Brochure

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European Network for Business and Industrial
Statistics (ENBIS)
Second Annual Conference on Business and
Industrial Statistics Rimini, Italy, September,
2002
 Statistical Efficiency the practical
perspective Ron S. Kenett
and Shirley Coleman
KPA Ltd. ISRU, Newcastle
University ron_at_kpa.co.il
Shirley.Coleman_at_ncl.ac.uk
This paper was supported by funding from the
Growth programme of the European Community and
was prepared in collaboration by member
organisations of the Thematic Network -
Pro-ENBIS- EC contract number G6RT-CT-2001-05059.
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Practical Statistical Efficiency
Background

• Churchill Eisenhart beer and statistics
• Bruce Hoadley vadors
• Blan Godfrey Youden address
• We expand on these ideas adding an additional
  component the value of the data actually
  collected
• We demonstrate the concept of Practical
  Statistical Efficiency (PSE) using four case
  studies.

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Practical Statistical Efficiency
PSE ER x T I x P I x V PS x P S x V
P x V M x V D

• VD value of the data actually collected
• VM value of the statistical method employed
• VP value of the problem to be solved
• PS probability that the problem actually
  gets solved
• VPS value of the problem being solved
• PI probability the solution is actually
  implemented
• TI time the solution stays implemented
• ER expected number of replications

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VD value of the data actually collected
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Readily accessible data, is like observations
below the lamppost where there is light - not
necessarily where you lost your key or where the
answer to your problem lies
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VM value of the statistical method employed
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
A mathematical definition of statistical
efficiency is given by Relative Efficiency of
Test A versus Test B Ratio of sample size for
test A to sample size for test B, where sample
sizes are determined so that both tests reach a
certain power against the same alternative.
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VP value of the problem to be solved
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Statisticians too often forget this part of the
equation. We frequently choose problems to be
solved on the basis of their statistical interest
rather than the value of solving them.
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PS probability that the problem actually gets
solved
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Usually no one method or attempt actually solves
the entire problem, only part of it. So this part
of the equation could be expressed as a fraction
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VPS value of the problem being solved
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
This is both a statistical question and a
management question. Did the method work and lead
to a solution that worked and were the data,
information and resources available to solve the
problem?
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PI probability the solution is actually
implemented
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Here is the non-statistical part of the equation
that is often the most difficult to evaluate.
Implementing the solution may be far harder than
just coming up with the solution.
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Management Approach
Statistical Method
Designed Experiments and Reliability
Quality by Design
Process Control Process Improvement
Control Charts
Sampling Plans
Inspection
Basic Statistical Thinking
Fire Fighting
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TI time the solution stays implemented
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Problems have the tendency not to stay solved.
This is why we need to put much emphasis on
holding the gains in any process improvement.
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ER expected number of replications
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
This is the part most often missed in companies.
If the basic idea of the solution could be
replicated in other areas of the company, the
savings could be enormous.
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Practical Statistical Efficiency
PSE ER x T I x P I x V PS x P S x V
P x V M x V D
Four Case Studies
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Four Case Studies
1. Tea packing

• Good commitment to project
• Specific problem to solve
• efficiency equalised between two lines initially
  at 54 and 68
• efficiency increased to 80

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Four Case Studies
2. Soft drinks Manufacture

• Introduction of KPIs
• efficiency charts not subtle enough to reflect
  the complex business
• which is seasonal and highly dependent on product
  changes and product mix
• casual commitment to project

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Four Case Studies
3. Heavy metal company

• Commitment to cost saving quick fixes
• improvements and process changes not maintained
• run chart shows how effluent increased when water
  usage was halved
• scatterplot shows relationship between water
  usage and mean and variance of effluent
• transient commitment to project

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Four Case Studies
3. Heavy metal company
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Four Case Studies
4. Major Utility

• Good commitment to project
• Chart highlights increases in component defects
• Ideas adopted
• Applied widely throughout the business

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Comparison of Case Studies
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3
4
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Comparison of Case Studies

• Longevity and probability components E(R) and
  T(I) are generally high
• V(PS) generally high otherwise the projects would
  not be started
• Differences mainly in V(D) and V(M) which reflect
  commitment to the project
• P(I) and P(S) not quite so important
• V(P) is the six sigma part, unless the value of
  the problem is high, the company may lose
  interest, however good the rest is!

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Practical Statistical Efficiency
PSE ER x T I x P I x V PS x P S x V
P x V M x V D

• The components should be evaluated before and
  after the project
• provides an efficient approach to compare
  projects
• encourages a broad view of the statisticians
  work
• delegates may like to experiment with PSE for
  their next projects
• we welcome your feedback and comments

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References

• Chambers, P.R.G, J.L. Piggott and S.Y. Coleman
  (2001), SPC a team effort for process
  improvement across four area control centers, J.
  Appl Stats, 28(3), 307-324.
• Coleman, S.Y and D.J. Stewardson (2002) Use of
  measurement and charts to inform management
  decisions, Managerial Auditing Journal, 17(1),
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• Coleman, S.Y., G. Arunakumar, F. Foldvary and R.
  Feltham (2001a), SPC as a tool for creating a
  successful business measurement framework, J.
  Appl. Stats, 28(3), 325-34.
• Coleman, S.Y., A. Gordon and P.R. Chambers
  (2001b), SPC making it work for the gas
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  343-51.
• Hoadley, B. (1986), A Zero Defect Paradigm,
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• Godfrey, A. Blanton (1989), "Statistics, Quality
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• Kenett, R. S. and Zacks, S. (1998), Modern
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• Kenett, R. S. and Albert, D. (2001), The
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