Teaching statistics to engineers

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Teaching statistics to engineers
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• Subject benchmark statements Engineering
• Engineering degree programmes should include
• Mathematics and science
• Information technology and communications
• Design creativity and innovation
• Business context
• Engineering practice
• Teamwork
• Integration of knowledge and understanding

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Statistics?

• Intellectual abilities
• Graduating engineers should be able to analyse
  and interpret data and, when necessary, design
  experiments to gain new data
• Tabulated content
• manipulation and sorting of data
• presentation of data in a variety of ways

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The wider world

• Richard Parry-Jones, Fords Chief Technical
  Officer (lecture to the RAE in 1999)
• New ways of managing variation at the RD stage
  are being developed as a result of the synergies
  between engineering and statistical science. 
• We have to develop appropriate strategies to
  deal with all sources of variation, so that the
  optimal remedial strategies can be jointly
  developed between product design and
  manufacturing engineers. 
• I like to call this approach statistical
  engineering - it is the only way forward that
  makes business sense, and at the same time is
  focused on customer desires. 

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Parry-Jones (continued)

• Very little of these powerful, statistically
  based engineering methodologies have permeated
  our profession.
• Ford have to teach them ..... Even with our
  vast resources, this represents a formidable
  challenge and it is sobering to think about the
  state of affairs in smaller companies. 
• ... I would ask that the use of statistical
  engineering methods be taught and embedded in the
  undergraduate curricula and professional
  experience requirements of our institutions.

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Six Sigma training providers

• ?50 excluding university short courses
• Typical Black Belt statistical curriculum

• Approx 14 days (out of 20 day training programme)

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Two-approaches to course design

• Make a list of topics in a statistically logical
  progression 
• For each topic, find example(s) from the
  students' field of application
• Identify the appropriate level of presentation

• Choose a series of tasks from a work process 
• Identify deliverables
• Identify the relevant statistical methods
• Identify the appropriate level of presentation

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A university syllabus (2nd year Mech. Eng.)

• Basic probability addition rule conditional
  probability multiplicative rule independent
  events permutations and combinations
• Discrete probability distributions binomial and
  Poisson
• Continuous probability distributions normal
• Random sampling sample mean and variance
  distribution of the sample mean and variance the
  t distribution the chi squared distribution
• Confidence intervals for the mean and the
  variance the central limit theorem
• Hypothesis testing
• Proportions confidence intervals and sample size
• Regression analysis
• Comparison of two samples independent sampling
  paired sampling

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Whats missing?

• Designed experiments (both screening and RS
  designs)
• Fitting response surfaces
• Analysis of data from CAE models (FE models,
  simulation models)
• What could go?
• hypothesis tests (except possibly as a tool for
  model selection)

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Process-based training the DMAIC process

• Define
• Measure     
• Operational definitions    
• Analysis of measurement systems, including intro
  to probability distributions
• Statistical control (process stability)   
• Process capability 
• Analyse
• Graphical methods
• Confidence intervals  
• Hypothesis testing           
• ANOVA    
• Regression

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DMAIC process (cont.)

• Improve
• Screening designs
• RS designs
• Transmission of variation and Monte Carlo
• Control
• Shewhart charts

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Ford/RSS Statistical Engineering course

• Origins
• Richard Parry-Jones 1999 lecture to the RAE
• Joint meetings (1999-2000) organised by IEE
  Quality Management Committee and RSS Quality
  Improvement Committee
• Tim Nicholls proposal develop materials for
  Ford to use internally (FTEP), RSS to promote
  within the UK University sector

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Underlying process product creation
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Examples of content
Deliverable A product design concept that can
achieve the functional target Statistics Least
squares fitting (line and curve) models for x/y
data
Deliverable A robustness assessment of the
design concept Statistics Two-level orthogonal
arrays effect plots and sensitivity analysis
Design Concept
Deliverable Measures of piece-to-piece
variation for a surrogate product Statistics
Run charts stable process model Normal plots
sample statistics
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List of statistical content

• Sample mean and standard deviation
• Scatter plots and linear regression
• Multiple regression (incl. residual plots)
• Probability distributions (mainly Normal)
• Half Normal plots
• Weibull analysis
• Experimental design
• Response surface methods
• Standard errors and t-ratios
• Measurement system analysis (incl. ANOVA)
• Run charts and process capability

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Coherence

• Three recurring themes
• transfer functions (regression models) link
  product outputs with product characteristics and
  process parameters (y ? x ? p and ?p ??x? ?y )
• statistical models which incorporate random
  variation
• precision of statistical estimates relationships
  between precision, sample size and resources
• Statistical ideas first occur very informally and
  are re-examined in greater depth
• motivated by engineering questions

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Case study
Optimise manufacturing process Excel SOLVER used
with process transfer function to identify
settings that achieve target OD at minimum cost
Assess process performance Capability indices
calculated for OD using data from a surrogate
process. Process transfer function used to
estimate the level of control required to achieve
Cp of 2.0
Optimal settings

• Cp of 2.0 requires SS variation of no more than
  ?0.5 rpm
• Subject to this requirement, the design can
  proceed into full production

Process transfer function Quadratic transfer
function established from an experiment relating
mean value of OD to three important process
parameters. Residual plots used to identify
outliers and p-values used to refine equation
Design next generation components Optimise
product and manufacturing process to achieve new
target effort with reduced variation
Carry-over design achieves new target effort
within narrower acceptable range of variation.
Estimated process transfer function
OD 6.55 0.16GS 0.13SS 0.15 MT 0.05GS2
0.05MT2 0.10GSxSS
Evaluate functionality of design concept A
quadratic transfer function is fitted using
interference fits data from bookshelved work on a
similar design.
Assess performance of measurement system A Gauge
RR study is conducted on measurements of OD
using ANOVA
The RR contribution is about 12 This is
acceptable by conventional standards but
improvements should be considered
The design concept is able to achieve the target
effort
Assess robustness of design concept An effects
plot is constructed from a 2-level experiment
using prototypes with x-values that represent the
extremes of the effects of the noise factors.
Identify key manufacturing process
parameters Half Normal plots of location and
dispersion effects are constructed from
measurements of OD in a two-level screening
experiment

• Worst-case noise scenario would not take effort
  outside acceptable range
• Ep had the largest effect. Further
  investigation of variation in Ep required

Quantify manufacturing variation A Normal plot
and run chart are constructed from measurements
of Ep using samples from a surrogate process.

• GS, SS and MT affect the mean value of OD
• DT affects the variation in OD, and should be
  set to a high level if possible

Verify the design A Weibull plot is generated
using the data from a test carried out with
prototypes.
Optimise the design A response surface is
developed by multiple regression, using results
from a three level full factorial experiment
The likely range of manufacturing variation is
less than was used in the robustness assessment
The design will meet the design intent over its
useful life.

• With OD of 6.5 mm, predicted effort is equal
  to target
• Manufacturing variation in OD and Ep will not
  take effort outside acceptable range

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Case study detail
Assess process performance Capability indices
calculated for OD. Process transfer function
used to estimate the level of control required to
achieve Cp of 2.0 (?p ??x? ?y)

• Cp of 2.0 requires SS variation of no more than
  ?0.5 rpm
• Subject to this requirement, the design can
  proceed into full production

Optimise manufacturing process
Design next generation components
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Discussion points

• Statistical Engineering should be taught by
  engineers in the context of design and
  engineering, supported by first class applied
  statisticians as necessary these methods should
  not be taught through a separate course in
  statistics.
• Is this practical?
• in universities?
• in industry?
• Fundamentals of Automotive Statistics was added
  to FTEP after the Statistical Engineering course

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