Six sigma

1. Research & Development @ JSW
Six Sigma Methodology & its applications

2. Presentation Layout
 Six Sigma: An overview
 Why Six Sigma?
 Six Sigma Levels
 Six Sigma Methodology and Management
 Key Roles for Six Sigma
 Tools for Six Sigma

3. Six Sigma overview
 The term “Six Sigma” was
coined by Bill Smith, an
engineer with Motorola
 Late 1970s - Motorola started
experimenting with problem
solving through statistical
analysis
 1987- Motorola officially
launched it’s Six Sigma
program
Sigma :
• A Greek term used in statistics to
represent standard deviation from
mean value, an indicator of the
degree of variation in a process.
• Sigma measures how far a given
process deviates from perfection.
• Sigma Level is a metric that
indicates how well that process is
performing.

4. What is Six Sigma?
 Six Sigma - A highly disciplined
process that enables organizations
deliver nearly perfect products and
services.
 The figure of six arrived statistically
from current average maturity of
most business enterprises
 It is a Quality Philosophy and the
way of improving performance by
knowing where you are and where
you could be.
Sigma Level
( Process
Capability)
Defects per
Million
Opportunities
2 308,537
3 66,807
4 6,210
5 233
6 3.4
99. 99966% accuracy

5. Six sigma methodology
 DMAIC : Six Sigma Improvement Methodology
 Used for improving quality and service problems; reducing
variation, process optimization
(Define, Measure, Analyse, Improve, Control)
• Define specific goals to achieve outcomes
• Measure reduction of defects
• Analyze problems, cause and effects must be
considered
• Improve process on bases of measurements and
analysis
• Control process to minimize defects

6. QUICK WINS
QUICK WINS
Sr.
No.
Source
Concerns/
Issues
Potential Quick
win opportunity
(solution)
Easy to
implement
Fast to
implement
Cheap
Within the
team
control
Easy
reversi
ble
1
Process
walk
through
1 Yes Yes Yes Yes Yes
2
Process
walk
through
2 Yes Yes Yes Yes Yes
3
Process
walk
through
3 Yes Yes Yes Yes Yes

7. Tools & Techniques
 7QC tools
 Check Sheets (collect data to make improvements)
 Pareto Charts (define problem and frequency)
 Cause and effect diagram (Identify possible causes to
solve problem)
 Histogram (Bar charts of accumulated data to evaluate
distribution of data)
 Scatter diagram (plots many data points and pattern
between two variables)
 Flow Chart (Identify unwanted steps)
 Control charts (Control limits around mean value)

8. Two basic types of Data
 Discrete Data
– Has only a finite or countable set of values
– Examples: zip codes, counts, or the set of words in a collection of documents
– Often represented as integer variables.
– Examples: Pass/Fail or Small/Medium/Large
 Continuous Data
– Has real numbers as attribute values
– Examples: temperature, height, or weight.
– Practically, real values can only be measured and represented using a finite
number of digits.
– Continuous attributes are typically represented as floating-point variables.

9. Check Sheets
 Data collection methodology
 Simple data collection form which help determine how often
something occurs
Sampling
 Using a sample of data, we draw conclusions about the entire
population of data.
 Sampling
 saves cost and time
 provides a good alternative to collecting all the data

16. Important elements of basic statistics (continuous data)
 Location
 Spread
 Shape (Normal Distribution)
of a set of numbers
Measures of Location
 Mean (average of data)
 Median (50th percentile / middle of data)
– not influenced by outlier
 Example

17. Measure of Spread
 Range ‘R’ = Max – Min
 Variance & Standard deviation
 Interquartile Range (IQR) = difference between the 75th
percentile point and the 25th percentile point
 Find IQR for 2 ,5, 7, 9, 3, 5, 10, 6, 12
1
)
( 2




n
x
xi



18. 1
)
( 2




n
x
xi


Normal Distribution – Measure of Shape
Sigma =  = Deviation
( Square root of variance )
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Axis graduated in Sigma
68.27 %
95.45 %
99.73 %
99.9937 %
99.999943 %
99.9999998 %
result: 317300 ppm outside
(deviation)
45500 ppm
2700 ppm
63 ppm
0.57 ppm
0.002 ppm
between + / - 1
between + / - 2
between + / - 3
between + / - 4
between + / - 5
between + / - 6


25. Control Chart
 The control chart is a graph used to study how a
process changes over time. Data are plotted in time
order.
 A control chart always has a central line for the average,
an upper line for the upper control limit and a lower line
for the lower control limit.
 Lines are determined from historical data. By comparing
current data to these lines, you can draw conclusions
about whether the process variation is consistent (in
control) or is unpredictable (out of control, affected by
special causes of variation).

