1. Problem Solving Techniques
MST326 lecture 3
25 January 2007
MATS326-3 problem.ppt

2. Outline of lecture Brainstorming Mind maps Cause-and-Effect diagrams
Failures Mode and Effects Analysis
Fault Tree Analysis
Design of Experiments
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MATS326-3 problem.ppt

3. Brainstorming
proposed by Alex Osborn “for the sole purpose of producing checklists of ideas”
technique to identify causes and develop solutions to problems
“seeking the wisdom of ten people rather than the knowledge of one person” [Kaizen Institute]
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MATS326-3 problem.ppt

4. Brainstorming no criticism is permitted wild ideas are encouraged
“only stupid question is one that is not asked” [Ho]
wild ideas are encouraged
often trigger good ideas from someone else
each person contributes one idea
further single ideas on second circuit
repeat until no further ideas
all contributions are recorded in view
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MATS326-3 problem.ppt

5. Brainstorming Osborn proposed 75 fundamental questions
can be reduced to:
 seek other uses?  adapt?
modify?  magnify?
minify?  substitute?
 rearrange?  reverse?
 combine?
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MATS326-3 problem.ppt

6. TRIZ Teorija Reshenija Izobretatel'skih Zadach
loosely translates as Theory of Inventive Problem Solving (TIPS)
40 Inventive Principles
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MATS326-3 problem.ppt

7. 40 inventive principles of TRIZ
IP 01: Segmentation IP 02: Taking out IP 03: Local quality IP 04: Asymmetry IP 05: Merging IP 06: Universality IP 07: Nested doll IP 08: Anti-weight IP 09: Preliminary anti-action IP 10: Preliminary action IP 11: Prior cushioning IP 12: Equipotentiality IP 13: The other way round IP 14: Spheroidality or curvature IP 15: Dynamics IP 16: Abundance IP 17: Another dimension IP 18: Mechanical vibration IP 19: Periodic action IP 20: Continuity of useful action IP 21: Rushing through IP 22: Blessing in disguise IP 23: Feedback IP 24: Intermediary IP 25: Self-service IP 26: Copying IP 27: Cheap short-lived objects IP 28: Mechanics substitution IP 29: Pneumatics and hydraulics IP 30: Flexible shells and thin films IP 31: Porous materials IP 32: Colour change IP 33: Homogeneity IP 34: Discarding and recovering IP 35: Parameter change IP 36: Phase transition IP 37: Thermal expansion IP 38: Strong oxidants IP 39: Inert atmosphere IP 40: Composite materials
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MATS326-3 problem.ppt

8. Mind maps attributed to Tony Buzan classic book “Use Your Head”
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MATS326-3 problem.ppt

9. Mind maps
Image from
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MATS326-3 problem.ppt

10. Cause-and-Effect diagrams
often referred to as a fishbone diagram
or an Ishikawa diagram
introduced by Kaoru Ishikawa
simple graphical method to record and classify a chain of causes and effects in order to resolve a quality problem
25 January 2007
MATS326-3 problem.ppt

11. Cause-and-Effect diagrams
Clarify the object effect
Pick causes
Determine the priority causes
Work out the counteractions for priority causes
implement appropriate solutions to eliminate or reduce the causes of problems
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MATS326-3 problem.ppt

12. Cause-and-Effect diagrams I
Clarify the object effect
a numerical measurement should be established against which subsequent improvement can be judged
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MATS326-3 problem.ppt

13. Cause-and-Effect diagrams II
Pick causes
create a team of people to brainstorm possible causes that may lead to the effect
study the actual effect in the problem environment
on a horizontal line draw diagonal branches for direct causes of the effect
using arrows onto the branches create sub-branches for appropriate secondary causes
confirm all elements of the diagram are correctly positioned
quantify the causes wherever possible
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MATS326-3 problem.ppt

14. Cause-and-Effect diagrams III
Determine the priority causes
analyse any existing data for the problem
if practical, create a Pareto diagram. 
otherwise, determine a ranking of the relative importance of each cause.
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MATS326-3 problem.ppt

15. Cause-and-Effect diagrams IV
Work out the counteractions for priority causes
put in place appropriate solutions to eliminate or reduce the causes of problems
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MATS326-3 problem.ppt

16. Cause-and-Effect diagram:
Image from
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MATS326-3 problem.ppt

17. Failures Mode and Effects Analysis
FMEA is
a useful tool for reliability analysis
systematic check of a product or process
function
failure causes
failure modes
failure consequences
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MATS326-3 problem.ppt

