagrams are
named after Vilfredo Pareto,
• an Italian sociologist and economist,
who invented this method of informationAlfredo Pareto
(1848-1923) (Europe)
presentation toward the end of the 19th century.
• The chart is similar to the histogram or bar chart, except
that
• the bars are arranged in decreasing order from left to
right along the abscissa.
• The fundamental idea behind the use of Pareto diagrams
• for quality improvement is that the first few (as presented
on the diagram) contributing causes to a problem usually
account for the majority of the result.
• Thus, targeting these "major causes" for elimination results
in the most cost-effective improvement scheme

Pareto diagrams

Pareto Principle

• The Pareto principle suggests that
most effects come from relatively few causes. Alfredo Pareto
• In quantitative terms: (1848-1923) (Europe)
• 80% of the problems come from 20% of the causes
(machines, raw materials, operators etc.);
• 80% of the wealth is owned by 20% of the people etc.
• Therefore
effort aimed at the right 20% can solve 80% of the
problems.
• Double (back to back) Pareto charts can be used to compare
'before and after' situations.
• General use,
to decide where to apply initial effort for maximum effect.

Pareto diagrams

Alfredo Pareto
(1848-1923) (Europe)

Pareto Chart (or)
Pareto diagram (or)
Pareto analysis

A Pareto chart is a bar graph.
The lengths of the bars represent
frequency or cost
(time or money), and are arranged with Alfredo Pareto
(1848-1923) (Europe)
longest bars on the left and the
shortest to the right.
To identify the ‘VITAL FEW FROM TRIVIAL MANY’ and to
concentrate on the vital few for improvement.
A Pareto diagram indicates which problem we should solve first in
eliminating defects and improving the operation.
The Pareto 80 / 20 rule
80 % of the problems are produced by

20 % of the causes.

Alfredo Pareto
(1848-1923) (Europe)

The Pareto Chart
Finding the right
Pareto Chart

Convex Pareto

Concave or
'spiky' Pareto

(clearly allows you to prioritize the action)

Prioritizing the action Alfredo Pareto
(1848-1923) (Europe)

Before and After

.

The Sub-Pareto Chart

The Pareto Curve

Scatter diagrams

• are used to study

possible relationships between two
variables.
• Although these diagrams
cannot prove that

one variable causes the other, they do
indicate the existence of a
relationship, as well as the
strength of that relationship.
• is composed of a
horizontal axis containing the
measured values of

one variable and
a vertical axis representing the

measurements of the

Scatter Diagram (or) Scatter plot (or) X–Y graph
• The purpose of the scatter diagram is
to display what happens to one variables when another variable is
changed.
• is used to test a theory that the two variables are related.
• The type of relationship that exits is
indicated by the slope of the diagram.

• The scatter diagram graphs
pairs of numerical data, with
one variable on each axis, to look for a
relationship between them. If the
variables are correlated, the points will
fall along a line or curve.
The better the correlation, the

tighter the points will

hug the line.

Scatter Diagram
Types

Positive

Negative
Degrees of correlation

None High
Curved

Low Perfect
Part-linear

Control chart
• In statistical process control, the

control chart, also known as the
'Shewhart chart' or
'process-behaviour chart' is a tool used to determine
whether a manufacturing or
business process is in a state of
statistical control or not.

• If the chart indicates that the
DR. WALTER A. SHEWHART
process is (1891–1967)
currently under control then it can be used with -TQC &PDSA
confidence to
predict the
future performance of the
process.

Control chart
• If the chart indicates that the
process being monitored is
not in control, the pattern it reveals can help

determine the

source of variation to be
eliminated to
bring the
process back into control.
• A control chart is a specific kind of DR. WALTER A. SHEWHART
run chart that allows significant change to be (1891–1967)
-TQC &PDSA
differentiated from the
natural variability of the process.
• This is key to
effective process control and
improvement.

Control chart
• They enable the
control of distribution of variation rather than
attempting to control each individual variation.
• Upper and
lower control and
tolerance limits are calculated for a
process and
sampled measures are regularly plotted about
a central line between the two sets of limits.
• The plotted line corresponds to the
stability/trend of the process.
• Action can be
taken based on trend rather than on
individual variation.
• This prevents
over-correction/compensation for
random variation, which would lead to many rejects.
DR. WALTER A. SHEWHART
(1891–1967)
-TQC &PDSA

Control charts

Mean and Control Limits

How control limits catch shifts

Additional limit lines

Stratification Analysis
• Stratification Analysis determines the extent of the
problem for relevant factors.
• o        Is the problem the same for all shifts?
• o        Do all machines, spindles, fixtures have the same problem?
• o        Do customers in various age groups or parts of the country have
similar problems?
• The important stratification factors will vary with each
problem, but most problems will have several factors.
• Check sheets can be used to collect data.
• Essentially this analysis seeks to develop a pareto diagram
for the important factors.

Stratification Analysis

• The hope is that the extent of the problem will not
be the same across all factors.
• The differences can then lead to identifying root cause.
• When the 5W2H and Stratification Analysis are
performed, it is important to consider a number of
indicators.
• For example, a customer problem identified by warranty
claims may also be reflected by various in-plant indicators.
• Sometimes, customer surveys may be able to define
the problem more clearly.
• In some cases analysis of the problem can be
expedited by correlating different problem
indicators to identify the problem clearly

Stratification (or) Flowchart (or) Run chart
• Stratification is a technique used in combination with other
data analysis tools. When data from a variety of sources or
categories have been lumped together, the meaning of the
data can be impossible to see

• When to Use
• Before collecting data.
• When data come from several sources or conditions, such
as shifts, days of the week, suppliers or population groups.
• When data analysis may require separating different
sources or conditions.

Benefit from stratification.

• Always consider before collecting data whether
stratification might be needed during analysis. Plan to
collect stratification information. After the data are
collected it might be too late.
• On your graph or chart, include a legend that identifies
the marks or colors used.

Data Analysis
• What is Data Analysis
• Data analysis is statistics + visualization + know-how
• Many of the methods for
        data analysis are based on
    multivariate statistics, which poses an additional
problem to the beginner:
• multivariate statistics cannot be understood without
a profound knowledge of simple statistics.
• Furthermore, several
               fields in science and engineering have
developed their own nomenclature
                    assigning different names to the
                         same concepts.