26. Control Limits
General model for a control chart
–UCL = μ + kσ
–CL = μ
–LCL = μ – kσ
where μ is the mean of the variable, and σ is the standard deviation
of the variable. UCL=upper control limit; LCL = lower control limit;
CL = center line. where k is the distance of the control limits from the
center line, expressed in terms of standard deviation units. When k
is set to 3, we speak of 3-sigma control charts. Historically, k = 3 has
become an accepted standard in industry.
USL & LSL = Voice of customer

27. Control Chart Example

28. Control Chart Examples
UCL
LCL
USL
LSL
Process not capable, not as per customer specifications

29. Control Chart Examples
UCL
LCL
USL
LSL
Process is out of control, but capable as per customer specifications

30. Process Capability
Process capability =
Tolerable (allowed) variation / Process (actual) variation
Cp = (USL-LSL) / (UCL-LCL)
- indicator of variation
 

31. Example
Upper specification = 30 minutes
Upper specification = 30 minutes
Lower specification = 20 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
Average service = 26.2 minutes

 = 1.35 minutes
= 1.35 minutes
The Aditya care lab process has an average turnaround time of 26.2
minutes and a standard deviation of 1.35 minutes.
The upper specification limit of 30 minutes and a lower specification
limit of 20 minutes.
The administrator of the lab wants to have three-sigma performance
for the lab. Is the lab process capable of this level of performance?

32. Cpk = Minimum of
Upper specification – x
3
x – Lower specification
3 ,
Upper specification = 30 minutes
Lower specification = 20 minutes
Average service = 26.2 minutes
 = 1.35 minutes
Assessing Process Capability
C
Cpk
pk =
= Minimum of
Minimum of
26.2
26.2 –
– 20.0
20.0
3(
3(1.35
1.35)
)
,
,
30.0
30.0 –
– 26.2
26.2
3(
3(1.35
1.35)
)
C
Cpk
pk =
= Minimum of 1.53, 0.94
Minimum of 1.53, 0.94 = 0.94
= 0.94 Process
Capability Index

33. Cp =
=
Upper specification - Lower specification
6
Cp
p =
=
30 - 20
6(1.35)
= 1.23 Process Capability Ratio
Upper specification = 30.0 minutes Lower specification = 20.0 minutes
Average service = 26.2 minutes
 = 1.35 minutes Cpk = 0.94 C
Cp
p = 1.23
Assessing Process Capability
Does not meet 3 (1.00 Cpk
pk) target
due to a shift in mean (Note variability is ok since Cp
p is over 1.0)

34. Scatter Diagram
 In actual practice, it is often essential to study the relation
of two corresponding variables.
 To study the relation of 2 variables such as the speed of the
bike & the fuel efficiency, scatter diagram is used.

39. Regression Analysis
 While correlations tells us only about the direction of association, it
does not throw much light on degree of association in one variable
with respect to association in another.
 Regression of ‘Y’ on ‘X’ results in a transfer function equation that can
be used to predict the value of ‘Y’ for given values
» Simple linear regression is for one X
» Multiple linear regression is for more than one X’s
 Simple linear regression:
Y = A + B X + C A = intercept of fitted line on Y axis
B = regression coefficient / slope
C = Error in the model

40. Simple Linear Regression Example
 R&D Dept. of a company wishes to predict the relationship between
amount spent on R&D and annual profit generated. It collects the data for
last 6 years and wants to sanction R&D budget accordingly for 2016.
» Company profit target for 2016 = 32 Cr. How much should be spent on
R&D in 2016?
R&D Expense,
Crores
Annual profit,
Crores
2010 2 20
2011 3 25
2012 5 34
2013 4 30
2014 11 40
2015 5 31

41. Regression Analysis Results
Coefficients Standard Error P-value
Intercept 20.0 2.65 0.002
R&D Expense 2.0 0.46 0.012
Regression Statistics
Multiple R 0.9091
R Square 0.8264
Adjusted R Square 0.7831
Observations 6
The regression equation is
Profit = 20.0 + 2.0 * R&D Expense
• 82.64% of linear variation in Y is explained by X in this fitted model.
P-value < 0.05
Coefficient of
determination

42. Multiple Regression Analysis
Y = A + B1X1 + B2X2 + C
• Suppose we are trying to predict rent of an apartment based on the no. of rooms
& its distance from the main market. The following information is collected.
• If you are looking for a two-bedroom apartment, 2km from the main market, what
rent should you expect to pay ?
Rent No. of rooms Distance (km)
3600 2 1
10000 6 2
4500 3 2
5250 4 3
3500 2 10
3000 1 4

43. Multiple Regression Analysis Results
Rent = 852 + 1381* No. of rooms
» Expected rent for 2-bed room = 3614
Distance is not seeming as an important factor as its P-value is more than 0.05.
Regression Statistics
Multiple R 0.9565
R Square 0.9149
Adjusted R Square 0.8581
Observations 6
Coefficients Standard Error P-value
Intercept 852.04 1146.27 0.511
No. of rooms 1380.97 259.50 0.013
Distance -5.44 142.13 0.972

44. Points to remember in Regression
 Don’t extrapolate beyond the range.
 Don’t assume causation. Regression predicts the statistical
relation. Theoretical/ Logical relation should be there.
 No. of schools vs. Incidents of Crime
 Regression may not give a good R2
– If X’s chosen are not the ‘real’ ones
– If X’s have intercations
– In case of multiple X’s having a curvilinear relationship with ‘Y’

45. THANK YOU