TAGUCHIS SIGNAL TO NOISE RATIO METHOD

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LECTURE 9

• TAGUCHIS SIGNAL TO NOISE RATIO METHOD

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Advantages of S/N Method
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When to Use the S/N Ratio for Analysis

• Whenever an experiment involves repeated
  observations at each of the trial conditions, the
  S/N ratio has been found to provide a practical
  way to measure and control the combined influence
  of deviation of the population mean from the
  target and the variation around the mean. In
  standard ANOVA they are treated separately.

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When to Use the S/N Ratio for Analysis (Cont.)

• S/N offers the following two main advantages
• It provides a guidance to a selection of the
  optimum level based on least variation around the
  target and also the average value closest to the
  target.
• It offers objective comparison of two set of
  experimental data with respect to variation
  around the target and the deviation of the
  average from the target value.

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Signal to Noise Ratio

• The relevance of the S/N ratio equation is tied
  to interpreting the signal or numerator of the
  ratio as the ability of the process to build good
  product, or of the product to perform correctly.
  By including the impact of the noise factors on
  the process or product as the denominator, we can
  then adapt the S/N ratio as the barometer of the
  ability of the system (product or process) to
  perform well in relation to the effect of noise.

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Signal to Noise Ratio (Cont.)

• By successfully applying this concept to
  experimentation, we can determine the control
  factor settings that can produce the best
  performance (high signal) in a process or product
  while minimizing the effect of those influences
  we can not control (low noise).

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Signal to Noise Ratio (Cont.)

• To obtain a better understanding of how this
  approach works and what it means, lets discuss a
  practical example (car radio) illustrated below

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Signal to Noise Ratio (Cont.)
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Signal to Noise Ratio (Cont.)

• For improved additivity of the control factor
  effects, it is common practice to take log
  transformation of µ2/s2 express the S/N ratio in
  decibels.
• The range of values of µ2/s2 is (0,8), while the
  range of values of ? is (-8, 8). Thus, in the log
  domain, we have better additivity of the effects
  of two or more control factors. Since log is a
  monotone function maximizing µ2/s2 is equivalent
  to maximizing ?.

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Signal to Noise Ratio (Cont.)

• Consider the following two sets of observations
  around the target and the deviation of the
  average from the target value.
• Let m75
• Observation A 55 58 60 63 65 60.2
• Dev. Of mean from target 75 - 60.2 14.8
• Observation B 50 60 76 90 100 75
• Dev. Of mean from target 75 - 75 0

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Signal to Noise Ratio (Cont.)
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Conversion of Results into S/N Ratios

• S/N -10log10(MSD) 10log
• Note that for the S/N to be large, the MSD must
  have a value that is small.

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Conversion of Results into S/N Ratios (Cont.)
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Conversion of Results into S/N Ratios (Cont.)

• These two sets of observations may have come from
  the two distributions shown in the figure above.
• Observe that the set B has an average value which
  equals to target value, but has a wide spread
  around it. For the set A, the spread is smaller,
  but the average itself is quite far from the
  target. Which of the two is better?

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Conversion of Results into S/N Ratios (Cont.)

• Based on the average value the product shown by
  obs. B appears to be better. Based on
  consistency, product A is better. How an one
  credit A for less variation? How does one compare
  the distances of the averages from the target?
  Surely comparing the averages is one method. Use
  of S/N ratio offers an objective way to look at
  the two characteristics together.

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Computation of S/N Ratio
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Computation of S/N Ratio (Cont.)
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Most Common S/Ns for the Static Case

• Nominal-is-Best (N.B.)

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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)

• Smaller-is-Better (S.B.)

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Most Common S/Ns for the Static Case (Cont.)

• Equation 7.4
• Smaller-is-Better S/N

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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)

• Larger-is-Better (L.B.)

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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Most Common S/Ns for the Static Case (Cont.)
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Usage of S/N in Experimental Design
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Usage of S/N in Experimental Design (Cont.)
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Usage of S/N in Experimental Design (Cont.)
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Usage of S/N in Experimental Design (Cont.)
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Usage of S/N in Experimental Design (Cont.)

• Previous Application of the same experiment
• Goal was to minimize the variability in a key
  dimension
• Objective of the exp. dimensionally stable in its
  operating conditions.

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Methodology of S/N
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)

• 3.

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Methodology of S/N (Cont.)

• 4.

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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)

• 6.

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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Methodology of S/N (Cont.)
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Examples of Usage

• Nominal-is-Best Type I