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McCarville & Montgomery

appropriate levels. These gage targets are called guard bands. This paper develops generał models for defect levels and gage losses for systems of gages and shows how response surface models can be used to optimize the system.

Introduction

Reduction of product and process variation has become a critical component of competitiveness in today's manufacturing industries. Morę recently, gage variability, and a thorough understanding of the components of gage variation, has also become significant. With quality levels measured in parts per million, and even parts per billion, the quality of measurement, especially at finał outgoing tests, must be high. However, for many high technology products accurate gages with Iow levels of variation are not yet available. Customers still expect perfection even when the industry has not yet developed capable gages to test critical product parameters.

In generał, the total observed variance for a product parameter can be decomposed into two components as follows:

^CT^total ^{= CT}^product ^{+ CT}^gage    (1)

where cr^product *^s the variability in the product distribution and a^g_age is a variance component that represents the variability due to the gage. With the knowledge received from the analysis of the product and gage variation it is feasible that the defect level being sent on to the customer can be estimated. Once estimated, a proper setting for the gage, or the guard band, can be determined to achieve the desired quality level dictated by the manufacturer or the customer.

Many manufacturers use multiple gages in series to assure Iow defect levels for products reaching their customers. This is common in the semiconductor industry. Often the product is tested in wafer form before being sent on to the finał packaging processes where it is tested again at least once. In cases such as this, the guard bands shoułd be set at optimum levels such that the quality levels can be achieved and the minimum loss is encountered when good product is rejected due to errors in the gages.

To illustrate, suppose that a critical product parameter is normally distributed with a mean of 1130 and a standard deviation of 80. The customer's upper specification limit is 1250. The probability of having a unit outside of the specification is 0.06681. That is, the reject level is 6.681%. Because 6.6681% is an unacceptable level of rejects to be sending on to the customer, a