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PE-7221
Quality Engineering and
Management (Taguchi Method)
Prof. Charlton S. InaoDefence University
College of Engineering
Bishoftu,Ethiopia
Chapter 2: Quality Loss Function
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Week 2 outline
Introduction to Quality Loss Function
Quality Loss Function for Various Quality
Characteristics Specification Tolerance
Tolerance Design
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Quality is often referred to as conformance to
specifications. However, Taguchi proposes
a different view of quality, one that relates it to
cost and loss in dollars, not just to the
manufacturer at the time of production but to
the consumer and to society as a whole.
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Loss is usually thought of as additional
manufacturing costs incurred up to the point that a
product is shipped. After that, it is society, thecustomer, who bears the cost for loss of quality.
Initially, the manufacturer pays in warranty costs.
After the warranty period expires, the customer
may pay for repair on a product. But indirectly, themanufacturer will ultimately foot the bill as a
result of negative customer reaction and costs that
are difficult to capture and account for, such as
customer inconvenience and dissatisfaction, andtime and money spent by customers.
As a result, the companys reputation will be
damaged, and eventually the market share will be
lost.
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Real growth comes from the market, cost, and
customer satisfaction. The money the customer
spends for a product and the perceived loss due to
poor quality ultimately come back as long-term
loss to the manufacturer.
Taguchi defines qualityas the loss imparted by
the product to the society from the time the
product is shipped.
The objective of the quality loss function is
quantitative evaluation of
loss caused by functional variation of a product.
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The loss function is calculated from the square of
the reciprocal of the process capability index
after multiplying a constant related to
economy. It is an economic forecasting value
that is imparted to the customer in the market.
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The Meaning of Quality
Quality is related to the loss to society caused by aproduct during its life cycle
The loss a customer sustains takes many forms, but isgenerally a loss of product function or properties.
Quality is judged by one true evaluator, thecustomer
According to Taguchi
Note: Genichi Taguchi is a Japanese electrical engineer who studied design of
experiments during the 50s and then wrote his own approach to
experimentation.
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Traditional Taguchis
There is Good or BadProducts only as per Limits.
When a product moves fromits target will cause the loss
even if the product lies ornot within Limits.
Traditional and Taguchis Definition of
Quality
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Taguchis U-shaped loss Function Curve
Measured
characteristic
Taguchi loss Fn
LTL Nominal UTL
Scrap or Rework Cost.
Loss
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Robust Design/Robustness
the state where the technology, product, or
process performance is minimally sensitive to
factors causing variability and aging, at the
lowest unit manufacturing cost.
-Dr. Genichi Taguchi
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Quality LossFunction for
Various Quality
Characteristics
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Classification of Quality
Characteristics
1. Nominalis the best (NTB) -dimension = shaft
2. Higher is the better (HTB)= efficiency, profit,yield
3. Lower is the better(HTB) =shrinkage, defect,pollution, contamination
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Nominal -the-Best Case
Control of aerosol flow from a spray can Boring an engine cylinder to an aim or target
diameter.
Controlling the diameter of a filament for a lightbulb.
Controlling the texture of an ice cream product
Controlling the gain of an op-amp
Maintaining the part geometry of an injection
molded part
Creating a particular hue(color) in mixing paint
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Smaller -the-Better Case
Microwave radiation leakage
Time to first print in the copy or printer machine
Paper jams in a copier,pack feed, printer defects
Defects on an image
Background density on a text image
Automotive exhaust pollution
Steering column vibration
EMI from consumer electronics
Corrosion of metals
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Taguchis Loss Function
Taguchis Loss Functionrecognizes the customersdesire to have products thatare more consistent, part topart, and a producers desireto make a low-cost product.This is modeled three ways.
As can be seen, the qualityloss function has three
components:
1) Cost coefficient, k2) Variance, S23) Bias squared, (y-m)2
Nominal the Best
(NB)
Higher the Better
(HB)
Smaller the Better
(SB)
USLLSL
Loss
in$
LSL
Loss
in$
USL
Loss
in$
h
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Type Of
Characteristic
Loss For
An Individual Part
Average Loss Per Part
In a Distribution
NB
HB
SB
])my(S[k)Y(L22
)]y/S3(1][y/1[k)Y(L222
)]y(S[k)Y(L22
)y/1(k)Y(L2
2
)my(k)Y(L
)y(k)Y(L2
Taguchis Loss Function
S2 = variance=2
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Loss in a Distribution
(more than one piece)
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Nominal =115
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Example: NTB Nominal =115
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Compute for the average
N data
1 112
2 113
3 112
4 1135 112
6 113
7 114
8 115
9 11210 113
11 114
12 112
13 114
average 113
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Calculate the variance,MSD
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Calculate for the Loss=k(MSD)
L=0.25(4.92)=$1.23
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Example for Smaller the Better
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Specification
Tolerancing
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In quality engineering, tolerance is not the
deviation between products.
Tolerance is defined as a deviation from target.
Tolerance is determined so that the loss caused
by the manufacturer and the one caused by the
customer are balanced.
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Taguchis Loss FunctionApplying The Loss Function To
Determine FactoryTolerances(Specification tolerances)
Example:
In automatic transmissions the shift pointsare supposed to occur at a certain throttle
position. Heavy-duty truck users areparticularly sensitive to this characteristic.Usually, it takes the producer $100.00 toadjust a valve body under warranty when acustomer complains of the shift point. Fromthe information the engineers haveavailable, the average customer would askfor an adjustment if the shift point is off fromthe nominal by 40 rpm transmission outputspeed on the first-to-second gear shift.Determine the limits that would define whenan adjustment should be made at thefactory to avoid the complaints in the future.
Here, the cost of adjustment is only $10.00.
Solution:
Loss = k (y-m)2
$100.00 = k (40)2
k = $0.0625 / rpm2
At the factory level,
Loss = k (y-m)2
$10.00 = 0.0625 (y-m)2
(y-m)2 = ($10.00 / 0.0625)= 160
(y-m) = (160)
= 13 rpm
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The End