00319 ®13881e58bc25457eba9c0e4eeefca9

322

McCaryille & Montgomery

time to find an acceptable guard band. Another is that the company will never know the actual risk of the gage and defect level being sent to the customers. Finally, it is not known how much good product is being thrown away. Therefore, if the guard band is initially set too aggressively, a substantial amount of good product may be thrown away unnecessarily.

Another common guard band approach is the "percentage" method. For example, if a specification limit is 120 volts maximum, then a 10% guard band method would set the guard band at 108 volts. This method of guard banding is often a standard in a company's Ä…uality poÅ‚icy such that all specifications are guard banded by a minimum percentage. The "percentage" method is not much morÄ™ scientific than the "best guess" method. However, it often works fairly well for some manufacturers because many gages have inconsistent variances that are proportional to the value of the parameter being measured. In other words, the gage error is much greater when measuring product that is approximately 500 ohms than when the gage is measuring product that is less than 10 ohms. However, the risk as well as the defect level being sent to the customers is still unknown and the loss due to the gage error is never identified.

Using a properly performed gage capability study, gage error can be determined prior to establishing guard bands. Methods for this are discussed in, for example, Montgomery (199 lb), Montgomery and Runger (1993a, b), the Western Electric Quality Control Handbook (1956), and many others. From this the risk associated with the gage can be determined. Utilizing EÄ…uation (2), the risk can be assessed. If the gage error is normally distributed, the calculations can be madÄ™ easier by converting to the standard normal distribution. Guard bands can be set by selecting the appropriate level of risk for the gage. The defect level being sent on to the customers is still unknown as is the yield loss due to the gage error.

The problem presented in this research was initially approached simultaneously in 1954 by Eagle (1954), and Grubbs and Coon (1954). Both Eagle and Grubbs assumed the product distribution to be normal and can therefore be transformed into the standard normal distribution. By diyiding the acceptable portion of the product distribution into bands of a given width, multiplying each band by its associated probability of being rejected, and summing these probabilities, the risk associated with rejecting a good unit can be approximated. In a similar procedurÄ™, the probability of accepting a defective unit is found. This procedurÄ™ is similar to the method presented in this research; however, the models shown in Equations (10) and (14) allow for multiple gages as well as non-normal product distributions.