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Taguchi Loss Function: Definition & Example

written by: N Nayab • edited by: Ginny Edwards • updated: 9/26/2010

What are the costs of poor quality? The conventional view points to losses to rework or scraping products made outside specifications. Taguchi Loss Function explains that the implications of poor quality run deeper and include social costs, and that such costs are a function of quality standards.

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    Taguchi Loss Function Taguchi Loss Function is a statistical method developed by Genichi Taguchi, a Japanese business statistician that shows how manufacture of each non-perfect part results in a loss for the company. This concept is a landmark in describing quality and has helped spread the concept of continuous improvement, and finds relevance in lean manufacturing and Six Sigma.

    Image Credit: flickr.com/Wouter Kiel

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    The Background

    Conventional industrial engineering considers quality costs as the cost of rework or scrap of items manufactured outside specification. Taguchi considered such private costs to the manufacturers as short-term costs, and introduced a new approach of understanding costs to society owing to non-conformance with specifications. He held that any item not manufactured to the exact specification results in some loss to the customer or the wider community. Such losses come with the customer needing to make an additional purchase or repairs due to early wear-out or the defect part not interfacing with other parts, and non-optimal utilization of the product owing to the need to build in safety margins and the like.

    Most manufacturers ignore the social costs of poor quality, oblivious to the fact that such social losses are actually long term costs for them, for it finds their way back to the manufacturer as negative feedback and reduced sales. Manufacturers looking to enhance brand reputation, gain market share and generate profits thereby need to eliminate such social costs by improving product quality.

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    The Concept

    Taguchi’s loss function explains that quality does not suddenly plummet and private and social costs do not rise suddenly when products are not in conformance to specifications. Instead, the losses to the manufacturer and the society are a function of the deviance or variability from the target value or best quality level. The private and social loss is zero at the target value, and the losses gradually increase as the product specifications deviate from the target value.

    The three characteristics that shape the definition of Taguchi loss function are:

    1. Nominal, where the best characteristic or target value is the median of the specified upper and lower acceptable limits, and the losses owing to deviance from the target value rise proportionate to the extent of deviance on either side of the mean. Here an example includes the frequency settings in radio and wireless equipment. For instance, the equipment not confirming exactly with the set frequency is defective increases the social costs for repair or replacement.
    2. Smaller-the-Better, where the ideal target value or best quality standard is zero, and the higher the actual value, the higher the private and social costs. Examples of such instances include heat loss in heat exchanger, or carbon dioxide emissions. For instance, the more heat lost by the heat exchanger, the less efficiently it functions, and the higher the social costs.
    3. Larger-the-Better, where the ideal characteristic or best quality standard is infinity, and the higher the actual value, the better, and the lower the actual value, the more the private and social costs. Examples of such instances include maximizing product yield from a process, agricultural output, and the like. For instance, the higher yields indicate better quality seeds, and lower yields increase the social costs.

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    Formula

    The Taguchi’s loss function for one piece of product is:

    Loss in Dollars = Constant*(quality characteristic – target value)^2

    The Average Taguchi loss per item for a sample set is

    Loss in Dollars= Constant*(standard deviation^2+ (process mean –target value) ^2)

    • ‘Constant’ is the coefficient of the Taguchi Loss, or the ratio of functional tolerance and customer loss. Functional tolerance is the value at which 50 percent of the customers view the product as defective, and customer loss is the average loss to the customer at this point.
    • ‘Quality characteristic’ indicates the actual value of the characteristic such as diameter, concentration or the like used as the basis to determine quality.
    • ‘Target value’ is the specified ideal value for this quality characteristic.

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    Taguchi Loss Function uses include assessing economic loss from a deviation in quality without having to develop the unique function for each quality characteristic.

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    References

    1. Erin Knight, Matt Russell, Dipti Sawalka, Spencer Yendell . Taguchi quality loss function and specification tolerance design. http://controls.engin.umich.edu/wiki/index.php/Taguchi_quality_loss_function_and_specification_tolerance_design. retrieved 23 September 2010.
    2. Deming, W. Edwards (1993). The New Economics: For Industry, Government, Education. MIT Press. ISBN 0-911379-05-3.

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