# Attribute Processes and Reject Analysis for Six Sigma

For attribute processes (those with quality measured in terms of defects in a sample or number defective), an implied Cpk will have to be calculated in the quality assessment of design and manufacturing. It is assumed that defects are occurring because of violation of a particular or a composite specification(s). The composite specification can be one-sided or two-sided, depending on the interpretation of the defects. For example, a wire bond defect could be the result of one-sided specifications, since it is assumed that in specifying the bond, only a mini- mum value is given. For solder defects, a composite specification can be assumed to be two-sided, since solder defects can be one- or two, sided, as in excessive or insufficient solder. The difference between implied one- or two sided specifications is that the number of defects representing the f(z) value under the normal curve should be halved for two-sided specifications, or used directly for one-sided specifications, resulting in different implied Cpk interpretations. The decision for one- or two-sided specifications for implied Cpk should be left to the appropriate design and manufacturing engineers.

An example of an attribute process calculation to generate an implied Cpk is for solder defects. They are usually measured in PPM or parts per million of defects obtained in production divided by the total number of solder joints in the product (total number of opportunities for solder defects). Solder defects may result from the combination of several specifications of design parameters such as component pad size, drill hole size, fabrication quality of plated metal surface, and the material and process parameters of the soldering equipment. A 100 PPM solder process (1 solder defect in 10,000 terminations or joints) is calculated to have a Cpk = 1.3 as follows:

1. 100 PPM defects (assuming a two-sided specification), 50 PPM per each tail of the normal curve

2. 50 PPM is f(z) = 0.00005 or z ~ 3.89, from standard normal curve tables.

3. Implied Cpk =z/3= 1.3

The assumptions are that the defects can occur on either side of the implied specifications, the process is normally distributed, and the process average is equal to the specification nominal. If this example of Cpk was for a wire bond machine, then it could be assumed that the defects occur due to one side of the specification limits of minimum pull strength. In this case, the Cpk can be calculated as follows:

1. 100 PPM defects (assuming a one-sided specification) is 100 PPM per one tail of the normal cxirve

2. 100 PPM is f(z) = 0.0001 or 2 = 3.72, from standard normal curve tables

3. Implied Cpk =z/3 = 1.24, which is lower quality than two-sided defects

It can be seen that the method of implied Cpk could lead to various interpretations of one- versus two-sided specifications when the Cpk methodology is used. If the six sigma interpretation of quality is used, the 100 PPM error rate is significant because it is larger than the target of 3.4 PPM. If a quality team has to report on their progress toward six sigma using 100 PPM current defect rate, then they canpresent the following arguments:

1. For two-sided specifications, f{z) = 0.00005 or z = 3.89. If a shift of 土1.5σis assumed，then all of the failures result from one side of the distribution, whereas the other side is much lower in defects, and therefore contributes no defects. The design is 3.89 + 1.5 = 5.39 or 5.39σin the classical six sigma definition.

2. For one-sided specifications, f(z) = 0.0001 or z = 3.72. If we assume a shift of ±1.5σthen the design is 3.72σ+ 1.5σ= 5.22σor 5.22σin the classical six sigma definition.