SPC - Statistical Process Control

Statistical Process Control (SPC) (Page 2 of 5)

What is expected to emerge from this exercise is a normal curve, wherein a big slice of the student population will have a height that is somewhere in the middle of the distribution, say 57-59 inches tall. The number of students belonging to other height groups will be less than the number of students in the 57"-59" category .

In fact, the number of students decreases at a calculable rate as the height group moves further away from the center. Eventually you might find only one shortest student at, say, 48", and one tallest student who probably stands at 66". Lastly, plotting the number of the students falling under different height ranges of equal intervals will result in a bell-shaped curve. Such a plot is called a histogram, a simple example of which is shown in Figure 2.

Figure 2. Example of a histogram of heights of students in a Grade 5

class; the y-axis corresponds to the number of students per category

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.

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.

BUY BOOKS on SPC!

HOME