Design for Six-Sigma in the School of Computing, Engineering and Physical Sciences

1
Design for Six-Sigmain the School of Computing,
Engineering and Physical Sciences
Introduction to quality control by Dr J. Whitty
2
Lessons structure

• The lessons will in general be subdivided in to
  eight number of parts, viz.
• Statement of learning objectives
• Points of orders
• Introductory material (Nomenclature)
• Concept introduction (Statistical measures)
• Development of related principles (Control
  charts)
• Concrete principle examples via reinforcement
  examination type exercises
• Summary and feedback
• Formative assessment, via homework task

3
Learning Objectives
After the session the students should be able to

• Distinguish between Quality control and Quality
  assurance from a statistical viewpoint
• Evaluate the central tendency and dispersion of
  realistic operational business data
• Use a test statistics to formulate quality
  control decisions
• Describe high-quality and hence six-sigma from a
  quantitative viewpoint

4
Nomenclature and Terminology
Statistical Quality Control (SQC) techniques are
used to measure the conformance of components and
services

• Quality the percentage of items that conform to
  an agreed design specification.
• QC/A Control and Assurance
• CV control value
• U/LCL Upper/Lower Control Limit
• Sigma One standard deviation
• Poka-Yoke mistake-proofing

5
Learning check
Based on our previous work you should now be able
to answer the following short answer examination
type questions.

• Generally during product manufacture which of the
  following incur the greatest costs (1).
• Direct Labour
• Fixed Overheads
• Material Costs
• Is MRP a push or pull process (2)
• Other than fixed name three other generic
  process-layouts (3)

6
Measures of the central tendency

• Mode
• The maximum value of the distribution e.g. the
  most occurring value (in reality this can be
  evaluated using a standard formula
• Median
• The central value of a set of data or a
  distribution. Can be evaluated using a standard
  method of using the CDF
• Arithmetic mean
• The central value assuming the data are
  distributed in accordance to an arithmetic
  progression
• Geometric mean
• The central value assuming the data are
  distributed according to a geometric progression
• Others (Harmonic-mean, Trimmonic-mean)

7
The mode

• For our data this occurs between 30-39 (the modal
  range)
• The construction shown can be employed to home in
  on the exact value
• Or the formula where Llower boundary, llower
  freq diff, uupper freq diff cthe class
  boundary width

8
The Median

• For our data we could evaluate this quantity two
  fold
• Approximate using by plotting the cumulative
  frequency diagram
• Via logical inference

9
Measures of Dispersion

• The range
• Largest value minus Smallest value
• Variance
• Mean Square variation from the mean
• Standard Deviation
• Square root of the variance

10
Decision Processes

• This is all very well and good however, how does
  this allow us to make research and managerial
  research decisions?
• To answer this we need to consider the pattern of
  the data, thus

11
The Normal distribution

• Many sets of data adhere to the normal
  distribution.
• The most important distribution of them all
• It is pretty much this property that allows us to
  obtain (research) management decisions
• The normal distribution is usually written
  N(µ,s2) with µ the population mean and s2 the
  variance

12
Properties of N(µ,s2)

• For any normal curve with mean mu and standard
  deviation sigma
• 68 percent of the observations fall within one
  standard deviation sigma of the mean.
• 95 percent of observation fall within 2 standard
  deviations.
• 99.7 percent of observations fall within 3
  standard deviations of the mean.

13
Exercise

• Example Using a z score If a population is
  N(111,33.82), find the probability that some
  value of 100 ltXlt150.

14
Exercise

• Using a z score and given that the population is
  N(37,4.352), find the probability that some value
  of Xgt150.

15
Samples

• If we are using a sample of values as a
  consequence of the central limit theorem the z
  score will change, thus

16
Example

• The mean expenditure per customer at a tire store
  is 60 and the sd 6. It is known that the
  nominal customer per day is 40. A new product
  costs 64, what is the probability of selling
  such a product per customer

17
Try one

• In a store, the average number of shoppers is
  448, with an sd of 21. What is the probability
  that 49 shopping hours have a mean between 441
  and 446.

18
Process Variables

• In essence the mean and standard deviations are
  Statistical Process Variables which can be
  employed to find out if a process or system is
  operating within established control limits

19
Class discussion

• Using our knowledge of the normal distribution
  decided on appropriate values of dU,L.. Hence
  evaluate the process UCL and LCL for the process
  with means of 33.8, 33.8 33.6 33.7 33.8.33.9 and
  33.2.
• Discuss methods of obtaining measures of
  normality

20
Class Discussion

• Using the hand-out of the distribution tables
  provided examine the following points
• In reality a number of samples are taken in order
  to ensure that natural random variation is
  eliminated from the process and hence quality
  controls.
• Discuss methods the use of the normal
  distribution for samples of low numbers. In
  particular what would you expect to happen the
  control limit values.
• How doe the choice of distribution affect the
  quality.
• Bearing in mind the central-limit theorem we
  discussed in the Math how can be remove random
  variation from samples.

