Since product or process yield depends on the accuracy of metrology and inspection, we must consider the costs of discarding a good device and the cost of accepting a bad device. Measurement risk is illustrated in Table I. Minimizing the cost of shipping a bad device is one purpose of metrology and inspection. However, if the sampling plan or methods are insufficient, bad devices will be shipped. But if specifications are too restrictive, then good devices may be rejected.

**Measurement Risk**

True State | Measured Result | Error |

Good | Good | None |

Bad | Bad | None |

Good | Bad | Type I (*alpha*) |

Bad | Good | Type II (*beta*) |

The probabilities of discarding a good device and of shipping a bad device are related to the variance of the measurement. These probabilities may be reduced by reducing variance, increasing sample size, or developing more robust processes.

TWO COOL®'s assembly and packaging template has two inputs for yield, Equipment Yield and Parametric Limited Yield Loss. Yield is the product of all of the independent yield mechanisms. Since *alpha* risk and *beta* risk are often described in terms of probabilities, we convert the probabilities of risk loss into *alpha* and *beta* yields. Then, since TWO COOL® has a formula builder, we can replace the equipment yield input with a formula that considers equipment yield, *alpha* risk and *beta* risk. Input the following formula into the Equipment Yield input cell:

**Equation 1**

=E*(1-A)*(1-B)

where:

E = Equipment Yield in decimal form (i.e. 0.999)

A = risk probability (i.e. 0.001)

B = risk (i.e. 0.0001)

Equation 1 includes all yield factors in the cost of scrap calculation for Assembly and Packaging cost of ownership. Using Equation 1 has one error however. Normally the cost of shipping bad product is much greater than the cost of rejecting good product. Equation 1 treats these costs equally. If both costs of measurement risk can be estimated then Equation 1 can be modified to reflect the difference in the costs of *alpha* risk and *beta *risk:

**Equation 2**

=E*(1-A)*(1-(B*S/R))

where:

E = Equipment Yield in decimal form (i.e. 0.999)

A = *Alpha* risk probability (i.e. 0.001)

B = *Beta* risk (i.e. 0.0001)

S = Cost of shipping a bad product (i.e. $100.00)

R = Cost of rejecting a good product (i.e. $10.00)

Normally R is equal to the Value of Incoming Unit at this Point in Process found in the administrative rates section of TWO COOL®.

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