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Taguchi’s Quality Loss Function

Taguchi’s Quality Loss Function concept combines cost, target and variation in one metric with specifications being of secondary importance.


Taguchi’s Quality Loss Function concept combines cost, target and variation in one metric withspecifications being of secondary importance.


Taguchi has defined quality as the loss imparted to society from the time a product is shipped. Societal losses include failure to meet customer requirements, failure to meet ideal performance and harmful side effects.






There are three common quality loss functions


1.              Nominal - the - best.


2.              Smaller - the - better.


3.              Larger - the – better






Although Taguchi developed so many loss functions, many situations are approximated by the quadratic function which is called the Nominal  the  best type.

Quadratic Los



The quadratic function is shown in figure. In this situation, the loss occurs as soon as the performance characteristic, y, departs from the target τ.


At τ, the loss is Rs. 0.


At LSL (or) USL, the loss is Rs. A.


The quadratic loss function is described by the equation L = k (y - τ) 2. Where,


L = cost incurred as quality deviates from the target.

y = Performance characteristic


τ = target


k = Quality loss coefficient.

The loss coefficient is determined by setting ∆ = (y – τ), the deviation from the target. When ∆ is the


USL (or) LSL, the loss to the customer of repairing (or) discarding the product is Rs. A.



K = A / (y – τ)2 = A / 2 .




The following figure shows the smaller  the  better concepts.


The target value for smaller  the  better is 0. There are no negative values for the performance characteristic.


The radiation leakage from a microwave appliance, the response time for a computer, pollution from an automobile, out of round for a hole etc. are the performance characteristics for this concept.




The following figure shows the concept of the Larger  the  better.

In the Larger  the  better concept, the target value is ∞ (infinity), which gives a zero loss. There are no negative values and the worst case is at y = 0. Actually, larger  the  better is the reciprocal of smaller  the  better. The performance characteristics in Larger  the  better are bond strength of adhesives, welding strength etc.

Taguchi quality loss function


Genichi Taguchi is a Japanese quality expert, known for the Quality Loss Function and for methodologies to optimise quality at the design stage – ―robust design. Taguchi received formal recognition for his work including Deming Prizes and Awards. Genichi Taguchi considers quality loss all the way through to the customer, including cost of scrap, rework, downtime, warranty claims and ultimately reduced market share.


Genichi Taguchi's Quality Loss Function


The Quality Loss Function gives a financial value for customers' increasing dissatisfaction as the product performance goes below the desired target performance. Equally, it gives a financial value for increasing costs as product performance goes


above the desired target performance. Determining the target performance is an educated guess, often based on customer surveys and feedback.


The quality loss function allows financial decisions to be made at the design stage regarding the cost of achieving the target performance.


Quality through Robust Design Methodology


Taguchi methods emphasised quality through robust design, not quality through inspection. Taguchi breaks the design process into three stages:


1. System design - involves creating a working prototype

2.  Parameter design - involves experimenting to find which factors influence product performance most


3.  Tolerance design - involves setting tight tolerance limits for the critical factors and looser tolerance limits for less important factors.


Taguchi‗s Robust Design methodologies allow the designer through experiments to determine which factors most affect product performance and which factors are unimportant.


The designer can focus on reducing variation on the important or critical factors. Unimportant or uncontrollable ―noise factors have negligible impact on the product performance and can be



Robust Design of Cookies This is easier explained by example. If your business makes cookies from raw ingredients, there are many possible factors that could influence the quality of


the cookie - amount of flour, number of eggs, temperature of butter, heat of oven, cooking time, baking tray material etc. With Genichi Taguchi‗s Robust Design methodologies you would set up


experiments that would test a range of combinations of factors - for example, high and low oven temperature, with long and short cooking time, 1 or 2 eggs, etc. The cookies resulting from each of these trials would be assessed for quality. A statistical analysis of results would tell you which the most important factors are, for example oven temperature affects cookie quality more than the number of eggs. With this knowledge you would design a process that ensures the oven maintains the optimal temperature and you would be able to consistently produce good cookies.

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