Data Analysis
• Thus one has to
gather considerable knowledge and experience in
order to perform the analysis of data efficiently.
• Possible applications of statistical methods can be in the fields
of medicine, engineering, quality inspection,
election polling, analytical chemistry, physics,
gambling

• Statistics and statistical methodology as the basis of
data analysis are concerned with two basic types of
problems
• (1) summarizing, describing, and exploring the data
(2) using sampled data to infer the nature of the
process which produced the data
• The first type of problems is covered by descriptive
statistics, the second part is covered by inferential
statistics.
• Another important aspect of data analysis is the data, which
can be of two different types: qualitative data, and
quantitative data .

Data Analysis

• Qualitative data does not contain quantitative information.
• Qualitative data can be classified into categories.
• In contrast, quantitative data represent an amount of something.
• A third distinction can be made according to the
     number of variables involved in the data analysis.
• If only one variable is used, the statistical procedures are
summarized as univariate statistics.
• More than one variable result in multivariate statistics.
• A special case of multivariate statistics with
       only two variables is sometimes called bivariate statistics.

Statistical Process Control (SPC)

Measures performance of a
process
Uses mathematics (i.e., statistics)
Involves collecting,
organizing, &
interpreting data
Objective:
Regulate product quality
Used to
– Control the
process as
products are
produced
– Inspect samples of
finished products


What is a process?

Inputs PROCESS Outputs

A process can be described as a
transformation of set of
inputs into desired
outputs.

WHY STATISTICS?
THE ROLE OF STATISTICS ………

µ

LSL T USL

Statistics is the art of
collecting, classifying, presenting, interpreting and
analyzing numerical data, as well as
making conclusions about the
system from which the
data was obtained.

January 9, 2013 73

Descriptive Statistics
Descriptive Statistics is the
branch of
statistics which
most people are
familiar.

It characterizes and summarizes the
most prominent features of a
given set of data
(means,
medians,
standard deviations,
percentiles,
graphs,
tables and
charts).

January 9, 2013 74

Inferential Statistics

Inferential Statistics is the

branch of statistics that deals with

drawing conclusions about

a population based on

information obtained from

a sample drawn from that

population.

January 9, 2013 75

Statistics
MEASURES OF CENTRAL TENDENCY
Usually, the first topic in statistics is
descriptive statistics.
The mean,
median and
mode are
used to describe statistical data.
Variance and
standard deviation help to
understand how the data is spread out.
Central tendency is a
typical or
representative score.
The three measures of central tendency are the
mode,
median, and
mean.

The term "measures of central tendency" refers to
.
finding the mean, median and mode.

Mean:
Average.
The sum of a set of data divided by the number of data.
(Do not round your answer unless directed to do so.)

Median:
The middle value, or the mean of the middle two values, when
the data is arranged in numerical order. Think of a "median"
being in the middle of a highway.

Mode:
The value ( number) that appears the most.
It is possible to have more than one mode, and it is possible to
have no mode. If there is no mode-write "no mode", do not write
zero (0) .

Mode
Mode is the data
value that
occurs at a
greater frequency than the others.
Data: 1, 2, 3, 3, 3, 4, 4, 5

Mode = 3
The mode, symbolized by
Mo, is the most frequently occurring score value.
If the scores for a given sample distribution are:

32 32 35 36 37 38 3 8 39 3 9 39 40 4 0 42 45

- then the mode would be 39 because a score of 39 occurs 3 times,
more than any other score.
- The mode may be seen on a frequency distribution as the score value
which corresponds to the highest point.
- For example, the following is a frequency polygon of the data
presented above:

Statistics - Mode

3

2 2

1 1

32 36 39 42 45
scores

Statistics - Mode
A distribution may have
- more than one mode if the two most frequently occurring
scores occur the same number of times.
For example, if the earlier score distribution were modified as follows:
32 32 32 36 37 38 38 39 39 39 40 40 42 45
- then there would be two modes, 32 and 39.
- Such distributions are called bimodal.
- The frequency polygon of a bimodal distribution is presented
below.

Statistics - Mode

3 3

32 39

Statistics - Mode

In an extreme case there may be no unique mode, as in the case of
a rectangular distribution.
The mode is not sensitive to extreme scores.
Suppose the original distribution was modified by changing the last
number, 45, to 55 as follows:
32 32 35 36 37 38 38 39 39 39 40 40 42 55
The mode would still be 39.

In any case,
the mode is a quick and dirty measure of central tendency.

Quick, because it is easily and quickly computed.

Dirty because it is not very useful; that is,
- it does not give much information about the distribution.

Statistics - Median
Median
The median is the
exact middle value of a
set of data values that have been sorted from the
lowest value to
highest.
If the number of data values
even, then the
median is the
average of the
two middle values.
Examples:
Data: 1, 2, 3, 4, 5
Median: 3

Data: 1, 2, 3, 4, 5, 6
Median: 3.5

Statistics - Median
The median, symbolized by
Md, is the score value which
cuts the distribution in half, such that half the scores fall above
the median and half fall below it.
Computation of the median is relatively straightforward.
The first step is to
rank order the scores from
lowest to highest.
The procedure branches at the next step:
- one way if there are an odd number of scores in the sample
distribution,
- another if there are an even number of scores.
If there is an odd number of scores as in the distribution below:
32  32  35  36  36  37  38
                                                  38
                                                          39  39  39  40  40  45  46
- then the median is simply the middle number.
In the case above the median would be the number 38, because there
are 15 scores all together with
7 scores smaller and 7 larger.

Statistics - Median

• If there is an even number of scores, as in the distribution below:
     32  35  36  36  37  38
                                           38 39
                                                           39  39  40  40  42  45
• then the median is the midpoint between the two middle scores:
• in this case the value 38.5.
• It was found by adding the two middle scores together and dividing
by two (38 + 39)/2 = 38.5.
• If the
two middle scores are the same value then the
                      median is that value.
• In the above system,
no account is paid to whether there is a
               duplication of scores around the median.
• In some systems a slight correction is performed to correct for
grouped data, but since the correction is slight and the data is
generally not grouped for computation in calculators or computers, it
is not presented here.

Statistics - Median

The median, like the mode, is
   not effected by extreme scores, as the following
distribution of scores indicates:
     32  35  36  36  37  38
                                           38 39
                                                         39  39  40  40  42  55
The median is still the value of 38.5.
The median is not as
    quick and
    dirty as the
    mode, but
    generally it is
    not the
preferred measure of
    central tendency.

Statistics – The Mean

The mean,
symbolized by ,
is the sum of the scores divided by the number of scores.
The following formula both defines and describes the procedure for
finding the mean:

where X is the sum of the scores and
N is the number of scores.

