Statistical Process Control and Process Capability key highlights
1. Reduction of process variability
2. Monitoring and surveillance of a process
3. Estimation of product or process parameters
If a product is to meet or exceed customer expectations, generally it should be produced by a
process that is stable or repeatable
SPC seven major tools are
1. Histogram or stem-and-leaf plot
2. Check sheet
3. Pareto chart
4. Cause-and-effect diagram
5. Defect concentration diagram
6. Scatter diagram
7. Control chart - Skewart - technically most complicated
The proper deployment of SPC helps create an environment
in which all individuals in an organization seek continuous improvement in quality
and productivity. This environment is best developed when management becomes involved in
the process. Once this environment is established, routine application of the magnificent
seven becomes part of the usual manner of doing business, and the organization is well on its
way to achieving its quality improvement objectives.
the statistical concepts that form the basis of SPC, we must first describe Shewhart’s theory of variability.
In any production process, regardless of how well designed or carefully maintained it is, a certain
amount of inherent or natural variability will always exist. This natural variability or
“background noise” is the cumulative effect of many small, essentially unavoidable causes. In
the framework of statistical quality control, this natural variability is often called a “stable
system of chance causes.” A process that is operating with only chance causes of variation
present is said to be in statistical control. In other words, the chance causes are an inherent
part of the process.
Other kinds of variability may occasionally be present in the output of a process. This
variability in key quality characteristics usually arises from three sources: improperly
adjusted or controlled machines, operator errors, or defective raw material. Such variability is
generally large when compared to the background noise, and it usually represents an unacceptable
level of process performance. We refer to these sources of variability that are not part
of the chance cause pattern as assignable causes of variation. A process that is operating in
the presence of assignable causes is said to be an out-of-control process.1
t1 forward, the presence of assignable causes has resulted in an out-of-control process.
Processes will often operate in the in-control state for relatively long periods of time.
However, no process is truly stable forever, and, eventually, assignable causes will occur,
seemingly at random, resulting in a shift to an out-of-control state where a larger proportion
of the process output does not conform to requirements.
The chart contains a center line that represents the average value of
the quality characteristic corresponding to the in-control state. (That is, only chance
causes are present.) Two other horizontal lines, called the upper control limit (UCL) and
the lower control limit (LCL), are also shown on the chart. These control limits are chosen
so that if the process is in control, nearly all of the sample points will fall between
them.
If the process is in control, all the
plotted points should have an essentially random pattern.
There is a close connection between control charts and hypothesis testing.
For example, the mean could shift instantaneously to a new value and remain there
(this is sometimes called a sustained shift); or it could shift abruptly; but the assignable cause
could be short-lived and the mean could then return to its nominal or in-control value; or the
assignable cause could result in a steady drift or trend in the value of the mean. Only the sustained
shift fits nicely within the usual statistical hypothesis testing model.
The hypothesis testing framework is useful in many ways, but there are some differences
in viewpoint between control charts and hypothesis tests. For example, when testing statistical
hypotheses, we usually check the validity of assumptions, whereas control charts are used to
detect departures from an assumed state of statistical control.
In general, we should not worry
too much about assumptions such as the form of the distribution or independence when we are
applying control charts to a process to reduce variability and achieve statistical control.
Furthermore, an assignable cause can result in many different types of shifts in the process
parameters. For example, the mean could shift instantaneously to a new value and remain there
(this is sometimes called a sustained shift); or it could shift abruptly; but the assignable cause
could be short-lived and the mean could then return to its nominal or in-control value; or the
assignable cause could result in a steady drift or trend in the value of the mean. Only the sustained
shift fits nicely within the usual statistical hypothesis testing model.
One place where the hypothesis testing framework is useful is in analyzing the performance
of a control chart. For example, we may think of the probability of type I error of the
control chart (concluding the process is out of control when it is really in control) and the
probability of type II error of the control chart (concluding the process is in control when it
is really out of control). It is occasionally helpful to use the operating-characteristic curve of
a control chart to display its probability of type II error. This would be an indication of the
ability of the control chart to detect process shifts of different magnitudes. This can be of
value in determining which type of control chart to apply in certain situations. For more discussion
of hypothesis testing, the role of statistical theory, and control charts, see Woodall
(2000).
We may give a general model for a control chart. Let w be a sample statistic that measures
some quality characteristic of interest, and suppose that the mean of w is mw and the
standard deviation of w is sw
A very important part of the corrective action process associated with control chart
usage is the out-of-control-action plan (OCAP). An OCAP is a flow chart or text-based
description of the sequence of activities that must take place following the occurrence of an
activating event. These are usually out-of-control signals from the control chart. The OCAP
consists of checkpoints, which are potential assignable causes, and terminators, which are
actions taken to resolve the out-of-control condition, preferably by eliminating the assignable
cause. It is very important that the OCAP specify as complete a set as possible of checkpoints
and terminators, and that these be arranged in an order that facilitates process diagnostic
activities. Often, analysis of prior failure modes of the process and/or product can be helpful
in designing this aspect of the OCAP. Furthermore, an OCAP is a living document in the sense
that it will be modified over time as more knowledge and understanding of the process is
gained. Consequently, when a control chart is introduced, an initial OCAP should accompany
it. Control charts without an OCAP are not likely to be useful as a process improvement tool.
three things we need:
in the x-bar chart , we specified a sample size of five measurements, three-sigma
control limits, and the sampling frequency to be every hour. Increasing Sample Size will reduce
the probability of type-II error