Supplement
6
Statistical Process Control
Summary
As indicated in Chapter 6, Statistical Process Control (SPC) charts are not a new tool. Their use goes back
to the 1920s at AT&T. Western Electric aggressively began applying the tools in the late 1940s and early
1950s. However, they were not widely used until the 1970s, when the use of quality control strategies
increased dramatically because of the competitive inroads made by Japanese automobile manufacturers.
SPC measures performance of a process, and helps to answer the question,
Is the process working in a
way where natural (or common) causes are the only source of variation?
If yes, then the process is in
statistical control. To get to that point operations managers and colleagues must eliminate the assignable
(or special) causes. Once the system is in control, then control charts provide a signal when out-of-control
situations occur and action to fix problems is necessary.
The key assumption in SPC is that natural variation will occur around a central tendency (in this case, the
average value) with an
acceptable
distribution. Many distributions occur in the natural world. SPC relies
heavily on the “normal” distribution, which has special probabilistic characteristics. Managers must
determine if it is possible to operate a process in control. Specific reasons will cause assignable variations
that are identifiable and controllable. These may include machine wear, misadjusted equipment, worker
training, or raw material variation. The second task of the manager is to eliminate assignable variations to
maintain control.
Since natural variation will have an acceptable distribution, we become less interested in the results of
individual results, and instead focus attention on average results. If the average result is consistent, and
the variation is acceptable, then the process is in control. Thus, SPC relies on samples. The analyst
samples a small number of items (usually 4 to 8) and continues to do so until it is possible to chart the
results, observe a distribution, and compute the mean and standard deviation of all the samples.
Based on engineering and managerial action, a desirable central tendency and distribution should
eventually occur. Once the system is in control, the next step is to apply control charts to monitor the
process.
There are two charts associated with variables (X-Bar-chart and the R-chart), both rely on the central limit
theorem, and used in conjunction with each other. X-Bar-charts monitor changes in the central tendency
of a process, while the R-chart monitors change in variation. The central limit theorem notes that as a
sample size increases, the sample means will follow a normal distribution; the overall mean of the sample
distribution will approximate the mean of the total population; and the standard deviation of the sample
distribution will approximate the population standard deviation divided by the square root of the sample
size. Sample size does not need to be large for this to happen. A normal distribution leads to knowing that
a predictable percentage of sample averages will fall within a range around the distribution’s mean.