Mean
The mean most frequently used is the
arithmetic mean, which is the same as the

average, although the
        geometric mean is
        used also
        at times.
It is the arithmetic mean that is referred to when the word mean is
used by itself.
Expected value is another way of saying the mean.
mean =    sum of data values / number of data values

         mean μ =    (1 + 2 + 3) / 3    =    6 / 3    =   2

The lower case Greek letter μ is used to represent the mean.
If the mean is from a sample of data, then
          x is used to represent the sample mean.
Also, variables and Sigma notation is used to write the
     general form of the mean.

The mean
Application of this formula to the following data
  32  35  36  37  38  38  39  39  39  40  40  42  45
yields the following results:

Use of means as a way of describing a set of scores is fairly
common;
•      batting average,
•      bowling average,
•      grade point average, and
•      average points scored per game
              are all means.
Note the use of the word "average" in all of the above terms.
In most cases when the term "average" is used, it refers to the
mean, although not necessarily.
When a politician uses the term "average income", for example,
he or she may be referring to the mean, median, or mode.

The mean is sensitive to extreme scores.
For example, the mean of the following data is 39.0,
somewhat larger than the preceding example.
32  35  36  37  38  38  39  39  39  40  40  42  55
In most cases the
mean is the
     preferred measure of
central tendency, both as a
description of the
     data and as an
estimate of the
parameter.
In order for the mean to be meaningful, however, the
     acceptance of the
interval property of
     measurement is
     necessary.
When this property is obviously violated, it is inappropriate and
misleading to compute a mean.

Kiwi Bird Problem

As is commonly known,
              KIWI-birds are native to
                                                      New Zealand.
They are born
exactly one foot tall and grow
                  in one foot intervals.
That is, one moment they are one foot tall and the next they are two
feet tall. They are also very rare.
An investigator goes to New Zealand and
            finds four birds.
The
                mean of the heights of four birds is 4, the
                                 median is 3, and the
                                                mode is 2.
What are the heights
of the four birds?
• Hint - examine the constraints of the mode first, the median second,
and the mean last.

Statistics
• Skewed Distributions and
Measures of Central Tendency
• Skewness refers to the asymmetry of the distribution, such that
a symmetrical distribution exhibits
no skewness. In a symmetrical distribution the
mean, median, and mode all fall at the same point,
as in the following distribution.

Statistics

• An exception to this is the case of a
bi-modal symmetrical distribution.
• In this case the mean and the median fall at the same point,
while the two modes correspond to the two highest points of
the distribution. An example follows:

Statistics
• A positively skewed distribution is asymmetrical and points in
the positive direction. If a test was very difficult and almost
everyone in the class did very poorly on it, the resulting distribution
would most likely be positively skewed.

• In the case of a positively skewed distribution, the mode is
smaller than the median, which is smaller than the
mean. This relationship exists because the mode is the point on
the x-axis corresponding to the highest point, that is the score
with greatest value, or frequency. The median is the point on the
x-axis that cuts the distribution in half, such that 50% of the
area falls on each side. Mo

Statistics
• The mean is the balance point of the distribution. Because
points further away from the balance point change the center of
balance, the mean is pulled in the direction the distribution is
skewed. For example, if the distribution is positively skewed,
the mean would be pulled in the direction of the skewness, or
be pulled toward larger numbers.

• One way to remember the order of the mean, median, and
mode in a skewed distribution is to remember that the mean is
pulled in the direction of the extreme scores. In a
positively skewed distribution, the extreme scores are larger, thus
the mean is larger than
the median.

Statistics
• A negatively skewed distribution is asymmetrical and points
in the negative direction, such as would result with a very easy test.
On an easy test, almost all students would perform well and only a
few would do poorly.

• The order of the measures of central tendency would be the
opposite of the positively skewed distribution, with the mean
being smaller than the median, which is smaller than
the mode.

Statistics
MEASURES OF VARIABILITY
• Variability refers to the spread or dispersion of scores.
• A distribution of scores is said to be highly variable if the
scores differ widely from one another.
• Three statistics will be discussed which measure variability: the
range, the variance, and the standard deviation.
• The latter two are very closely related.
Range
Range is the highest data value minus the lowest data
values.
Data: 1, 2, 3, 4, 5, 6, 7
Highest Data Value: 7
Lowest Data Value: 1 Range: 7 - 1 = 6
• It is a quick and dirty measure of variability, although when a test
is given back to students they very often wish to know the range of
scores.
• Because the range is greatly affected by extreme scores,
it may give a distorted picture of the scores.

Statistics
• The following two distributions have the same range, 13, yet appear
to differ greatly in the amount of variability.
• Distribution 1 32 35 36 36 37 38 40 42 42 43 43 45
• Distribution 2 32 32 33 33 33 34 34 34 34 34 35 45
• For this reason, among others, the range is not the most
important measure of variability.

Variance
• Variance is used to measure
how far the data is away from the mean.
• The distance of the data point from the
mean is a deviation.
• The deviations are added together to get a value
representing all the deviations together.
• However, since some deviations can be negative, the
total could be zero.
• To account for this, the deviations are squared and then
added together.
• When divided by the number of
deviations,
the result is
variance.

Statistics
Standard Deviation
• The standard deviation is just
the square root of the variance.
• A statistic is an algebraic expression combining scores into a single
number.
• Statistics serve two functions:
• they estimate parameters in
population models and they describe the
              data.
• i.e., Population variance, standard deviation
Sample variance, standard deviation

• The variance, symbolized by
                "s2", is a measure of variability. Th
             standard deviation, symbolized by
                "s", is the
positive square root of the variance.

Statistics
• Variance :formula:

• Note that the variance could almost be the
average squared deviation around
the mean if the expression were divided by N rather than N-1.
• It is divided by N-1, called the degrees of freedom (df), for
theoretical reasons.
• If the mean is known, as it must be to compute the numerator of the
expression, then only N-1 scores that are free to vary.
• That is if the mean and N-1 scores are known, then it is possible to
figure out the Nth score.
• One needs only recall the KIWI-bird problem to convince oneself
that this is in fact true.

Statistics
• The formula for the
variance presented above is a definitional formula, it defines
what the variance means.
• The variance may be computed from this formula, but in
practice this is rarely done.
• The computation is performed in a number of steps, which are
presented below:

Steps
1. Find the mean of the scores.
2. Subtract the mean from every score.
3. Square the results of step 2.
4. Sum the results of step 3.
5. Divide the results of step 4 by N-1.
6. Take the square root of step 5.
7. The result at step 5 is the sample variance,
at step 6, the sample standard deviation.