21
The t-distribution

• Due to the reasons we have just outlined the
  general tool used in-order to determine the upper
  and lower deviation limits is the Students
  (actually Gossett) t-distribution. As this is
  actually a family of distributions each being
  function of the degrees-of-freedom. And hence the
  size of the samples!

22
Control limits

• In the analysis of a certain CNC milling
  operation the following data are obtained from a
  systematic random sampling process of 12
  components.
• Evaluate the process control value
• The UCL and LCL.
• Discuss the minimum advisable design tolerances
  which can be produced by the machine.

Sample A B C D E F
mean 37.7 37.8 37.3 37.6 37.3 37.2
Range 0.3 0.5 0.4 0.4 0.5 0.4
23
Class example

• Data are obtained from process times of health
  and safety inspection times, a systematic random
  sampling of15 different tests.
• Evaluate the process control value
• The UCL and LCL.
• Discuss the minimum advisable waiting time which
  should be quoted for the inspection.

Sample A B C D E F
mean 7.7 7.8 7.3 7.6 7.3 7.2
Range 0.2 0.4 0.3 0.2 0.4 0.3
24
Control charts

• These are of upmost importance in not only
  recommending to design engineers specific
  tolerance limits for a specific process but also
  for designs which push-the-envelope of both
  product (and services). That is, the development
  of the so called Yoka-Yoke operations.

For operations with continuous process variables.
The x-bar and R charts are usually of most use.
25
Condition monitoring

• Since this is an introductory (first-year)
  course. You will only ever be asked to evaluate
  control limits and describe how the charts are
  plotted.
• In addition, you may be requested to describe how
  such charts can be used for condition-monitoring,
  in particular, the following features
• Two-points in the danger area (4-sigma)
• Four-to-five points above/below the CV
• Trends (Positive/negative/cyclic)

26
Short Examination type questions

• Give the technical term of mistake-proofing. (1)
• Write down a formula linking the design and
  process tolerances. (1)
• Define QC and QA. (2)
• What distribution should be used to evaluate the
  control limits if the sample-size is less than
  30. (2)
• State three principal prohibitive quality costs
  (3)

27
Six Sigma

• The precise definition of Six Sigma is not
  important (at this stage but we will look at this
  in detail later in the lecture or even next
  week) the content of the program is
• A disciplined quantitative approach for
  improvement of defined metrics
• Can be applied to all business processes,
  manufacturing, finance and services

28
Focus of Six Sigma

• Accelerating fast breakthrough performance
• Significant financial results in 4-8 months
• Ensuring Six Sigma is an extension of the
  Corporate culture, not the program of the month
• Results first, then culture change!

Adapted from Zinkgraf (1999), Sigma Breakthrough
Technologies Inc., Austin, TX.
29
Six Sigma Reasons for Success

• The Success at Motorola, GE and AlliedSignal has
  been attributed to
• Strong leadership (Jack Welch, Larry Bossidy and
  Bob Galvin personally involved)
• Initial focus on operations
• Aggressive project selection (potential savings
  in cost of poor quality gt 50,000/year)
• Training the right people

30
The right way!

• Plan for quick wins
• Find good initial projects - fast wins
• Establish resource structure
• Make sure you know where it is
• Publicise success
• Often and continually - blow that trumpet
• Embed the skills
• Everyone owns successes

31
Why Six-Sigma works

• Consider the 99 quality level
• 5000 incorrect surgical operations per week!
• 200,000 wrong drug prescriptions per year!
• 2 crash landings at most major airports each
  day!
• 20,000 lost articles of mail per hour!
• These are NOT satisfactory
• Companies should strive for Six Sigma quality
  levels
• A successful Six Sigma programme can measure and
  improve quality levels across all areas within a
  company to achieve world class status
• Six Sigma is a continuous improvement cycle

32
Not very satisfactory!

• Companies should strive for Six Sigma quality
  levels
• A successful Six Sigma programme can measure and
  improve quality levels across all areas within a
  company to achieve world class status
• Six Sigma is a continuous improvement cycle

33
Scientific method (after Box)
34
Improvement cycle

• PDCA cycle

Plan
Do
Act
Check
35
Alternative interpretation
Prioritise (D)
Measure (M)
Hold gains (C)
Interpret (D/M/A)
Improve (I)
Problem (D/M/A) solve
36
Statistical background
Some Key measure

