2. Unit I: Quality Engineering
An overall quality system
Quality engineering in production design
Quality engineering in design of production processes.
3. Unit II: Loss Function and Quality Level
Derivation and use of quadratic loss function
Eco. consequences of tightening tolerances as a means to improve quality
Evaluations and types tolerances (N-type, S-type and L-type)
Tolerance design and tolerancing:
Functional limits
Tolerance design for N-type, L-type and S-type characteristics.
4. Unit III: Allocation for Multiple Components;
Parameter and Tolerance Design
Introduction to parameter design
Signal to noise ratios
Parameter design strategy
Some of the case studies on parameter and tolerance designs
5. Unit IV: Analysis of Variance (ANOVA)
NO-way ANOVA
One-way ANOVA
Two-way ANOVA
Critique of F-test
ANOVA for four level factors
Multiple level factors.
6. Unit V: Orthogonal Arrays
Typical test strategies – Better strategies, Efficient strategies
Steps in designing
Conducting and analyzing an experiment
Interpolation of experimental results
Interpretation methods
Percent contributor
Estimating the mean
7. Unit VI: IS-9000 Quality System
Six-sigma
Bench marking
Quality circles
Brain Storming
Fishbone diagram
Problem analysis
8. Recommended Books:
1. Quality Engineering in Production Systems; G. Taguchi, A. Elsayed et al;
McGraw Hill Intl. Edition,1989
2. Taguchi Techniques for Quality Engineering; Phillip J. Ross; McGraw Hill,
Intl. 2nd Ed, 1995.
3. Quality Management; Kanishka Bedi; Oxford University Press; 10th
Edition, 2013.
4. Taguchi Methods Explained: Practical Steps to Robust Design; Papan P.
Bagchi; Prentice Hall Pvt. Ltd., New Delhi.
5. Design of Experiments using the Taguchi Approach; Ranjit K. Roy; John
Wiley & sons Inc. 2001.
9. QUALITY LOSS FUNCTION
In 1986, Taguchi presented the quadratic quality loss function for reducing
deviation from the target value.
According to the traditional concepts of quality, the product was certified
as good quality if the measured characteristics were within the
specification & vice versa. This is shown in figure.
This means that all products that meet the specifications are equally good.
But in reality it is not so. The product whose response is exactly on target
gives the best performance. As the product’s performance deviate from
the target, the quality becomes progressively worse
.
10.
11. According to Taguchi’s viewpoint, the quality loss function is a measure
for the evaluation of deviations from the target values of the product,
even when these lie within specifications. The quality loss function
focuses on the economic and societal penalties incurred as a result of
purchasing a nonconforming product.
The loss refers to the cost that is incurred by society when the
consumer uses a product whose quality characteristics differ from the
nominal. The concept of societal loss is a departure from traditional
thinking.
Taguchi identifies these losses to society not only in terms of rejection,
scrap, or rework, excessive costs of operating the product but also in
terms of pollution that is added to the environment, products that
wear out too quickly, or other negative effects that occur.
12. Dr. G. Taguchi developed a systemized statistical approach to
product and process improvement
The approach emphasizes moving quality upstream to the
design phase
Based on the notion that minimizing variation is the primary
means of improving quality
Special attention is given to designing systems such that
their performance is insensitive to environmental changes
13. Taguchi's philosophy involves three central ideas:
1. Products and processes should be designed so that they are robust to
external sources of variability.
2. Exptl design methods are engg. tool to help accomplish this objective.
3. Operation on-target is more imp. than conformance to specifications.
In order to reduce expected losses with respect to the quadratic loss
function, the process mean should be close to the target and process
standard deviation should be small.
Thus, if the quality characteristic concentrates on the target value with
minimum standard deviation, then it is said that the product has minimum
quality loss.
The quadratic quality loss function has been applied in online and off-line
quality control, for obtaining the economic design of control charts, of
sampling plans, and of specification limits.
14. To quantify loss to society, Taguchi used the concept of a quadratic loss
function (QLF). Figure S7.2 shows Taguchi’s concept of a quadratic loss
function.
16. Quality Loss for “the smaller the better” type
Eg: Radiation leakage from a microwave oven, Response time of
computer, Pollution from automobile etc.
17. Quality Loss for “The larger the better” type
Eg: Bond strength of adhesive.
18. Derivation and use of quadratic loss function
The taguchi Loss function L(y) is represented as
L(Y) = K x (y-m)2,
Where,
K is the constant whose value is dependent on the cost structure
of the process
Y is the value of the quality characteristic, and
m is the target value of the quality characteristic
The term (y-m) represents the deviation of the quality
characteristic from the target value. target value . At zero deviation,
the performance is on target, and the loss is zero.
