PE-7221 2nd Week Quality Loss Function

7/27/2019 PE-7221 2nd Week Quality Loss Function

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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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PE-7221 2nd Week Quality Loss Function