Target m

37
Statistical background
Control limits

/
-

3
s
Target m

38
Statistical background
Required Tolerance
U
S
L
L
S
L

/
-

3
s
Target m

39
Statistical background
Tolerance
U
S
L
L
S
L

/
-

3
s
Target m

/
-

6
s
Six-Sigma
40
Statistical background
Tolerance
U
S
L
L
S
L

/
-

3
s
1
3
5
0
1
3
5
0
p
p
m
p
p
m
Target m

/
-

6
s
41
Statistical background
Tolerance
U
S
L
L
S
L

/
-

3
s
1
3
5
0
1
3
5
0
p
p
m
p
p
m
0
.
0
0
1
0
.
0
0
1
p
p
m
p
p
m
Target m

/
-

6
s
42
Statistical background

• Six-Sigma allows for un-foreseen problems and
  longer term issues when calculating failure error
  or re-work rates
• Allows for a process shift
• Thus the distributions described ealier almost
  always operate within design tolerances.
• Even when the envelope is pushed this has less of
  an effect on quality

43
Statistical background
Tolerance
U
S
L
L
S
L
1
.
5
s
3
.
4
6
6
8
0
3
p
p
m
p
p
m
0

p
p
m
3
.
4
p
p
m
m

/
-

6
s
44
Performance Standards
?
PPM
Yield
2 3 4 5 6
308537 66807 6210 233 3.4
69.1 93.3 99.38 99.977 99.9997
Current standard
World Class
Process performance
Defects per million
Long term yield
45
Performance standards
First Time Yield in multiple stage process
Number of processes
3s
4s
5s
6s
1 10 100 500 1000 2000 2955
93.32 50.09 0.1 0 0 0 0
99.379 93.96 53.64 4.44 0.2 0 0
99.9767 99.77 97.70 89.02 79.24 62.75 50.27
99.99966 99.9966 99.966 99.83 99.66 99.32 99.0
46
Financial Aspects
Benefits of 6s approach w.r.t. financials
47
Summary
Have we met out learning objectives?
Specifically are you able to

• Distinguish between Quality control and Quality
  assurance from a statistical viewpoint
• Evaluate the central tendency and dispersion of
  realistic operational business data
• Use a test statistics to formulate quality
  control decisions
• Describe high-quality and hence six-sigma from a
  quantitative viewpoint

48
Examination type questions

• Statistical process control has been used in the
  manufacturing industry since the 1980s to improve
  the quality of engineered components
• Define high-quality from a quantitative viewpoint
  (4)
• With reference to the answer in part (a) how does
  quality differ from reliability (6).
• During a drilling operation an inspector records
  the following sizes from a standard slot drill,
  10.01, 10.03, 10.04, 10.01, 10.04, 10.06.
  Estimate a suitable process tolerance assuming
  that the measurements are normally
  distributed. (8
• ..

49
Examination type questioncontinued

1. Assuming that there is no reason to believe that
   the values can be taken as process mean values,
   with ranges of, 0.05, 0.02, 0.02, 0.02, 0.03,
   0.04, calculate
2. The process CV. (2)
3. The UCL and LCL (9)
4. The minimal allowable design tolerance for the
   process, giving reasons for you answer. (5)
5. Describe how design packages such as ANSYS and
   MATLAB can be employed to facilitate six-sigma
   methodologies (6)

This is this weeks research task
50
Summary
Have we met out learning objectives?
Specifically are you able to

• Distinguish between Quality control and Quality
  assurance from a statistical viewpoint
• Evaluate the central tendency and dispersion of
  realistic operational business data
• Use a test statistics to formulate quality
  control decisions
• Describe high-quality and hence six-sigma from a
  quantitative viewpoint

51
Examination type questions

• Statistical process control has been used in the
  manufacturing industry since the 1980s to improve
  the quality of engineered components
• Define high-quality from a quantitative viewpoint
  (4)
• With reference to the answer in part (a) how does
  quality differ from reliability (6).
• During a drilling operation an inspector records
  the following sizes from a standard slot drill,
  10.01, 10.03, 10.04, 10.01, 10.04, 10.06.
  Estimate a suitable process tolerance assuming
  that the measurements are normally
  distributed. (8
• ..

52
Examination type questioncontinued

1. Assuming that there is no reason to believe that
   the values can be taken as process mean values,
   with ranges of, 0.05, 0.02, 0.02, 0.02, 0.03,
   0.04, calculate
2. The process CV. (2)
3. The UCL and LCL (9)
4. The minimal allowable design tolerance for the
   process, giving reasons for you answer. (5)
5. Describe how design packages such as ANSYS and
   MATLAB can be employed to facilitate six-sigma
   methodologies (6)

This is this weeks research task