offline quality tool # Total Quality Management

1. TAGUCHI’S
QUALITY
LOSS
FUNCTION
Genichi Taguchi

2. 2
Overview
• Taguchi Design of Experiments
• Background of the Taguchi Method
• The Taguchi Process
Robust Design – The Taguchi Philosophy

3. INTRODUCTION
• Taguchi Methods is a statistical methods
developed largely by GENICHI TAGUCHI to
improve quality of manufactured goods.
• The philosophy of off-line quality control.
• Innovations in the design of experiments.

4. Taguchi Loss Function Definition
• Taguchi defines Quality as “the loss imparted by
the product to society from the time the product
is shipped.”
• LOSS = Cost to operate, failure to function, M &
R costs (Maintenance & Repair) , customer
satisfaction, poor design, depletion of resource,
environmental cost.
• Product to be produced “being within
specification”???

5. Taguchi’s Vs Traditional Approach
Taguch’s Traditional
When a product moves from
its Target will cause the loss
even if the product lies or
not within Limits
There is Good or Bad
Products only as per Limits

6. 6
• Introduced by Dr. Genichi Taguchi (1980)
– Comparable in importance to Statistical Process Control (SPC), the
Deming approach and the Japanese concept of TQC
• Unique aspects of the Taguchi method
– The Taguchi definition of quality
– The Taguchi Quality Loss Function (QLF)
– The concept of Robust Design
 The Taguchi definition of quality
– Ideal quality refers to a target value for determining the quality level
– Ideal quality is delivered if a product or service tangible performs its
intended function throughout its projected life under reasonable
operating conditions without harmful side effects
– Ideal quality is a function of customer perception and satisfaction
– Service quality is measured in terms of loss to society
• The traditional definition is “conformance to specifications”
Background of the Taguchi Method

7. Taguchi’s Quadratic Quality Loss Function
• Quality Loss Occurs when a product’s deviates
from target or nominal value.
• Deviation Grows, then Loss increases.
• Taguchi’s U-shaped loss Function Curve.

8. Taguchi’s U-shaped loss Function Curve.
LTL Nominal
Measured
characteristic
UTL
Taguchi loss Fn
Scrap or Rework Cost.
Loss

9. • Many factors/inputs/variables must be taken into consideration
when making a product especially a brand new one.
• The Taguchi method is a structured approach for determining
the “best” combination of inputs to produce a product or
service.
– Based on a Design of Experiments (DOE) methodology for determining
parameter levels
• DOE is an important tool for designing processes and products
– A method for quantitatively identifying the right inputs and parameter
levels for making a high quality product or service
• Taguchi approaches design from a robust design perspective.
Taguchi Design of Experiments

10. • “Products and services should be designed to be inherently
defect free and of high quality”
– Meet customers’ expectations also under non-ideal conditions
• Disturbances are events that cause the design performance to
deviate from its target values
• Taguchi divide disturbances into three categories
– External disturbances: variations in the environment where the
product is used
– Internal disturbances: wear and tear inside a specific unit
– Disturbances in the production process: deviation from target values
• A three step method for achieving robust design (Taguchi)
1. System/Concept design
2. Parameter design
3. Tolerance design
• The focus of Taguchi is on Parameter design
Robust Design (I)

11. 11
1. Concept Design
– Scientific and engineering principles and experience are used
to create a prototype that will meet the functional
requirements and also create the process that will build it.
– The process of examining competing technologies for
producing a product - Includes choices of technology and
process design.
– A prototype design that can be produced and meets customers’
needs under ideal conditions without disturbances.
Robust Design (II)

12. 2. Parameter Design
– The selection of control factors (parameters) and their
“optimal” levels
 The objective is to make the design Robust!
– Control factors are those process variables management
can influence.
 Ex. the procedures used and the type and amount of training
 Often a complex (non-linear) relationship between the control
factors and product/design performance
– The “optimal” parameter levels can be determined
through experimentation.
Robust Design (III)

13. 3. Tolerance Design
– Development of specification limits
 Necessary because there will always be some variation in the
production process
 Taguchi fiercely advocates aiming for the target value not just
settle for “inside the specification limits”!
– Occurs after the parameter design
– Often results in increased production costs
 More expensive input material might have to be used to meet
specifications
Robust Design (IV)

14. 14
• The traditional model for quality losses
– No losses within the specification limits!
The Taguchi Quality Loss Function (I)
• The Taguchi loss function
– the quality loss is zero only if we are on target
Scrap Cost
LSL USL
Target
Cost

15. Scrap Cost
LSL USL
m
Loss
(y)
The Loss Function: L(y) = k (y-m)2
‘k’ is a proportionately constant, ‘m’ is the target value, and ‘y’ is the value of the
quality characteristic.
No loss when no deviation.
The constant “k” can be evaluated if the loss L(y) is known for any particular value of
the quality characteristic: it is influenced by the financial importance of the quality
characteristic.

16. To determine constant k, suppose tolerance range is (m-∆,m+∆). This represents max
permissible variation. Suppose consumer’s average loss is A when the Q characteristic
is at the limit of functional tolerance. Using L(y) = k (y-m)2, we find k as
A= k∆2 or k= A / ∆2
The loss function can be written as
L(y) = A / ∆2 (y-m)2
The expected loss is the mean loss over many instances of the product. The expectation
is taken wrt the distribution of the Q characteristic Y.
We have
E(L(y)) = E(k(y-m)2) = k(MSD), MSD is mean std dev of y
MSD = Summation of (yi-m)2 / n, i=1to n
L(y)
m
m-∆ m+∆
A

17. Ex: Customer tolerances for the height of a steering
mechanism are 1.5+- 0.020 m. For a product that just
exceeds these limits, the cost to the customer for getting
fixed is Rs 50. Ten products are randomly selected and yield
the following heights (in meters) :
1.53,1.49,1.50,1.49,1.48,1.52,1.54,1.53,1.51 and 1.52. Find
the average loss per product item.

18. Ex: Customer tolerance for the height of a steering mechanism are 1.5+- 0.020 m. For a product that just
exceeds these limits, the cost to the customer for getting fixed is Rs 50. Ten products are randomly selected
and yield the following heights (in meters) : 1.53,1.49,1.50,1.49,1.48,1.52,1.54,1.53,1.51 and 1.52. Find
the average loss per product item.
Sol. Target value m=1.5m,
Loss function is given by L (y) = k(y-m)2
y-is height of steering mechanism, k is proportionality constant.
k= A/ ∆2=50/(0.02)2=125000.
The loss function is
L(y)=125000 (y-1.5)2
The expected loss per item is given by
E(L(y))= 125000 (y-1.5)2 , where ((y-1.5)2 is estimated as follows:
Summation of i= 1to 10 (yi-1.5)2 / 10 = (1.53-1.5)2+….) /10 =0.00049
Expected loss per item is 125000*.00049=61.25