Measures of dispersion
Quartiles
If we divide a cumulative frequency curve into
quarters,
             the value at the lower quarter is referred to as
the lower quartile,
             the value at the middle gives the median and the
value at the upper quarter is the upper quartile.
A set of numbers may be as follows:
         8, 14, 15, 16, 17, 18, 19, 50.
        The mean of these numbers is 19.625 . However,
the extremes in this set (8 and 50) distort the range.
        The inter quartile range is a method of measuring
the spread of the numbers by finding the middle
50% of the values.
         It is useful since it ignore the extreme values. It is a
method of measuring the spread of the data.
The lower quartile is (n+1)/4 th value
    (n is the cumulative frequency, ie 157 in this case)
and
        the upper quartile is the 3(n+1)/4 the value.
        The difference between these two is the inter
quartile range (IQR).
In the above example,
         the upper quartile is the 118.5th value and
         the lower quartile is the 39.5th value.
If we draw a cumulative frequency curve, we see that
the lower quartile, therefore, is about 17 and
        the upper quartile is about 37.
Therefore the IQR is 20 (bear in mind that this is a rough
sketch- if you plot the values on graph paper you
will get a more accurate value).

Measures of dispersion measure how spread out a set of data is.
Variance and Standard Deviation
The formulae for the variance and standard deviation are given below.
m means the mean of the data.
.
Variance = s2 = S (xr – m)2
n
The standard deviation, s, is the square root of the variance.
What the formula means:
(1) xr - m means take each value in turn and subtract the mean from each value.
(2) (xr - m)² means square each of the results obtained from step (1).
This is to get rid of any minus signs.
(3) S(xr - m)² means add up all of the results obtained from step (2).
Example: (4) For variance divide step (3) by n, which is the number of numbers
Find the variance and standard deviation of the following numbers: the answer to step (4).
(5) For the standard deviation, square root
         1, 3, 5, 5, 6, 7, 9, 10 .                 The mean = m = 46/ 8 = 5.75
x          (Step 1): (Step 2):
      xr - m
1 (1 - 5.75) -4.75 (xr - m)² (Step 4):  n = 46, therefore
3 (3 - 5.75) -2.75 22.563       variance = 61.504/ 46 = 1.34 (3sf)
5 (5 - 5.75) -0.75    7.563 (Step 5):
5 (5 - 5.75) -0.75     0.563        standard deviation = 1.16 (3sf)
6 (6 - 5.75)   0.25    0.563
7 (7 - 5.75)   1.25    0.063
9 (9 - 5.75)   3.25    1.563
10 (10 - 5.75)   4.25 10.563
46              18.063
(n) (Step 3): S(xr - m)² 61.504

Grouped Data
There are many ways of writing the formula for the standard deviation. The one above is for a
population of numbers. The formula for the standard deviation when the data is grouped is:
.

Example:
The table shows marks (out of 10) such questions, it is often easiest to
In
obtained by 20 people in a test set your working out in a table:
Mark (x) Frequency (f) fx fx²
1 0 0 0
2 1 Sf = 20
2 4
3 1 3 9
Sfx = 118
4 3 12 48 Sfx² = 764
5 2 10 50 variance = Sfx² - ( Sfx )²
6 5 30 180 Sf ( Sf )
7 5 35 245 = 764 - (118)²
8 2 16 128 20 ( 20 )
9 0 0 0 = 38.2 - 34.81 = 3.39
10 1 10 100
Work out the variance of this data.
20 118 764

Population Vs. Sample (Certainty Vs. Uncertainty)

A sample is just a subset of all possible values

sample
population

Since the sample does not contain all the possible values, there
is some uncertainty about the population.
Hence any statistics, such as mean and standard
deviation, are just estimates of the true population
parameters.

January 9, 2013 107

Population and sample
Population is the entire (complete) collection of all the
measurements of an observed quality characteristic
        -variation pattern is not known
A Sample is a collection of measurements selected from some large
source or population  - i.e., a part of the population
Population: Smooth curve

      (‘) prime symbol is used to identify parameters
Parameters: mean (μ),
population standard deviation (σ ).

- has finite number of items  e.g., production of shafts in a day
- it is impossible to measure all the population
  - the conclusion about the population is derived from the
mean and standard deviation of the sample
Types:    Finite population             - finite number
               Infinite population           - infinite number
               Existent population         - concrete individuals
               Hypothetical population  - possible ways- population of head
                and tail obtained by tossing a coin an infinite number of times

Population and sample
Sample:
Statistic – average (x), and sample standard deviation (s)
Histogram

To analyze and draw conclusion about the universe, a sample is
selected at random to represent the population
- small section selected is - sample
- process of such selection is - sampling

Normal curve

-the normal curve is the most important frequency curve
- is also known as Gaussian curve and probability curve
- is symmetrical
- is unimodal
- is bell shaped distribution with mean, median, and mode having
   the same value.
-The normal distribution is fully defined by the population mean
and population
50.00%
  standard deviation
68.26%

95.45%

99.73%
-∞ +∞
-3σ -2σ -1σ +1σ +2σ +3σ
-0.6745σμ +0.6745σ
Area under the normal distribution curve

Normal curve
The mean (μ), and standard deviation (σ ) are the
population parameters
The mean (x), and standard deviation (s) are for the
sample quantity drawn from the population
For practical usage
It is necessary to convert from mean values and standard deviations
other than zero and one respectively
This procedure called normalizing involves substituting
z = x – μ thus the values read from the table represent the area
σ
∞
under normal curve from – to z = x - μ
σ

σ= 1.5
Normal curves with different standard
deviations but identical means

σ= 3.0

σ= 4.5

5 8 11 14 17 20 23 26 29 32 35

Variance Shown in a Probability Distribution

Control Chart (or) Statistical process control

VARIATIONS
• Different types of control charts can be used, depending upon the
type of data.
• The two broadest groupings are for
variable data and
attribute data.
• Variable data are measured on a continuous scale.
For example: time, weight, distance or temperature

can be measured in fractions or decimals.
The possibility of measuring to
greater precision defines variable data.

Attribute data
are counted and
cannot have fractions or decimals.
Attribute data arise when you are determining only the
presence or absence of something:
success or failure,
accept or reject,
correct or not correct.

For example,
a report can have
four errors or five errors,
but it cannot have
four and a half errors.

