A typical production line consists of multiple sources of materials and multiple distinct operations for fabrication and assembly of parts into the next-higher level of product assembly. Figure 4.2 is an example of a multistep manufacturing process line. Some of the issues pertaining to six sigma quality for this line are as follows:
• If the line is to be upgraded to six sigma quality, it is logical to assume that, at a minimum, all of the incoming parts and the individual operations of the line are to be upgraded to six sigma.
• The goal of six sigma quality for each incoming part and operation is a good management tool, since the individual part or operation can be analyzed or upgraded, independently of other parts.
• The output quality of the line, even if all of the incoming component parts and operations are of six sigma quality, is not at six sigma. The defects from all operations add up to reduce line output quality from the six sigma target.
The yield of the line is dependent on the complexity of the parts and manufacturing operations. The more parts and operations, the lower the yield. In addition, more operations require a much higher level of quality for each operation in order to obtain a reasonable overall line yield.
Although each operation or an incoming part could be evaluated for six sigma or a targeted Cpk quality, the evaluation of the total line quality is not readily apparent, and there can be many different options to do so. This section will explore different approaches to this condition.
• The yield of the line can be calculated using different methodologies, as shown in the previous section. This yield can result in different test strategies, depending on the economics of the alternative test methods to be used to bring up the final line quality to the specified level.
Treating the line yield as a Poisson distribution can result in quickly estimating the line FTY by adding the DPUs of each of the different processes. For example, in a line with three steps process— A, B, and C—the FTY calculations would be as shown in Table 4.1. Total line yield can be calculated from either the multiplication of the individual yields of each step or the addition of the individual DPUs of each step, then converting the total DPUs to the total yield using the Poisson distribution. The results should be the same, since the probability of the defects in each process step is assumed to be independent.
An alternate method for calculating the yield is to use the approximation FTYα= 1 - a instead of the calculations shown in fable 4.1. When several parts are made in each operation, then the total yield can be calculated using either of the above two methods, as shown in Table 4.2, using n parts through the three-step process line.