Design for Six-Sigma
in the School of Computing, Engineering and Physical Sciences
Design reliability
by Dr J. Whitty
1
Lessons structure
• The lessons will in general be subdivided
in to eight number of parts, viz.:
1)
2)
3)
4)
5)
Statement of learning objectives
Points of orders
Introductory material (Six-sigma philosophies)
Concept introduction (Design for Six-sigma)
Development of related principles (Product
relability)
6) Concrete principle examples via –
reinforcement examination type exercises
7) Summary and feedback
8) Formative assessment, via homework task
2
School of Computing,
Engineering & Physical Sciences
Learning Objectives
3
After the session the students should be able to:
 Describe world class high-quality and
hence six-sigma from a quantitative
viewpoint
 Use acceptable industrial standard to
evaluate control limits
 Describe generic operational design
processes
 Accurately distinguish between quality
and reliability
 Evaluate the reliability of simple
systems
Learning Check: Six Sigma
Prioritise (D)
Measure (M)
Hold
gains (C)
Interpret
(D/M/A)
Improve (I)
4
Problem (D/M/A)
solve
Examination type
questions
• Statistical process control has been used in the
manufacturing industry since the 1980s to
improve the quality of engineered components
a. Define high-quality from a quantitative viewpoint (4)
b. With reference to the answer in part (a) how does quality differ
from reliability (6).
c. 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
………..
5
Examination type question
continued
d. 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:
d.
e.
f.
The process CV. (2)
The UCL and LCL (9)
The minimal allowable design tolerance for the process,
giving reasons for you answer. (5)
e. *Describe how design packages such as ANSYS
and MATLAB can be employed to facilitate sixsigma methodologies (6)
*This is this weeks research task
6
What is Engineering Design?
• The systematic and creative application of
scientific and mathematical principles to
practical ends such as the design,
manufacture, and operation of efficient and
economical structures, machines, processes,
and systems.
7
The basic purpose of any organization is to
provide products or services to their customers.
Thus, the design of these
products and services is
essential to the livelihood
of a company.
But, what are the
characteristics of an
Effective Design?
8
1. Idea Generation
(Product Design)
A Design
Process
2. Feasibility Study
(Performance Specifications)
3. Preliminary Design
(Prototype)
4. Final Design
(Final Design Specifications)
5. Process Planning
(Manufacturing Specifications)
9
The Design
Process
Idea
generation
Feasibility
study
Product Yes Preliminary
feasible?
design
No
Final
design
Prototype
Process
planning
Design & Manufacturing
Specifications
10
Manufacturing
The Product Design process
• It is difficult to say the
least to encompass all of
these facets into an all
encompassing model of
the design process.
• If fact many texts are
dedicated to the subject
and French does attempt
to summarize the
process as concisely
enough for general use.
11
A generic design
process
Market Need
MR
Initial problem definition
P. D. S.
Design brief
Conceptual
Design
To detail design
12
From sales
A generic produce design
process cont…
From conceptual design
Detail
Design
To MR
Synthesis & analysis
Product Presentation
Sales
Product testing
Product appraisal
13
The conceptual design
phase
Conceptual
Design
Ideas generation
Possible solutions
Proposed solutions
Solutions
Development
Stop
14
• As noted
previously this
phase is
actually a subprocess and my
be modelled as
shown.
Make or Buy
Decision
BOM
Process selection &
Design process
Purchas
e
Make
Process
Identification
Operations
Equipment
Production
times
Utilizations
Alternatives
Result
Process
Selection
CAPP
Route
Sheet
CAD
Assembly Chart
Components
Group
Technology
Liaison
Sequence
Analysis
1 & 11
Precedenc
e
Diagram
Operation
Process
Chart
Sub Assemblies
Assemblies
Packaged Product
15
Facilities Design
Product
Process
Design
Decisions
Facilities Planner
Organizational Objectives
Facility Planning Tools
Evaluate
Pareto Charts
Alternatives
1.
2.
3.
4.