Control Chart
• is a graphical representation of the collected information
- information may be measured quality characteristics
• detects the variation in the process and
• warns if there is any deviation from the specification

Essential features of a control chart

Upper Control Limit
Variable Values

Central Line

Lower Control Limit

Time

Control Chart
Purposes
• Show changes in data pattern
– e.g., trends
• Make corrections before process is out of control
• Show causes of changes in data
– Assignable causes
• Data outside control limits or trend in data
– Natural causes
• Random variations around averag

In the charts,
• If all the points (sample averages and ranges) are
within the control limits,
- then the process is said to be in “Statistical control”
• If any one point or more in the control charts go
outside the control limits,
- then the process is said to be “out of control”

Quality Characteristics

Variables Attributes
1. Characteristics that you 1. Characteristics for which you
measure, focus on defects
e.g., weight, length

2. May be in whole or
2. Classify products as either
in fractional numbers ‘good’ or ‘bad’, or
count # defects
– e.g., radio works or not

3. Continuous random variables 3. Categorical or discrete random
variables

Control Chart Types

Control Charts

Variables Attributes
Charts Charts

R X p & np c&u
Chart Chart Chart Chart

Control Chart
Classification:
For variables- X and R charts
• Measures where the metric consists of
a number which indicates a precise value is called
Variable data.
– Time
– Miles/Hr
For variables
Sample average
Range
Grant average
Grant range
Control limits

X chart R chart
- upper limit - upper limit
- lower limit - lower limit
Both the charts should be plotted together
If the sub group size is 6 or less LCLR = 0

Variables charts

– X and R chart (also called averages and range chart)
– X and s chart
– chart of individuals (also called X chart, X-R chart, IX-
MR chart, Xm R chart, moving range chart)
– moving average–moving range chart (also called MA–
MR chart)
– target charts (also called difference charts, deviation
charts and nominal charts)
– CUSUM (also called cumulative sum chart)
– EWMA (also called exponentially weighted moving
average chart)
– multivariate chart (also called Hotelling T2)

X Chart

Type of variables control chart
– Interval or ratio scaled numerical data
• Shows sample means over time
• Monitors process average and tells whether changes have occurred.
These changes may due to
1. Tool wear
2. Increase in temperature
3. Different method used in the
second shift
4. New stronger material

• Example: Weigh samples of coffee & compute means of
samples; Plot

R Chart

Type of variables control chart
– Interval or ratio scaled numerical data
• Shows sample ranges over time
– Difference between smallest & largest values in
inspection sample
• Monitors variability in process,
• it tells us the loss or gain in dispersion.
This change may be due to:
1. Worn bearing
2. A loose tool
3. An erratic flow of lubricant to machine
4. Sloppiness of machine operator
• Example:
Weigh samples of coffee &
compute ranges of samples;

Construction of X and R Charts
• Step 1: Select the Characteristics for applying a control chart.
• Step 2: Select the appropriate type of control chart.
• Step 3: Collect the data.
• Step 4: Choose the rational sub-group i.e Sample
• Step 5: Calculate the average ( X) and range R for each sample.
• Step 6: Cal Average of averages of (X) and average of range (R)
• Steps 7:Cal the limits for X and R Charts.
• Steps 8: Plot Centre line (CL), UCL and LCL on the chart
• Steps 9: Plot individual X and R values on the chart.
• Steps 10: Check whether the process is in control (or) not.
• Steps 11: Revise the control limits if the points are outside.

X Chart
Control Limits

UCL = x + A R From
x 2 Tables
LCL = x − A R
x 2

Sub group average X = (x1 + x2 +x3 +x4 +x5 ) /5

Sub group range R = Max Value – Min value

R Chart Control Limits

UCL R = D 4 R
From Tables

LCL R = D 3 R

Problem8.1 from TQM by V.Jayakumar Page No 8.5

Control Chart
Description Control charts for individual measurements
(e.g., the sample size = 1) use the moving range of two successive
observations to measure the process variability.
The combination of the X Chart for Individuals and the Moving Range chart
is often called an X and Rm or XmR Chart.

X-Bar R Chart (Mean-Range Chart)

X-Bar Sigma Chart (Mean-Sigma Chart)

X-Bar Sigma Chart with Variable Subgroup Sample Size

EWMA (Exponentially Weighted Moving Average Chart)

MA Chart (Moving Average Chart)

CuSum Chart (Tabular Cumulative Sum Chart )

Types of Control Charts for Attribute Data
Measures where the metric is composed of a classification in
one or two (or more) categories is called Attribute data.
Description Type Sample Size

Control Chart for (defectives) p Chart may change
proportion non conforming units
Control Chart for (defectives) np Chart must be constant
no. of non conforming units in a
sample
Control Chart for (defects) c Chart must be constant
no. of non conformities in a
sample
Control Chart for (defects) u Chart may Change
no. of non conformities per unit

p Chart for Attributes

(also called proportion chart)

Type of attributes control chart
– Nominally scaled categorical data
• e.g., good-bad, Yes/No
• Shows % of nonconforming items
Example: Count # defective chairs &
divide by total chairs inspected;
Plot
– Chair is either defective or not defective

p Chart
(also called proportion chart)

p = np / n
where p = Fraction of Defective
np = no of Defectives
n = No of items inspected in sub group
p = Average Fraction Defective = ∑np/ ∑n = CL

p (1 −p )
UCL p =p +z
n

p (1 −p )
LCL p =p −z
n

p Chart
Control Limits

p (1 − p )
UCL p = p + z
n z = 3 for
99.7% limits
p (1 − p )
LCL p = p − z
n

Purpose of the p Chart

Identify and correct causes of bad quality
The average proportion of defective articles submitted for
inspection, over a period.
To suggest where X and R charts to be used.
Determine average Quality Level.

• Problem 9.1 Page no 9.3 TQM by V.Jayakumar

np CHART

P and np are quiet same
Whenever subgroup size is variable, p chart is used.

