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9 August, 07:03

A quality characteristic has a specification (in cm) of 0.40 ± 0.03. If the value of the quality characteristic exceeds 0.40 by the tolerance of 0.03 on either side, the product will require a $180 repair. In the given scenario, the Taguchi loss function is correctly represented by which of the following equations? (A) L (x) = 2,000 (x - 0.43) 2 (B) L (x) = 200,00 (x - 0.37) 2 (C) L (x) = 200,000 (x - 0.40) 2 (D) L (x) = 200 (x - 0.03) 2

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  1. 9 August, 09:48
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    option (C) L (x) = 200,000 (x - 0.40) ²

    Explanation:

    Given:

    quality characteristic = 0.40

    Tolerance = 0.03

    Repair cost = $180

    Now,

    Taguchi loss function is given as:

    Loss (in $) = Constant * (Quality characteristic - Target value) ²

    For quality characteristic of 'x' target value 't'

    and constant A

    L (x) = A * (x - t) ²

    substituting the given values, we get

    $180 = A * (0.03) ² [x - t = tolerance]

    or

    $180 = A * 0.0009

    or

    A = 200,000

    Hence,

    Taguchi loss function

    L (x) = 200,000 (x - 0.40) ²

    Hence,

    the correct answer is option (C) L (x) = 200,000 (x - 0.40) ²
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