Operations Management / Supply Chain Management

Module 05.03 Key Concepts: Statistical Process Control

Variability is inherent in every process.  Some variation is “natural” (common cause) and other variation is “special” (assignable cause).

Statistical Process Control provides a statistical signal when assignable causes are present and then facilitates detection and elimination of these assignable causes of variation.  Statistical process control measures the performance of a process, it does not help to identify a particular specimen produced as being “good” or “bad,” in or out of tolerance.

Statistical process control requires the collection and analysis of data – therefore it is not helpful when total production consists of a small number of units.  While statistical process control can not help identify a “good” or “bad” unit, it can enable one to decide whether or not to accept an entire production  lot.  If a sample of a production lot contains more than a specified number of defective items, statistical process control can give us a basis for rejecting the entire lot.

Natural variation, also called common cause variation, affect virtually all production processes and output measures follow a probability distribution.  For any distribution there is a measure of central tendency and dispersion. If the distribution of outputs falls within acceptable limits, the process is said to be “in control”.
Assignable variation, also called special cause variation, generally indicates some change in the process that can be traced to a specific reason.  The objective is to discover when assignable causes are present, then eliminate the bad causes or incorporate the good causes.

To measure the process, we take samples and analyze the sample statistics following the steps shown by the authors as presented in detail in the text.

The beginning point in Statistical Process Control is creation of a Run Chart.  Run Charts are employed to visually represent data and monitor a process to see if the long-range average is changing.  A Run Charts is the simplest tool to construct and use.  Points are plotted on the graph in the order in which they become available.  Such things as machine run time, yield, scrap, sales, delivery time, missed deliveries, etc. can be easily plotted.  A danger in using a Run Chart is that every variation in data is seen as significant.  One of the most valuable uses is to identify meaningful trends or shifts in the average.

A Statistical Process Control Chart is prepared from data and control limits are calculated from the data presented.

A Statistical Process Control Chart displays the individual data (a Run Chart) with statistically determined Upper and Lower Control limits drawn on either side of the Process average.  Typically these control limits are set as the (Average + (3 x Standard Deviation)) for the Upper Control Limit and the (Average – (3 x Standard Deviation)) for the Lower Control Limit.  The fluctuation of points within the Control Limits results from variation attributable to the process.  This results from “common” causes within the system and can only be affected by changing that system.  However, points outside of the limits come from “special” causes (people error, unplanned events, etc.) that are outside the way the process normally operates.  These “special” causes must be investigated and appropriate corrective action taken.

Statistical Process Control is normally thought of as a tool for manufacturing only.  Machine parameters are monitored and action taken when values are out of control limits.  However, this tool has vast application to non-manufacturing areas as well.  For example, the Marketing Team can measure item sales or family level sales in different sales territories.  When sales are outside of control limits they can ask the Customer Service Team or Sales Representatives to follow-up with customer to see if “something special” happened.  Enterprise Resources Planning Systems have a function called a Demand Filter that can be used as a flag for unusual customer orders.  This is based on Statistical Process Control theory.  Similarly, order-to-receipt lead-time can be monitored by Statistical Process Control to identify “special cause variation” for supply points.

You may not have access to standard deviation data so there are approaches available to calculate control limits here as well.  We will illustrate with a example of control charts for variables like weight, lead time, etc. – any characteristic that has a “real” numerical value.  This may be in whole numbers or fractions.  An “x-chart” tracks changes in the central tendency of the data and an “R-chart” indicates a gain or loss of dispersion.  These two charts are used together.

In the text there is methodology presented for determining control limits if you are given the standard deviation as well as if you are not.  Both are useful.

Then we can use the calculated control limits to track future data and identify if the process is out of control or if we have special cause variation occurring.

An R-Chart is a type of variables control chart that shows sample ranges over time.  The Range represents the difference between smallest and largest values in sample a sample set.  It monitors process variability independent from process mean.

As mentioned above, the X Bar Chart and R Bar Charts are used together and can detect different unusual occurrences.  And yes, these techniques have real practical utility as demonstrated by an example for Darden Restaurants that the authors present.
The following steps are used in the creation of Control Charts as illustrated above:
  • Collect 20 to 25 samples, often of n = 4 or n = 5 observations each, from a stable process and compute the mean and range of each.
  • Compute the overall means ( X Bar  and R Bar  ), set appropriate control limits, usually at the 99.73% level, and calculate the preliminary upper and lower control limits
    • If the process is not currently stable and in control, use the desired mean, m, instead of  X Bar to calculate limits.
  • Graph the sample means and ranges on their respective control charts and determine whether they fall outside the acceptable limits
  • Investigate points or patterns that indicate the process is out of control – try to assign causes for the variation, address the causes, and then resume the process
  • Collect additional samples and, if necessary, re-validate the control limits using the new data

There are several other types of Control Charts described in the text.  We will not cover in detail here.   The overall approach is the same regardless of Chart utilized.

 It is important to be able to identify various patterns in Control Charts to determine if the process is in control and identify special occurrences.  Several examples are presented in the text.

There is a difference between statistically determined control limits and what we normally refer to as Specification Limits for a product or service.  Control Limits are derived from the data while Specification Limits are defined by the customer of a product, service, or intermediate state of a product or service (internal customer).  Of course these are also relevant in the design phase.  Ideally, processes should be established that assure product / service specifications can be met on a regular basis.  This brings us to the topic of Process Capability.


The natural variation of a process should be small enough to produce products that meet the standards required.  However, often a process in statistical control does not necessarily meet the design specifications.  Process capability is a measure of the relationship between the natural variation of the process and the design specifications.

Process Capability analysis compares the 6 sigma (standard deviation) spread of a process with the specification limits.   The 6 sigma spread of the process should be smaller than the specification range.

The Process Capability Ratio is useful when the process follows a normal distribution with a central mean.  This is not always the case so an alternate approach can be utilized in other situations.  It is referred to as the Process Capability Index.

We discussed continuous improvement previously and presented many tools to use in the process.  From a process standpoint, it is important to minimize variation as much as possible so that control limits will be well within specification limits.  In this way customer expectations (from a specification standpoint) should be fulfilled.

Acceptance Sampling is a form of quality testing used for incoming materials or finished goods.  In this process, inspection personnel take samples at random from a lot (shipment) of items and then inspect each of the items in the sample.  The decision is then made to either accept or reject the whole lot based on the inspection results.  This approach only screens lots and does not drive quality improvement efforts.