If sub group size is constant, then np is used.
FORMULA: Central Line CLnp = n p
Upper Control Limit, UCLnp = n p +3√ n p (1- p )
Lower Control Limit, LCLnp = n p -3 √ n p (1- p )
Where p = ∑ np/∑n =Average Fraction Defective
n = Number of items inspected in subgroup.
• Problem No 9.11 page No 9.11 in TQM by V.Jayakumar

c Chart

• (also called count chart)
• Type of attributes control chart
– Discrete quantitative data
• Shows number of nonconformities (defects) in a unit
– Unit may be chair, steel sheet, car etc.
– Size of unit must be constant
• Example:
Count no of defects (scratches, chips etc.) in

each chair of a sample of 100 chairs;

Plot

c Chart
Control Limits

UCLc = c + 3 c Use 3 for
99.7% limits

LCLc = c − 3 c

Control Chart

• Attribute Control Chart Templates
• p-Chart (Fraction or Percent of Defective Parts, Fraction or
Percent Non-Conforming),
• np-Chart (Number of Defective Parts, Number of Non-
Conforming),
• c-Chart (Number of Defects, Number of Non-Conformities ) and
• u-Chart (Number of Defects per Unit, Number of Non-Conformities
Per Unit ).
• The p-Chart and u-Chart templates come in versions which
support variable subgroup sample sizes.

p-Chart (Percent Defective Parts, or Percent Defective Non-Conforming)

np-Chart (Number Defective Parts, or Number Non-Conforming

c-Chart (Number Defects, or Number Non-Conformities)

u-Chart (Number of Defects Per Unit, or Number of Non-Conformities per Unit)

u-Chart with Variable Subgroup Sample Size

SPC control limits at the 1-, 2- and 3-sigma levels

Process capability
• Control limits- as a function of the averages
• Specifications-
permissible variation in the
size of the part, and are therefore, for

individual values
• The specification or
tolerance limits are established by
design engineers to meet a particular
function
• The specifications have an

optional location
• The control limits,
process spread ( process capability),
distribution of averages, and

distribution of individual values are
interdependent and
determined by the

Process capability
• Even the process (average value of items) is in control, the
individual item may
not be within the limits
• So it is necessary to see whether the

process is capable of producing the items

within the specified limits
• This can be achieved by
carrying out the process capability
• Process capability is an industrial term that characterizes how
tolerance specification of a product relates to the

centering (bias) and
- variation (Process Capability standard deviation, SD or s)
of the process.
• High capability means that the

process can readily produce a product

Process capability

• Low capability means that the
process will likely produce products
outside the tolerance specifications
(i.e., defective products or defects).
• Process capability may be defined as the
minimum spread of the
specific quality characteristic measurements
• Quality characteristic will have a normal distribution with
mean μ and standard deviation σ
• The upper normal tolerance limit μ + 3 σ
• The lower normal tolerance limit μ – 3 σ
• The spread of the normal distribution between the
natural tolerance limits 6 σ, is the process capability
• If the process capability 6 σ is less than the
specification limits (USL-LSL), the process is capable,
otherwise not

Process Capability
• The process capability ratio (PCR or Cp) is the ratio between
the specification limits and the
process capability
• PCR or Cp = (USL-LSL) / 6 σ
If Cp is >1.00, the process is capable of meeting the specifications
If Cp is < 1.00, the process is not capable of meeting the
specifications
• One common measure of process capability is called
process capability index Cpk, which is calculated as
Cpk = (Tolerance specification - bias)/3SD.
- upper capability index = CpU = (USL - μ) / 3 σ
- lower capability index = CpL = (μ - LSL ) / 3 σ
- process capability index Cpk = { min. CpU, CpL }
• If the tolerance specification were 12%,
• SD 2%, and
• Bias 0.0%,
Cpk would be 2.00, which is considered the
ideal capability,
• i.e., a six-sigma process because
six multiples of the SD fit within the tolerance specification.

Process Capability
• If the tolerance were 12%, SD 4%, and Bias 0.0%,
Cpk would be 1.00,
- which is considered the minimum capability for a production
process and corresponds to a three-sigma process.
• If the tolerance were 12%, SD 2%, and Bias 3.0%,
Cpk would be 1.50.
Although this initially starts out as
a six-sigma process when there is no bias,
- the effect of a bias of 1.5 sigma actually reduces the process
capability and makes this equivalent to a four-point-five
process.
This would still be considered a good production process if
adequately controlled,
- but it would still be desirable to eliminate the bias if possible

Process Capability
Parts per Million
• Many companies now measure defects in parts per million.
• We will recall that
3 sigma deviations each side of the process mean will
encompass 99.73% of the population.
• We have been looking at
Process Capability using +- 3 sigma so we are really
looking at 99.73% of the population.
• To give us some safety, we wanted the
+- 3 sigma to fall within 75% of the tolerance.
• This equates to +- 4 sigma at 100% of the tolerance.
• If the +- 3 sigma had covered the total
tolerance 0.27% would not be encapsulated in the spread that
we were using.
• This would equate to 2,700 defective parts per million,
1,350 exceeding top limit and
1,350 failing to reach bottom limit.
• Many companies now try for figures much less than this.
• If you use +-5 sigma instead of +- 3 sigma in your calculations
you will be fairly close to 1 part per million defects provided
the process remains centralized and in control.

Capability Ratio % Total = 6 sigma / Total Tolerance
Cm = Total Tolerance / 6 sigma

Six sigma
• Six Sigma was intended to
improve the quality of processes that are already
under control –
- major special causes of process problems have been removed.
The output of these process usually follows a
Normal distribution with the process capability defined as
± 3 sigma.
The process mean will vary each time a process is executed
using different equipment, different personnel, different
materials, etc.
The observed variation in the
process mean was ± 1.5 sigma.
Motorola, one of the world’s leading manufacturers of electronic
equipments introduced in 1980s, the concept of
6 sigma process quality to enhance the quality and
reliability of the products by the then CEO, Bob Galvin.
Motorola decided
a design tolerance (specification width) of ± 6 sigma
was needed so that there will be only
3.4 ppm defects -- measurements outside the design
tolerance.
This was defined as Six Sigma quality.

Six sigma
• Since shifts or biases equivalent to 1.5s are difficult to detect
by statistical QC, a six-sigma process provides
- better guarantee that products will be produced within the desired
specifications and
- with a low defect rate.
• Another way of looking at this is that a six-sigma process can
be monitored with any QC procedure,
• e.g., with 3 SD limits and low N, and any important
problems or errors will be detected and can be corrected.
• As process capability decreases to
• five-sigma to
• four-sigma to
• three-sigma,
• the choice of QC procedure becomes more and more
important in order to detect important problems.
• Processes with lower capability may not even be controllable to a
defined level of quality!

Allowable total error, TEa,
• This latter situation is illustrated in the accompanying figure,
- where the tolerance specification is replaced by a Total
Error specification,
- which is a common form of a quality specification for a
laboratory test.
For example,
- the CLIA criteria for acceptable performance in proficiency testing
events are given in the form of an allowable total error, TEa,
- thus there is a published list of TEa specifications for regulated
analytes.
In terms of TEa,
- Six Sigma Quality Management sets
a precision goal of TEa/6 and
an accuracy goal of 1.5(TEa/6) or TEa/4.
- In terms of the industrial process capability,
the combination of the six-sigma
precision and
accuracy goals results in a Cpk of 1.5.