19. The loss function represented by the above Eqn is shown in the
figure. It possesses the following characteristics:
The loss must be zero when the quality characteristic of a
product meets its target value
The magnitude of the loss increases rapidly as the quality
characteristic deviates from its target value.
The loss function must be a continuous (second order) function
of the deviation from target value, and differential everywhere.
20. Taguchi determined the loss function from Taylor series
expansion about the target value m. Thus
L(y) is minimum at y = m, the first derivative L’(m) = 0.
The terms with higher powers of (y-m) can be ignored as being
too small for consideration.
So, the loss function can be rewritten as
432
)).((""
!4
1
)).(('"
!3
1
)).(("
!2
1
)).(('
!1
1
)()( mymLmymLmymLmymlmLyL
2
)).(("
!2
1
)()( mymLmLyL
21. The expression is a constant and can be rep. as K.
The loss function thus becomes,
and can be interpreted as loss about the process mean plus the
loss due to displacement of the process mean from the target.
If the process mean coincides the target, the loss term L(m) is
zero and the Loss function reduces to
2
).()( myKyL
)("
!2
1
mL
2
).()()( myKmLyL
22. Average Loss per unit:
In mass production, the average loss per unit is expressed as,
n
mykmykmykmyk
yL n
22
3
2
2
2
1 ).(...).().().(
)(
n
mymymymy
kyL n
22
3
2
2
2
1 )(...)()()(
.)(
MSDkyL .)(
24. Tolerance
• Tolerance --The total amount by which a
specified dimension is permitted to vary
(ANSI Y14.5M)
• Every component
within spec adds
to the yield (Y)
25. Economic consequences of tightening tolerances as a
means to improve quality
The tolerance assignment approach used by most organizations
offers opportunities to reduce cost and improve quality through
tolerance relaxation. While quality improvement based on relaxed
tolerances seems counterintuitive, a quick look at how tolerances
are assigned and the consequences of overly-stringent tolerances
reveal why this is so.
We assign tolerances to nominal dimensions to make parts
producible and interchangeable. Tolerances are generally inversely
proportional to manufacturing cost, and this is due to the fact that
tighter tolerances are usually more difficult to achieve.
Manufacturing costs generally increase as tolerances are tightened,
and so does rejection likelihood. From a cost perspective, we want
tolerances to be as large as possible (consistent with assembly and
performance requirements).
26. The process variance can be lowered by tightening the process
tolerance, with extra cost incurred.
In case the conventional on-line PCI is used for process capability
analysis during the product development, designer engineers naturally
intend to raise the PCI value by locating the process mean near the
target value, and by reducing the tolerance value to ensure a better
product quality.
However, simply increasing the PCI value can easily create additional
and unnecessary production costs that result from extra efforts and
expensive devices for ensuring tolerance control.
27. The tolerance cost can be formulated in various function expressions.
To evaluate the tolerance cost, the tolerance cost function as
developed in the literature [Chase et al., 1990) is adopted
Where, a, b, and c are the coefficients for the tolerance cost function,
and t is the process tolerance.
From the above cost expression, it can be noted that a tight process
tolerance results in a higher tolerance cost, due to additional
manufacturing operations, more expensive equipment needed and
slower production rates, while a loose process tolerance results in a
lower tolerance cost
tc
ebaTCM .
.)(
28. The designers would most likely establish the process mean as close
as possible to the design target , within the process feasible range,
and attempt to decrease the process variance as much as possible
within the process capability limits in order to attain a higher PCI
value.
In other words, with the exclusive use of the process mean and
process tolerance as the determinants of conventional PCI,
regardless of the cost impact on customer and production, there is a
tendency for designers to position the process mean as close to the
target value as possible, and solely cut down the process tolerance
to lower capability limit in order to increase the PCI value.
29. Reducing the process variance is normally completed by
tightening the tolerance value through tolerance design which
usually involves additional cost.
Therefore, in addition to the constraints from feasible ranges and
capability limits, the influence exerted by the relevant costs
representing the selected process mean and process tolerance,
should be considered as well.
The costs related to process mean and process tolerance must be
contained in PCI expression, when referred to as off-line process
capability analysis, during product design and process planning.
36. A spring is used in the operation of a camera shutter. The
manufacturing process suffers from a degree of variability, in terms of
the spring constant (measured in oz/in), which significantly effects the
accuracy of the shutter times. The functional limits for this spring
constant are m±0.3oz/in (m=0.5oz/in), and the average cost for
repairing or replacing a camera with a defective spring is Rs. 20.