16
Layout
Handling
Storage
Unit load
design
7 Management & Planning tools
Affinity Diagram
Interrelationship diagraph
Tree diagram
Matrix diagram
Contingency diagram
Activity network diagram
Prioritization matrix
Reliability Block Diagrams
• Most systems are defined through a combination of
both series and parallel connections of
subsystems
• Reliability block diagrams (RBD) represent a
system using interconnected blocks arranged in
combinations of series and/or parallel
configurations
• Reliability block diagrams can consider active and
stand-by states to get estimates of reliability
The individual subsystem/ components
being estimated from:
17
Series Systems
1
2
• For n components in series, the
probability of failure is then
• Therefore, for a series system, the
system probability of failure is the
sum of the individual component
probabilities
• In case the component probabilities are
not small, the system probability of
failure can be expressed as
18
Series Systems (cont’d)
• Reliability is the complement of the
probability of failure
• For the two components in series,
the system reliability can be
expressed as
• Assuming independence
• For n components in series the
system is the product of the
individual component reliabilities
19
1
Parallel Systems
2
• For n components in parallel, the
probability of failure is then
• Therefore, for a parallel system, the
system probability of failure is the
product of the individual component
probabilities
• The reliability of the parallel system of
n components is
20
Example Problem
Compute the reliability and probability of failure for the following
system. Assume the failure probabilities for the components are R1 =
0.99, R2 = 0.98 and R3 = 0.97.
2
1
3
21
Things to Consider
• Reliability block diagrams can also be used to assess
– Voting systems (k-out-of-n logic)
– Standby systems (load sharing or sequential
operation)
• Simple systems can be assessed by gradually
reducing them to equivalent series/parallel
configurations
• For complex systems, great effort is needed to
identify the ways in which the system fails or survives
– Fault trees can be used to decompose the main
failure event into unions and intersections of subevents
22
Further reliability examples
1. A car has four wheels to which tyres are fixed,
each with a reliability of 0.999 over a year. What
is the readability of four tyres, over the year, as a
single system.
2. A trailer has eight wheels which tyres are fixed, if
the wheels are mounted in pairs such that one
tyre does not effect the performance of another
within designate pairs find the reliability of the
trailer if one tyre has a probability of failure of 1%.
3. A system contains four-major sub-systems with
the most and least critical reliabilities begin 0.95
and 0.99. Evaluate the reliability of the system
assuming the remaining sub-systems are equally
distributed.
23
Session Summary
• Have we met our learning objectives, in
particular are you will be able to:





24
Describe world class high-quality and hence
six-sigma from a quantitative viewpoint
Use acceptable industrial standard to evaluate
control limits
Describe generic operational design processes
Accurately distinguish between quality and
reliability
Evaluate the reliability of simple systems
Examination type
question
•
25
An assembly pipe-flange consisting of four main sub-system is
required on an oil-refinery and If it is known that the flange seal is
least reliable at 0.94; the pipes reliabilities are 99.6%. The reliabilities
of all other sub-systems being normally distributed.
(a) Evaluate the reliability of the assembly [4]
(b) Calculate the effect on the reliability of the assembly if a second
seal is included in the assembly [6]
(c) the inspection department provides accurate measurements in
mm of a sample of seven seals thus, 57.5, 57.8, 57.6, 57.8,
57.7, 57.5, 57.4. Assuming the said sample is normally
distributed evaluate the nominal dimension and tolerance. [8]
Examination type
question (cont’d)
(d) The design engineer states that the due to the
physics of the situation the tolerance should be
57.2/57.5 and suggest one way of improving quality
would be to make the seals in-house as oppose to
purchasing from the existing supplier. A condition
monitoring regime is put in place to investigate the
quality of a CNC milling machine with the following
mean and range data:
26
Sample
1
2
3
4
5
6
Mean
57.68
57.21
57.22
57.58
57.61
57.25
range
0.3
0.5
0.4
0.4
0.5
0.4
Examination type question
(cont’d)
(d) The design engineer states that the due to the
physics of the situation the tolerance should be
57.2/57.5 and suggest one way of improving
quality would be to make the seals in-house as
oppose to purchasing from the existing supplier.
Sample
1
2
3
4
5
6
Mean
57.68
57.21
57.22
57.58
57.61
57.25
range
0.3
0.5
0.4
0.4
0.5
0.4
(i)
(ii)
Evaluate the process control value. [4]
Calculate the upper and lower control and warning limits;
given that the means were taken form a normally
distributed sample of size 10. [12]
(iii) Can the process be used to improve the seal quality [6]
[35 marks]
27