Laboratory TE Criteria vs Process
Capability
• Laboratories evaluate process capability when they perform method
validation studies.
• They don't calculate an index such as Cpk,
• they do combine the effects of inaccuracy and imprecision for
comparison with the allowable total error.
• Commonly used TE criteria include
• TEa > bias + 4SD,
• TEa > bias + 3SD, and
• TEa > bias + 2SD, all of which are used on a decision-making
tool called the Method Decision Chart.
• If the criterion requires that TEa > bias + 4SD,
• this corresponds to a four-sigma process if there is no bias,
• e.g., if TEa is 12%,
bias is 0%, and
SD is 3%,
Cpk would be 1.33,
which is a good production process that should be controllable to
the desired quality.

Laboratory TE Criteria vs Process
Capability
this corresponds to a three-sigma process if there is no bias,
e.g., if TEa is 12%,
bias is 0%, and
SD is 4%,
Cpk would be 1.00, which is the minimal capability needed for a
production process.
this corresponds to a two-sigma process if there is no bias,
e.g., if TEa is 12%,
bias is 0%, and
SD is 6%,
Cpk would be 0.67, which is unacceptable for production according
to industrial guidelines.
• Process performance, as evaluated by commonly used laboratory
TE criteria, does not approach the six-sigma capability desired for
industrial processes. Improvements in laboratory methods are still
needed to achieve five-sigma to six-sigma capability.

Stages or fundamentals in six sigma
the DMAIC Roadmap

DMAIC and Lean tools deployed in the
Shewhart Cycle

DMAIC six sigma approach.

• The six sigma approach for projects is
DMAIC
(define, measure, analyze, improve and control).
• These steps are the most common
six sigma approach to project work.
• Some organizations omit the D in
DMAIC because it is really management work.
• With the D dropped from
DMAIC the Black Belt is charged with
MAIC only in that six sigma approach.
• We believe define is
too important be left out and sometimes management
does not do an adequate job of defining a project.
• Our six sigma approach is the full DMAIC

Define (DMAIC)
• Define is the first step in our six sigma approach of DMAIC
• DMAIC first asks leaders to define our core processes.
• It is important to define the selected
project scope,
expectations,
resources and
timelines.
• identifies specifically
what is part of the project and
what is not, and
explains the scope of the project.
• Many times- process documentation are at a general level.
• Additional work is often required to adequately
understand and correctly document the processes.
• As the saying goes “The devil is in the details.”

Measure (DMAIC)
- most important thing to know is where we are going.
- some of the first information you need before starting any
journey is your current location.
• The six sigma approach asks - to quantify and benchmark
the process using actual data.
• At a minimum
consider the
mean or average performance and some estimate of the
dispersion or
variation
(maybe even calculate the standard deviation).
Trends and cycles can also be very revealing.
• The two data points and
extrapolate to infinity is
not a six sigma approach.
• Process capabilities can be calculated
once there is performance data

Analyze (DMAIC )
- project is understood - baseline performance documented - verified
that there is real opportunity,
- then - do an analysis of the process.
- the six sigma approach applies
statistical tools to validate
root causes of problems.
- any number of tools and tests can be used.
objective is to understand the process at a level sufficient

to be able to formulate options for improvement.
• compare the various options with each other to determine the
most promising alternatives.
• as with many activities, balance must be achieved.
• superficial analysis and understanding will lead to
unproductive options being selected,
forcing recycle through the process to make improvements.
• at the other extreme is the paralysis of analysis.
• striking the appropriate balance is what makes the
six sigma highly valuable.

Improve (DMAIC )
• six sigma approach ideas and
solutions are put to work.
- discovered and validated all known
root causes for the existing opportunity.
• The six sigma approach requires to
identify solutions.
• Few ideas or opportunities are so good that all are
an instant success.
- there must be checks to assure that the
desired results are being achieved.
- some experiments and
trials may be required in order to find the best solution.
• When making trials and experiments
it is important that all project associates understand that
these are trials and
really are
part of the
six sigma approach.

Control (DMAIC )
• Many people believe the
best performance you can ever get from a process is at
the very beginning
• Over time there is an expectancy that slowly things will get a little
worse until finally it is time for another major effort towards
improvement.
• Contrasted with this is the
Kaizen approach that seeks to make everything
incrementally better on a continuous basis.
• The sum of all
these incremental improvements can be quite large.
• As part of the
six sigma approach performance tracking
mechanisms and measurements are in place to assure,
at a minimum, that the
gains made in the project are not lost over a period of
time.
• As part of the control step we encourage
sharing with others in the organization.
• With this the six sigma approach really
starts to create phenomenal returns, ideas and
• projects in one part of the organization are
translated in a very rapid fashion to implementation
in another part of the organization.

Dr.Kaoru Ishikawa, Professor at Tokyo University
& Father of Q C in Japan.

• CAUSE ANALYSIS TOOLS are Cause and Effect diagram,
Pareto analysis & Scatter diagram.
• EVALUATION AND DECISION MAKING TOOLS are
decision matrix and multivoting
• DATA COLLECTION AND ANALYSIS TOOLS are check sheet,
control charts, DOE, scatter diagram, stratification, histogram,
survey.
• IDEA CREATION TOOLS are Brainstorming, Benchmarking,
Affinity diagram, Normal group technique.
• PROJECT PLANNING AND IMPLEMENTATIONTOOLS are Gantt
chart and PDCA Cycle.

Second seven tools
• In the quality improvement movement in Japan in the
latter half of the 20th century, the Japanese Union of
Scientists and Engineers (JUSE) were influential in defining a
set of basic tools that could be used for improving
processes. These came to be known as the first seven tools.
• These mostly were useful for quantitative problems, so a
second set of seven tools was defined for the more
qualitative problems that arise, such as around customer
needs. These are:
• Relations Diagram
• Affinity Diagram
• Tree Diagram
• Matrix Diagram
• Matrix Data Analysis Chart
• Process Decision Program Chart
• Activity Network
• Just to complicate things, the Matrix Data Analysis Chart,
which is somewhat complex to use, is often replaced with the
Prioritization Matrix. And for further fun, alternative names are
used, for example the Relations Diagram is sometimes called
the 'Interrelationship Digraph'

Relations Diagram
• In many problem situations, there are multiple complex
relationships between the different elements of the problem,
which cannot be organized into familiar structures such as
hierarchies or matrices. The Relations Diagram addresses
these situations by showing relationships between items with a
network of boxes and arrows.
• The most common use of the Relations Diagram is to show the
relationship between one or more problems and their
causes, although it can also be used to show any complex
relationship between problem elements, such as
information flow within a process.

