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FIGURE 20-21. Scatter plot solder quality and certification score.

an unsatisfactory product or service than it does to produce a satisfactory one. There are many costs associated with producing unsatisfactory goods and services. These costs are in labor, materials, facilities, and the loss of customers. The cost of producing a proper product can be reduced significantly by the application of statistical process control charts.

Control Charts and the Normal Distribution The construction, use, and interpretation of control charts is based on the normal statistical distribution as indicated in Figure 20-22. The centerline of the control chart represents the average or mean of the data (X). The upper and lower control limits (UCL and LCL), respectively, represent this mean plus and minus three standard deviations of the data (XX ± 3s). Either the lowercase s or the Greek letter ct (sigma) represents the standard deviation for control charts.

The normal distribution and its relationship to control charts is represented on the right of the figure. The normal distribution can be described entirely by its mean and standard deviation. The normal distribution is a bell-shaped curve (sometimes called the Gaussian distribution) that is symmetrical about the mean, slopes downward on both sides to infinity, and theoretically has_an infinite range. In the normal distribution 99.73 percent of all measurements lie within XX + 3s and XX — 3s; this is why the limits on control charts are called three-sigma limits.

Companies like Motorola have embarked upon a six-sigma limit rather than a three-sigma limit. The benefit is shown in Table 20-4. With a six-sigma limit, only two defects per billion are allowed. Maintaining a six-sigma limit can be extremely expensive unless the cost can be spread out over, say, 1 billion units produced.

Control chart analysis determines whether the inherent process variability and the process average are at stable levels, whether one or both are out of statistical control (not stable), or whether appropriate action needs to be taken. Another purpose of using control 