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HOME The Control chart is the fundamental tool of Statistical Process Control (SPC). |
A Process Control Primer
Adapted from the original which appeared
in the Mar/Apr 96 issue of Desktop Engineering Magazine, www.deskeng.com. There are two basic kinds of control charts: the x bar chart
and the R chart. The x bar chart measures the average of the
process; the R chart measures its dispersion, or variability.
The two are always used in conjunction. Variation is a natural part of all processes. Control charts
allow you to distinguish between normal, expected variation,
called common cause variations, and unusual variations,
known as special cause variations, which require action.
Common cause variations should be ignored; responding to changes
within the control limits actually decreases output quality.
Building the R Chart The R chart tracks intra-sample variability. R stands for
range: the distance between the high and low measurements for
a particular sample. R bar, the average of all ranges, becomes the centerline for
the R chart, the line from which process deviation is measured. R = high measurement - low measurement The upper and lower control limits (UCL and LCL) are computed
based on R bar and a pair of constants D3 and D4, which depend
on the sample size and must be looked up in a table of control
chart constants.
A sample that falls above the upper control limit indicates
a problem in the process. One main goal of quality control is
the reduction of variability. A sample that falls below the lower
control limit - an extremely rare occurrence - represents uncommonly
low variability. It's worth responding to, not in order to correct
the situation, but to try to repeat it. Building the chart The x bar chart tracks sample-to-sample variability. Samples
of the process output - one or more consecutively produced parts
- are taken at intervals. The average is computed for each sample.
n = the sample size N = the number of samples xi - individual data points The average of all the averages (also called the Grand Average) is then computed. This becomes the centerline of the x bar control chart.
S is the standard deviations of the process. This is estimated
from the sample data, thus:
With the small sample sizes typical of SPC, a formula based
on the range of the samples - the differences between the high
and low measurements - provides a better estimate of the standard
deviation than does the standard formula for s printed in a statistics
textbook:
A data set consisting of averages will follow a normal distribution.
(There's a nifty theory in statistics, called the Central Limit
Theorem, that proves this.) In a normal distribution, 99.73%
of the data will fall within 3s (standard deviations) of means.
If you set the limits of your x bar chart at 3s from the Grand
Average, no more than 3 out of 1,000 sample averages should fall
beyond these limits. A sample with an average beyond these control
limits indicates a problem with the process. Process Capability Process capability is the ratio of the width of your manufacturing
tolerances to the natural variability of the manufacturing process.
Cpk, the measure of process capability, is the smaller of:
The higher the value for Cpk the better. A process with a Cpk of around 1.3 or better is up to the task. A process with a Cpk of 1.0, can, on its best day, just barely pull off the job in question. If Cpk is less than 1.0, some out-of-tolerance output is inevitable. |