Affinity Diagram ('KJ' diagram)

• A diagram that is used as a method of sorting qualitative data,
which usually comes in the form of short phrases or sentences
(eg. 'Customers are unhappy with delivery delays').
• It is often done with Post-it Notes, although the original
method used 3" x 5" cards.
• It is a great method of working as a group to sort out issues
and fuzzy situations.
• It is also useful for sorting such as customer comments from
surveys.
• Building an Affinity Diagram is often known as 'doing a KJ',
after its originator, Kawakita Jiro (this is in order of surname,
given name, as in the Japanese tradition

Affinity diagram

Affinity diagram (KJ)

Affinity Diagram -Moving the cards

.

Affinity Diagram

Exit interview comments
from checkout operators

Tree diagram
• is used to find feasible measures for problem solving to clarify the
content of an area to be improved through branching at each
node or view point
Creating a Tree diagram
• Establish the basic objective, Think primary means, Deploy
secondary means and beyond, Conform the relationship between
the objectives and means and complete the tree diagram, Evaluate
the basic means
To minimize Gear box replacement Time Measures Development type tree
diagram Purchase
By machining
Fabricate

Ideas to be produced by Brain storming
Reduce men
Improving co-ordination
Motivate

To minimize Service training
Gear box Improve expertise
Replacement In house training
time
Plan
Making RC/new units
Readily available Collect in advance

Engage men for
cleaning
Improve house keeping
Practice cleanliness

Tree diagram
or Systematic Diagram or Dendrogram

Using the Tree Diagram in Problem Solving

Horizontal tree diagram Vertical tree diagram

Matrix Diagram
• The Matrix Diagram allows a many-to-many comparison of two lists,
by turning the second list on its side to form a matrix.
- indicated in the cell where the row and column of the two items cross.
- use of different symbols to indicate different comparison levels and
the weighting of the items being compared.
- different shapes of matrix for comparing more than the basic two
lists. - the L-Matrix, C-Matrix, T-Matrix, X-Matrix and Y-Matrix.
• The Matrix Diagram is a core tool in Quality Function Deployment
(QFD).
The C-Matrix is a variation on the Matrix Diagram, which is one of the
second seven tools.
• The C-matrix compares three lists simultaneously, such as the
people, products and processes in a factory.
• Being three-dimensional, it is difficult and complex to produce and
draw.
• It becomes easier if there are few relationships to map.

Matrix diagram

Relationships between lists

Many-to-many relationships in a matrix

Matrix diagram

Showing and summing strength of relationship

Matrix Data Analysis Chart (MDAC)
• When comparing a large set of items, the complexity of the situation can make it
difficult to determine how different factors relate to one another.
• It can be useful to find groups of items that behave in similar ways.
• For example, a washing powder may have different efficiencies at achieving
'softness' and 'stain removal' in garments made of acrylic, polyester, wool and
various fiber mixtures. If similar affects are found in a group of fibers, then
changing the powder ingredients may affect the whole group in a similar way.
• The Matrix Data Analysis Chart (or MDAC) helps classify items by identifying two
major characteristics common to all items and then plotting each item as a point on
a standard x-y chart. This makes it easier to see how the individual items relate both
to the characteristics and to one another, thus:

Process Decision Program Chart (PDPC)
• The Process Decision Program Chart ( PDPC) provides a simple
method to help in identifying both risks and countermeasures.
• If the plan is displayed diagrammatically (typically in a Tree Diagram),
then identified risks and countermeasures are added in
subsequent boxes, as below.
• This may appear to be quite trivial, but as with many other tools, the
construction and thought involved is as important as the final diagram.

Problem Decision Program Chart (PDPC)
used with a cutting machine
.

Work Breakdown Structure (WBS)
• When planning a project, a simple way of discovering the
tasks to be performed by
- starting at the higher level and then
- breaking things down one level at a time.
• For example a software project will start with requirements,
design, etc.
• The Design is of the architecture, verification, etc.
• The architecture is of user-interface, database manager,
etc. and so on.
• This hierarchy can be shown in a Work Breakdown
Structure (WBS).
• When you have got down to allocable units,
you can then assign people and
resources to each task and
link these tasks together in an Activity Network.

Activity Network - 'Arrow Diagram'
• this is a classic project planning tool for piecing together a multi-
task complex set of interdependent activities.
• It allows you to calculate what task starts when, what float
there is in the project, etc.
• Also called an 'Activity-on-Node Diagram', the alternative (but
potentially more troublesome) method of doing this is with an 'Activity-on-
Arrow Diagram', or simply 'Arrow Diagram'.

PERT & CPM
• The PERT Chart is another name for the Activity Network.
• PERT is the older name, and is believed to have originated
in the US Navy in the 1950s.
• PERT stands for Programmed Evaluation and Review Technique.
• PERT Charts are often used in combination with the Critical
Path Method (CPM).
• The Critical Path Method (or CPM) is the method by which
the critical path through a project schedule is calculated.
• It helps answer the question 'How long is this project going
to take?’
• The critical path is the sequence of tasks which have zero float.
• Thus, if any task on the critical path finishes late, then the whole
project will also finish late.
• There is always at least one critical path.
• CPM is a fairly involved approach with many calculations.
• Fortunately, many Project Management software programs, such as
Microsoft Project, do this work for you.

Float
• Float, or slack time, is the amount of time that a task in a
project schedule can be delayed without affecting the
completion time of the overall project.
• Total float is the total amount of float in a project schedule (i.e. the
sum of the float for all tasks) and represents the total 'wasted time'.
• Load balancing is the shuffling of tasks to try and minimize the total
float.

Activity Network Diagram
(Activity-on-node diagram)

Critical Path Method
Calculating the early start and finish

Calculating the late start and finish

Calculating the slack and finding the critical path

Gantt Chart
• The Gantt Chart is a simple horizontal Bar Chart,
where bars represent the actual calendar time which is
planned for each task (see the illustration).
• The scale used for the time will depend on the overall
size of the project and the estimation increment used.
• The Gantt Chart is named after its originator, Henry L.
Gantt.
• Gantt Charts can be produced on a computer, using such
as Microsoft Project.

.

The Gantt Chart and Resource Histogram

Comparing the Activity Network
and the Gantt Chart

The Quality Staircase

• qs

Tqm3 ppt

More Related Content

Viewers also liked (8)

Similar to Tqm3 ppt (20)

More from Coomarasamy Chidambaram (12)

Recently uploaded (20)

Tqm3 ppt

Editor's Notes