04/11/2023 1

Taguchi Loss Function

A quality characteristic understudy has a manufacturing specification (in cm )of 0.20+/- 0.05.Historical data indicates that if the quality characteristic takes on values larger than 0.25 cm or smaller than 0.15 cm ,the product fails and a cost of $75 is incurred. Based on these data , a)Determine the Taguchi Loss Function. B)Estimate the loss for a quality characteristic of 0.135 cm.

seshasayee m k

04/11/2023 2

Solution

a) L(x)=k(x-T)²b) x-T=0.05 $75=k(0.05)² K=30000The Loss Function is L(x)=30000*(x-T)(x-T) b)L(0.135)=30000(0.135-0.200)² =30000(-0.65)² =30000(0.4225) =$126.75

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04/11/2023 3

Reliability

• An automated production system shown in next fig with three operations turning milling and grinding .Individual parts are transformed from the turning center to the milling center and then to the grinder by a robot .Thus if one machine or the robot fails the entire production process stops .The probability that any one component of the system will fail however does not depend on any other component of the system .Conceptually we can think of the robot and machines are in series.

• A)If we assume that the reliability of the robot ,Turning center milling machine and grinder are .99/.98/.99/.96 respectively what is the reliability of the complete system ?

• B)Suppose the system is redesigned with two grinders that operate in parallel .If one grinder fails the other grinder may still work and hence the total system will continue to function .such a system is shown. what is the reliability of this new configuration ?

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04/11/2023 4

Series Production System

Rs= (P1)(P2)(P3)(P4)

Robot(P1)

TurningP2

MillingP3

GrinderP4

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Solution

• The reliability of the system can be computed as

• Rs = (.99) (.98)(.99)(.96) = .92 or 92 %

• This means that there is .92 probability that the system will be working over a specified period of time .

• The probability of failure of each operation in the system is independent of the other .

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04/11/2023 6

Series Production System

Robot(P1)

TurningP2

MillingP3

GrinderP4

GrinderP5

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04/11/2023 7

Solution

• RG of the grinders • = RGrinder = 1-((1-P4)(1-P5))• = 1-((1-.96)(1-.96))• = .9984• = 99.84% Notice the Total Grinder reliability has gone up by adding extra

machine . Total reliability of the system –using .9984 as the reliability of

the grinders .Essentially we have replaced the parallel grinders with one grinder whose reliability is .9984 .Thus we have

Rsystem =(.99)(.98)(.99)(.9984)=.96 or 96%

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