SPC - Statistical Process Control; the Normal Distribution; Skewed Distributions; Process Capability Indices

Statistical Process Control (SPC) (Page 2 of 4)

What's notable about normal distributions is that regardless of their standard deviation value, the % of data falling under a given number of standard deviations is constant. For example, say that the standard deviation of process 1 is 100, and the standard deviation of process 2 is 200. Process 1 and Process 2 will have different data distribution shapes (Process 1 being more stable), but for both processes, 66% of the data under the normal curve will fall within +/- one (1) standard deviation from the mean of the distribution (i.e., between {mean - 1 sigma} and {mean + 1 sigma}), and 37% of the data will be outside it. Table 1 shows the percentages of data falling under different numbers of sigma.

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Control Charting

Table 1. % Data Falling Under Different Numbers of +/- Sigma

# of Sigma's	% of Data Covered	% of Data Outside
+/- 1 Sigma	66%	37%
+/- 2 Sigmas	95%	5%
+/- 3 Sigmas	99.73%	0.27%
+/- 4 Sigmas	99.9936%	0.0063%
+/- 5 Sigmas	99.99995%	0.00005%

Skewed Distributions

Perfectly normal curves are hard to come by with finite samples or data. Thus, some data distributions that are theoretically normal may not appear to be one once the data are plotted, i.e., the mean may not be at the center of the distribution or there may be slight non-symmetry. If a normal distribution appears to be 'heavy' or leaning towards the right side of the distribution, it is said to be skewed to the left. A normal distribution that's leaning to the left is said to be skewed to the right.

Many response parameters encountered in the semiconductor industry behave normally, which is why statistical process control has found its way extensively into this industry. The objective of SPC is to produce data distributions that are stable, predictable, and well within the specified limits for the parameter being controlled.

In relation to the preceding discussions, this is equivalent to achieving data distributions that are centered between the specified limits, and as narrow as possible. Good centering between limits and negligible variation translates to parameters that are always within specifications, which is the true essence of process control.

Control Charting

It is often said that you can not control something that you do not measure. Thus, every engineer setting up a new process must have a clear idea of how the performance of this new process is to be measured. Since every process needs to satisfy customer requirements, process output parameters for measurement and monitoring are generally based on customer specifications. Industry-accepted specifications are also followed in selecting process parameters for monitoring.

Control charting is a widely-used tool for process monitoring in the semiconductor industry. It employs control charts (see Fig. 3), which are simply plots of the process output data over time. Before a control chart may be used, the process engineer must first ensure that the process to be monitored is normal and stable.

A process may have several control charts - one for each of its major output parameters. A new control chart must have at least the following: the properly labeled x- and y-axes, lines showing the lower and upper specification limits for the parameter being monitored, and a line showing the center or target of these specifications. Once a control chart has been set up, the operator must diligently plot the output data at predefined intervals.

After 30 data points have been collected on the chart (may be less if measurement intervals are long), the upper and lower control limits of the process may already be computed. Control limits define the boundaries of the normal behavior of the process. Their values depend only on the output data generated by the process in the immediate past. Control limits are therefore independent of specification limits. However, both sets of limits are used in the practice of SPC, although in different ways.

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