vdoc

Chapter 19: B. Statistical Process Control 253
Control charts comprise perhaps the most important part of SPC. We will first
study some of the basic concepts of control charts and then study them in more
detail in the following two sections.
CONTROL CHARTS
A control chart can be defined as:
1. A device for describing in concrete terms what a state of statistical
control is.
2. A device for judging whether control has been attained or not and thus
detecting whether assignable causes are present or not.
3. A device for attaining a stable process.
Suppose that we take a sample of size n from a process approximately at regular
intervals, and suppose that for each sample we compute a sample statistic (say) X.
This statistic may be the sample mean, fraction of nonconforming product, or any
other appropriate measure. Now since X is a statistic, it is subject to some fluctuations
or variations. If no special causes are present, the variation in X will have
characteristics that can be described by some statistical distribution. By taking
enough samples, we can estimate the desired characteristics of such a distribution.
For instance, we now suppose that the statistic X is distributed as normal and we
divide the vertical scale of a graph in units of X, and horizontal scale in units of
time or any other such characteristic. Then, we draw horizontal lines through the
mean and the extreme values of X, called the center line and the upper and lower
control limits, which results in a tool that is known as a control chart. A typical control
chart is shown in Figure 19.6.
The main goal of using control charts is to reduce the variation in the process
and bring the process target value to the desired level.
If we plot data pertaining to a process on a control chart, and if the data
conform to a pattern of random variation that falls within the upper and lower
limits, then we say that the process is in statistical control. If, however, the data
fall outside these control limits and/or do not conform to a pattern of random
variation, then the process is considered to be out of control. In the latter case,
an investigation is launched to track down the special causes responsible for the
process being out of control, and to correct them.
If any particular cause of variation is on the unfavorable side, an effort is made
to eliminate it. If, however, the cause of variation is on the favorable side, an effort
Part IV.B
Quality
characteristic
Upper control limit (UCL)
Center line
Lower control limit (LCL)
Time (or sample number)
Figure 19.6
A pictorial representation of the components of a control chart.