Statistical Methods
for Economists
Lecture 11 & 12
Taguchi methods
•David Bartl
•Statistical Methods for Economists
•INM/BASTE

Outline of the lecture
•Introduction to Taguchi methods
•Taguchi Loss Function
•The expected loss
•Total Quality Costs
•Capability indices

Taguchi methods
•Taguchi’s methods – statistical methods developed by
•Dr. Genichi Taguchi  (*1st January 1924  †2nd June 2012)
•to improve the quality of manufactured goods.
•
•There are two classes of Taguchi’s methods:
•online methods used in the production process
•offline methods used in the pre-production phases
•
•The fundamental concept used of the online methods is the Loss Function.

Taguchi methods:  Taguchi Loss Function
etc.


Taguchi methods:  Taguchi Loss Function



Taguchi methods:  Taguchi Loss Function:  Remarks
•Taguchi’s Loss Function evaluates every loss caused to the customer
by the supplier due to the (physical) impossibility to keep the absolute precision.
•
•The link between the quality and the Loss Function
is the main contribution to the Quality Engineering;
it also allows to plan the costs.
•
•The Loss Function measures the decreased quality within the tolerance interval.

The Loss Function
•Symmetric N-tolerance
•Non-symmetric N-tolerance
•S-type tolerance (small)
•L-type tolerance (large)
•

Taguchi Loss Function:  Symmetric N-tolerance



Taguchi Loss Function:  Symmetric N-tolerance



Taguchi Loss Function:  Symmetric N-tolerance



Taguchi Loss Function:  Non-symmetric N-tolerance



Taguchi Loss Function:  Symmetric N-tolerance



Taguchi Loss Function:  Symmetric N-tolerance



Taguchi Loss Function:  S-type tolerance (small)



Taguchi Loss Function:  S-type tolerance (small)



Taguchi Loss Function:  S-type tolerance (small)



Taguchi Loss Function:  L-type tolerance (large)



Taguchi Loss Function:  L-type tolerance (large)



Taguchi Loss Function:  L-type tolerance (large)



The expected loss
•Symmetric N-tolerance
•Non-symmetric N-tolerance
•S-type tolerance (small)
•L-type tolerance (large)
•

The expected loss



The expected loss:  Symmetric N-tolerance



The expected loss:  Symmetric N-tolerance



The expected loss:  Symmetric N-tolerance



The expected loss:  The estimates of  E[Y]  and  Var(Y)



The expected loss:  The estimates of  E[Y]  and  Var(Y)



The expected loss:  The estimates of  E[Y]  and  Var(Y)



The expected loss:  The estimates of  E[Y]  and  Var(Y)



The expected loss:  The cost of the quality



The expected loss:  The cost of the quality



The expected loss:  The cost of the quality



Total
Quality Costs
•Quality Cost Monitoring
•Taguchi’s approach
to Quality Cost Monitoring
•

Quality Cost Monitoring
•We concentrate on Quality Cost Monitoring on the side of the manufacturer.
•There are several approaches to Quality Cost Monitoring, including:
•monitoring based on PAF (Prevention, Appraisal, Failure) models
•monitoring based on process models
•monitoring based on Taguchi’s approach
•
•We here concentrate in Taguchi’s approach.

Taguchi’s approach to Quality Cost Monitoring



Checking
all (100%) pieces
of production
•
•

Checking all (100%) pieces of production



Checking all (100%) pieces of production



Checking all (100%) pieces of production



Checking one out of every  n  pieces of production
•
•

Checking one out of every  n  pieces of production



Checking one out of every  n  pieces of production



Checking one out of every  n  pieces of production



Checking one out of every  n  pieces of production



Checking one out of every  n  pieces of production



Remarks



Remarks
(?)


Remarks
(?)


Checking attributes



Checking attributes



Capability indices
•Capability index  Cp
•Capability index  CpK
•

Capability indices



Capability indices



Capability indices



Capability index  Cp



Capability index  CpK