What is the loss function? Hence, what is the loss associated with
producing a spring of constant 0.25oz/in versus the loss associated
with one at 0.435oz/in.
37. Suppose you are manufacturing green paint. To determine a
specification for the pigment, you must determine both a
functional tolerance and customer loss. The functional
tolerance, Δ0 is a value for every product characteristic at which
50% of customers view the product as defective. The customer
loss, A0, is the average loss occurring at this point. Your target is
200g of pigment in each gallon of paint.
The average cost to the consumer is $10 per gallon from returns or
adjusting the pigment. The paint becomes unsatisfactory if it is out
of the range . Calculate the loss imparted to society from a
gallon of paint with only 185g of pigment.
38. This figure is a rough approximation of the cost imparted to society
from poor quality.
39. Evaluations of tolerances (N-type, S-type and L-type)
The literature indicates three type of tolerances:
the nominal - the best (N-type)
the smaller - the better (S-Type)
the larger – the better (L-Type)
“The nominal - the best” type is required in many cases
when a nominal characteristic can vary in two directions.
40. Tolerance design and tolerancing:
Tolerance design is used to determine and analyze tolerances around the
optimal settings recommended by the parameter design.
The purpose of tolerance design is to set acceptance regions for the design
parameters. Tolerance design is required if the reduced variation obtained by
the parameter design does not meet the required performance. The
tolerance is usually given in the form of an upper and lower bound.
Tolerance is needed because the excessive variations in the design parameter,
which corresponds to larger a;, will lead to excessive variability of the quality
characteristics, a;. As a result, we get an unacceptable quality loss.
Therefore, tolerance limits should be set to limit the variations of design
parameters. Typically, tightening tolerances mean purchasing better- grade
materials, components, or machinery, which increases cost.
46. According to Taguchi’s quality engineering philosophy and
methodology, there are three important steps in designing a product
or process:
System design,
Parameter design and
Tolerance design.
SYSTEM DESIGN
The aim of system design is to create a product that indeed possesses
the properties intended for it at the planning stage. This involves the
development of a prototype, choice of materials, parts, components,
assembly system and manufacturing processes, so that the product
fulfils the specified conditions and tolerances at the lowest costs.
47. PARAMETER DESIGN:
Parameter design tries to determine the connections between
controllable and noise factors, in order to ascertain the best
combination of factor levels in the manufacturing process,
having the purpose of achieving robustness, and improving
quality, without increasing costs.
TOLERANCE DESIGN:
Tolerance design tries to narrow the ranges of the operating
conditions, so that the most economical tolerances are
obtained.
59. Robust Parameter Design
A statistical / engineering methodology that aim at reducing
the performance “variation” of a system.
• The selection of control factors and their optimal levels.
The input variables are divided into two board categories.
Control factor: the design parameters in product or process design.
Noise factor: factors whoes values are hard-to-control during normal
process or use conditions
The “optimal” parameter levels can be determined through
experimentation
61. Signal, Noise and Control Factors:
i) Signal Factors :
These are parameters set by the user to express the intended value for
the response of the product. Example- Speed setting of a fan is a signal
factor for specifying the amount of breeze. Steering wheel angle – to
specify the turning radius of a car.
ii) Noise Factors:
Parameters which can not be controlled by the designer or parameters
whose settings are difficult to control in the field or whose levels are
expensive to control are considered as Noise factors (Disturbances).
The noise factors cause the response to deviate from the target specified
by the signal factor and lead to quality loss.
iii) Control Factors: Parameters that can be specified freely by the designer.
Designer has to determine best values for these parameters to result in
the least sensitivity of the response to the effect of noise factors.
64. Analysis of Variance (ANOVA)
A technique which subdivides the total variation of a set of data
into meaningful component parts associated with specific sources
of variation for the purpose of testing some hypothesis on the
parameters of the model or estimating variance components.
65. ANOVA
To obtain the most desirable iron castings for an engine block, a design
engineer wants to maintain the material hardness at 200 BHN. To
measure the quality of the casting being supplied by the foundry the
hardness of the 10 castings chosen at random from a lot is measured
and displayed in the table below
Sample Hardness Sample Hardness
1. 240 6. 180
2. 190 7. 195
3. 210 8. 205
4. 230 9. 215
5. 220 10. 215
73. Design of Experiments
A designed experiment is an experiment where one or more variables,
called independent variables, believed to have an effect on the
experimental outcome are identified and manipulated according to a
predetermined plan. Data collected from a designed experiment can be
analyzed statistically to determine the effect of the independent
variables, or combinations of more than one independent variable.