18. Failures Mode and Effects Analysis
Requires a thorough knowledge of
functions of the components
contribution of those components to function of the system
For every failure mode at a low level, failure consequences are analysed at
the local level
the system level
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MATS326-3 problem.ppt

19. Failures Mode and Effects Analysis
FMEA is usually qualitative but may also be quantitative
initiated during planning and definition of a project to investigate qualitative reliability demands of the market
during design and development, for quantitative reliability activities
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20. Table From Evans and Lindsay Chapter 13
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MATS326-3 problem.ppt

21. Failures Mode and Effects Analysis
design-FMEA for design reviews
definition and limiting of the system
choice of complexity level
check of component functions
check of system functions
identification of possible failure modes
identification of consequences of failures
possibility of failure detection and failure localisation
assessment of seriousness of failure
identification of failure causes
interdependence of failures
documentation
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MATS326-3 problem.ppt

22. Failures Mode and Effects Analysis
quantitative design-FMEA a.k.a. FMECA Failure Mode, Effects and Criticality Analysis
consider every component
quantify and rank different failure modes
F = probability of failure
A = seriousness (consequences of failure)
U = probability of detection
subjective judgements on a scale of 1-5 or 1-10
Product (F*A*U) = Risk Priority Number (RPN)
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MATS326-3 problem.ppt

23. Failures Mode and Effects Analysis
Process-FMEA for
pre-production engineering
design of process control
process improvement
FMEA is efficient where component failure leads directly to system failure
for more complex failures, FMEA may be supplemented by Fault Tree Analysis (FTA)
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MATS326-3 problem.ppt

24. Some URLs for FMEA http://www.fmeainfocentre.com/
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MATS326-3 problem.ppt

25. Fault Tree Analysis
Logical chart of occurrences to illustrate cause and effects
developed by DF Haasl, HA Watson, BJ Fussell and WE Vesely
initially at Bell Telephone Laboratories then North American Space Industry
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MATS326-3 problem.ppt

26. Fault Tree Analysis Common symbols used 1 main event basic event
incompletely analysed event
restriction
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27. Fault Tree Analysis Common symbols used 2 or-gate and-gate
transfer to or from another place
& 1 +
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28. Figure From Evans and Lindsay Chapter 13
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29. Design of Experiments
originally conceived by Ronald Aylmer Fisher at Rothampstead Experimental Station during the 1920s
analysing plant growing plots under different conditions, and needed to eliminate systematic errors.
Image from
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MATS326-3 problem.ppt

30. Experimental design Randomisation
Replication - repetition so that variability can be estimated
Blocking - experimental units in groups (blocks) which are similar
Orthogonality - statistically normal.
Use of factorial experiments instead of one-factor-at-a-time
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MATS326-3 problem.ppt

31. Design of Experiments full factorial experiment
where a number of factors may influence the output of a process, it is possible to study all combinations of levels of each factor
if the number of factors considered increases, then number of experiments required increases more rapidly. 
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MATS326-3 problem.ppt

32. Design of Experiments
For two levels of n-variables, the number of experiments required is 2n
4 experiments for two variables (low-low, low-high, high-low and high-high)
16 experiments for four variables
64 experiments for six variables.
If three levels (low - normal - high) or more are to be studied, then a full factorial experiment soon becomes impractical.
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MATS326-3 problem.ppt

33. Design of Experiments
results plotted to indicate the influence of each of the factors studied
when one factor affects the response, this is known as the main effect.
when >1 factor affects the response, this is termed an interaction.
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34. Design of Experiments Genichi Taguchi developed orthogonal arrays
fractional factorial matrix
permits a balanced comparison of levels of any factor with a reduced number of experiments.
each factor can be evaluated independently of each of the other factors. 
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MATS326-3 problem.ppt

35. Arrays from http://www.york.ac.uk/depts/maths/tables/orthogonal.htm
Orthogonal arrays
L4: three two-level factors
L9: four three level factors
Arrays from
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MATS326-3 problem.ppt

36. Common orthogonal arrays
Levels
Equivalent Full Factorial L4
3 x 2 8 L8
7 x 2
128 L9
4 x 3 81
L12
11 x 2
2 048
L16
15 x 2
32 768
L25
6 x 5
15 625
L27
13 x 3
Table from Tony Bendell “Taguchi Methods”, 1989
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MATS326-3 problem.ppt

37. Taguchi Quality Loss Function L(x) = k ( x - t )2
L = the loss to society of a unit of output at value x  
t = the ideal target value
k = constant
as non-conformance increases, losses increase even more rapidly
25 January 2007
MATS326-3 problem.ppt