1. Taguchi Quality Loss Function
Guided By -
Prof. Jagtar Singh (Department of Mech. Engg. SLIET Longowal)
Submitted By –
Janpriy Sharma (PG-MSE )
Ankit Rathi (PG-MSE )
Minesh Bhadoria (PG-MSE )
Vinamara Patel (PG-MSE )

2. TAGUCHI DEFINITION OF QUALITY
The quality of a product is defined as the loss imparted by the product to society from the time the product is shipped to the customer. The loss may be due to failure, repair, variation in performance, pollution, noise, etc. A truly high quality product will have a minimal loss to society.
The following are the types of loss:
Product returns
Warranty costs
Customer complaints and dissatisfaction
Time and money spent by the customer
Eventual loss of market share and growth

3. What is Taguchi Quality Loss Function ?
The loss which we are talking about is the loss due to functional variation/process variation.
Taguchi quantified this loss through a quality loss function. The quality characteristic is the object of interest of a product or process. Generally, the quality characteristic will have a target.

4. QUALITY LOSS FUNCTIONS
Nominal – The Best
Smaller – The Better
Larger – The Better

5. QUALITY LOSS FUNCTIONS (Contd.)
Nominal – The Best Case
When we have a characteristic with bi-lateral tolerance, the nominal value is the target. That is, if all parts are made to this value, the variation will be zero and it is the best.
For example: A component with a specification of 10 ± 0.01 mm has the nominal value of 10 mm. Similarly, if the supply voltage has a specification of 230 ± 10 V. Here the nominal value is 230 V.

6. Quality Loss Functions (Contd.)
Nominal – The Best case
When the quality characteristic is of the type Nominal–the best, the quality loss function is given by
L(Y) = K(Y – T)2
Y = value of the quality characteristic (e.g., length, force, diameter etc.)
L(Y) = loss in Rs. per product when the quality characteristic is equal to Y
T = target value of Y
K = proportionality constant or cost coefficient which depends on the cost at the specification limits and the width of the specification

7. Graphical Representation for QLF for Nominal the Best Case

8. Graphical Representation for QLF for Nominal the Best Case (Contd.)
A0 = Loss incurred (In Rs.) in tolerance zone of consumer tolerance
T = Target Value
Y= Achieved Value

9. Problem on QLF for Nominal The Best Case

10. Estimation of Average Quality Loss Function
The quality loss we obtain is for a single product. The quality loss estimate should be an average value and should be estimated from a sample of parts/products. Suppose we take a sample of n parts/products. Then we will have y1, y2, ..., yi values (where, i = 1, 2, 3, ..., n)
Let the average of this sample = Y, this Y may or may not be equal to the target value (T).

12. Smaller- The Better QLF
Smaller–the better: It is a non negative measurable characteristic having an ideal target as zero.
For example: Tyre wear, pollution, process defectives, etc.

13. Smaller – The Better QLF (Contd.)
For this case the target value T = 0 Substituting this in Loss Function Equation we get
L(Y) = K(Y – 0)2 = K Y2
And K= L(Y) = A0
K Δ20

14. Graphical Representation for QLF for Smaller - The Better Case

15. Estimation of Average Quality Loss for Smaller – the Better

16. Numerical Problem on Smaller – The Better Case

17. Numerical Problem (Contd.)

18. Larger - The Better QLF
It is also a non negative measurable characteristic that has an ideal target as infinity
For example: Fuel efficiency, strength values, etc.
Mathematically, Larger the better QLF is inverse of Smaller – The Better characteristic.
L(Y) = K(1/K2)
And K= L(Y) x K2 = A0 x Δ20

19. Graphical Representation and Average Loss Function Calculation

20. What is Robust Design ?
A product or a process is robust if its performance is not affected by the noise factors.
Robust design is a procedure used to design products and processes such that their performance is insensitive to noise factors.

21. Robust Design (Contd.)
In order to achieve a robust product/process one has to consider both location effect and dispersion effect. Taguchi has suggested a combined measure of both these effects. Suppose m is the mean effect and σ2 represent variance (dispersion effect).
These two measures are combined into a single measure represented by m2/σ2. In terms of communications engineering terminology m2 may be termed as the power of the signal and σ2 may be termed as the power of noise and is called the SIGNAL TO NOISE RATIO (S/N ratio).
The data is transformed into S/N ratio and analysed using ANOVA and then optimal levels for the factors is determined. This leads to the development of a robust process/product

22. Signal To Noise Ratio (S/N Ratio)
The signal to noise ratio (S/N ratio) is a statistic that combines the mean and variance.
The best levels of control factors are those that maximize the S/N ratio.
The objective in robust design is to minimize the sensitivity of a quality characteristic to noise factors.
In setting parameter levels we always maximize the S/N ratio irrespective of the type response (i.e. maximization or minimization). These S/N ratios are often called objective functions in robust design.

23. Types of S/N Ratio Smaller–the better Nominal–the best
Larger–the better

24. Mathematical Formulation of Various Types of S/N Ratio
Smaller–the better - The desired value (the target) is zero. These problems are characterized by the absence of scaling factor (ex: surface roughness, pollution, tyre wear, etc.).
The S/N ratio (ɳ) is given by
where n is the number of replications.

25. Types of S/N Ratio (Contd.)
Nominal the Best -In these problems, the quality characteristic is continuous and non-negative. Its target value is non-zero and finite. We can use adjustment factor to move mean to target in these types of problems.

26. Types Of S/N Ratio (Contd.)
Larger the Better - The ideal target value of this type quality characteristic is (as large as possible). Quality characteristics like strength values, fuel efficiency, etc. are examples of this type. The S/N ratio ( ) is given by

27. Refrences
Applied Design of experiments And Taguchi Method by P. Shahabudeen and K. Krishnaiah PHI Learning.
Introduction to Quality Engineering, Taguchi, Asian Productivity Organization, UNIPUB, White Plains, New York.
Statistical Quality Control By M. Mahajan by Dhanpat Publication.
businessdictionary.com/definition/Taguchi-loss-function
brighthubpm.com/six-sigma/88546-taguchi-loss-function-definition-and-example/
Wikipedia.com