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# Appendix A

## Equations for Signal-to-Noise (S/N) Ratios

### Nondynamic S/N Ratios

• Nominal-the-Best
• Smaller-the-Better
• Larger-the-Better

### Nominal-the-Best Type (Type I)

Let data points be

### Nominal-the-Best Type (Type II)

Let data points be

We can also show the nominal-the-best S/N ratio as:

In this equation, the error variance (Ve) is an unbiased estimate of σ2.

Note: The higher the S/N ratio becomes, the smaller the variability is. Maximizing this S/N ratio is equivalent to minimizing standard deviation or variation.

#### Smaller-the-Better Type

Let data points be

Note: Maximizing this S/N ratio minimizes the mean and standard ­deviation.

#### Larger-the-Better Type

Let data points be

Maximizing ...

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