Experiment design: The arrangement in which an experimental program
is to be conducted, and the selection of the versions (levels) of one or
more factors or factor combinations to be included in the experiment.
The statistically designed experiment is able to extract a maximum
amount of information from a limited set of observations
Factor: An assignable cause which may affect the responses (test results)
and of which different versions (levels) are included in the experiment.
74. Full And Fractional Factorial Designs:
Factorial experiments: Experiments in which all possible treatment
combinations formed from two or more factors, each being studied at two or
more versions (levels), are examined so that interactions (differential effects)
as well as main effects can be estimated.
Full factorial experiments are those where at least one observation is
obtained for every possible combination of experimental variables. For
example, if A has 2 levels, B has 3 levels and Chas 5 levels, a full factorial
experiment would have at least 2x3x5=30 observations.
Fractional factorial or fractional replicate are experiments where there are
some combinations of experimental variables where observations were not
obtained. Such experiments may not allow the estimation of every
interaction. However, when carefully planned, the experimenter can often
obtain all of the information needed at a significant savings.
Balanced Design: An experimental design where all cells (i.e. treatment
combinations) have the same number of observations.
75. Response variable:
The variable (output(s) of a process ) being investigated , also called the
dependent variable.
Primary variables: (aka main factors, main effects, inner array)
The controllable variables believed most likely to have an effect. These may
be quantitative, such as temperature, pressure, or speed, or they may be
qualitative such as vendor, production method, or operator.
Background variables: (aka subsidiary factors, outer array)
Variables, identified by the designers of the experiment, which may have an
effect but either can not or should not be deliberately manipulated or held
constant. The effect of background variables can contaminate primary
variable effects unless they are properly handled.
Experimental error:
In any given experimental situation, a great many variables may be potential
sources of variation. So many, in fact, that no experiment could be designed
that deals with every possible source of variation explicitly.
76. Treatment :
A treatment is the factor being investigated (material, environmental
condition, etc.) in a single factor experiment. In factorial experiments (where
several variables are being investigated at the same time) we speak of a
treatment combination (Also known as a run) and we mean the prescribed
levels of the factors to be applied to an experimental unit.
Interaction:
A condition where the effect of one factor depends on the level of another
factor.
77. Replication
Replication—The collection of more than one observation for the same
set of experimental conditions. Replication allows the experimenter to
estimate experimental error. If variation exists when all experimental
conditions are held constant, the cause must be something other than
the variables being controlled by the experimenter.
Experimental error can be estimated without replicating the entire
experiment. Replication also serves to decrease bias due to
uncontrolled factors.
78. Randomization
A schedule for allocating treatment material and for conducting
treatment combinations in a DOE such that the conditions in one
run neither depend on the conditions of the previous run nor
predict the conditions in the subsequent runs.
In order to eliminate bias from the experiment, variables not
specifically controlled as factors should be randomized. This means
that allocations of specimens to treatments should be made using
some mechanical method of randomization, such as a random
numbers table. Randomization also assures valid estimates of
experimental error.
79.
80. Developing a Cause-and-Effect Diagram:
1. Construct A Straight Horizontal Line (Right Facing)
2. Write Quality Characteristic At Right
3. Draw 45° Lines From Main Horizontal (4 Or 5) For Major Categories: Manpower,
Materials, Machines, Methods And Environment
4. Add Possible Causes By Connecting Horizontal Lines To 45° "Main Cause" Rays
5. Add More Detailed Potential Causes Using Angled Rays To Horizontal Possible
Cause Lines
81. Generic Fishbone C&E Diagram
Methods Manpower
Materials Machines
Effect
under
Study
Environment
Main Causes
Primary Cause Primary Cause
2nd Cause 2nd Cause
2nd Cause
82. Building the ‘Experiment’ Working From a Cause & Effect
Diagram
Fine Grained
Chemical Yield
Raw Material
Reaction
Transportation
Moisture
Content
Catalyzer
Crystallization
Package
Over Weight
Shortage of
Weight
Discharge
Method
Sol. A Conc.
Sol. B Temp.
pH
Time
Stir RPM
Sol A
Pour Speed
Quality
Type
Quantity
Spillage
Road
Container
Cover
Time
Concentration
Temperature
Weight Size
Maint. Of
Balance
Accuracy of
Balance
Operator
Type of
Balance
Method of
Weighing
‘Mother Crystal’
Steam
Press.
Steam
Flow
RPM of
Dryer
Charge Speed
Wet Powder
Temperature
