April 23, 2008

Assess Stability

This posting discusses the third step in the Hoerl-Snee Process Improvement Strategy.   Refer to the figure in the posting on April 4 for an overview of the process.    Use Britz et al (2000) and Hoerl and Snee (2002) as references.

Assess Stability

After collecting data on key measures, the next step is to analyze process stability based on that data.  First we define a stable process or one that is in-control.   Shewhart (1931, p. 6) states: “..a phenomenon will be said to be controlled when, through the use of past experience, we can predict, at least within limits, how the phenomenon may be expected to vary in the future.”   More recently, Montgomery (2005, p. 148) states: “In any production process, …., a certain amount of inherent or natural variability will always exist.  …. this natural variability is often called a ‘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.  … We refer to those sources of variability that are not part of the chance cause pattern as ‘assignable causes.’  A process that is operating in the presence of assignable causes is said to be out of control.”   Montgomery references Shewhart for the terminology chance and assignable causes.   He states that many now use the terminology common cause rather than chance cause and special cause rather than assignable cause.  

An important characteristic of a stable or in-control process is that it is predictable.   This comes from Shewhart’s definition.  That is, one can predict future behavior from past behavior.   Breyfogle (2003, p. 1109) and Wheeler (1993, p. 124 and 128) state that an in-control process is predicable whereas a process that is not in-control is unpredictable.   This means that statistical methods such as t tests and ANOVA are inappropriate for unstable processes.

The definitions stated above immediately suggest methods for identifying whether a process is in-control.   They include run charts and SPC control charts.   A run chart is a time plot of quality characteristic and a control chart is a run chart with control limits.   Using the points on these charts that signal lack of control, we can conduct investigations to determine what caused these points to be different.  Two previous postings that do that are:

  • Rosin yield run chart on March 21.   The team found that their cause was a drop in air pressure.
  • Customer complaint process posted on January 30.   The investigation identified the high defect rate in October, 91 was due to a supplier using the wrong material.

Two major reasons for assessing stability and removing assignable causes prior to addressing common-cause variation are:

  • Detecting and removing assignable causes is easier than reducing the variation due to common causes.   Remove the low hanging fruit first.
  • The analysis approach to removing assignable causes is different than reducing common-cause variation.   Common causes affect variation in all data points for a stable process.   When searching for the root cause of variation in specific observations due to an assignable cause, one can focus on the differences between these observations and the others.

Consider the possibility of wasting effort when a process is in-control (stable) but some results do not meet targets.   Managers could pressure staff to find the cause of specific results not meeting targets.    That is, managers could direct staff to find causes for specific undesirable outcomes when the variation is present in all outcomes.

1.     Breyfogle, Forrest W. (2003). Implementing Six Sigma: Smarter Solutions Using Statistical Methods, Second Edition, John Wiley & Sons, Inc.
2.     Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
3.     Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxbury.
4.     Montgomery, Douglas C. (2005). Introduction to Statistical Quality Control, John Wiley & Sons, Inc.
5.     Shewhart, Walter A. (1931). Economic Control of Quality of Manufactured Product, D. Van Nostrand Company, Inc.
6.     Wheeler, Donald J. (1993). Understanding Variation: The Key to Managing Chaos, SPC Press, Inc.


February 11, 2008

Example Illustrating Four Variation Types

The Customer-Complaint-Process Example illustrated two types of variation, i.e., special and common cause.   The example, taken from Britz, Emerling, et (2000, p. 29), in this post illustrates four types of variation, i.e.,

·        Off-target

·        Common Cause

·        Special Cause

·        Structural.

Off-target variation occurs when the process average does not meet the organization’s desired target.  Structural variation occurs when causes occur in a predictable manner.    For example, the waiting line for a table at a restaurant might be longer on Saturday evenings than on other days.

Distribution Center On-Time Delivery Example

Shawn was perplexed when she examined Figure 1 showing a plot of weekly on-time deliver percentages at her distribution center.  The corporation’s goal was to deliver 97.5% of orders each week in a timely manner.  During the past quarter, the center had only met that goal twice.   In addition, a review to the center’s activities during the two satisfactory weeks did not reveal any unusual behavior.

The overall average of weekly on-time delivery percentages was 94% which was significantly below the corporate goal of 97.5%.    The average of weekly on-time percentages must be greater than 97.5% in order for the center to consistently meet its goal of 97.5%.   If the average of all weekly on-time delivery percentages exactly equaled 97.5% then about half of the weeks would have on-time delivery percentages less than the goal of 97.5%.   Assume that a target of 99% on-time deliveries would permit the center to consistently meet the goal of 97.5% for each week.   This gap between the target (99%) and the weekly averages of 94% is Off-target variation.


Figure 1

Figure 2 suggests that the variation in on-time delivery percentages is due to common-cause variation.   One reason is that all of the plotted points are less than the Upper Control Limit (UCL) and greater than the Lower Control Limit (LCL).   Factors contributing to Common-Cause Variation are:

·        Number and complexity of orders in each week

·        Truck schedules

·        Personnel availability

The conclusion is that an analysis of the actions during the two weeks where the center met the goal of 97.5% would be an inefficient approach to improving the system.   Analyzing all of the weeks where the same common-causes are active would be more effective in identifying process improvements.

The next post will illustrate special-cause and structural variation.

Figure 2


1.     Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.


February 07, 2008

Statistical Thinking and Statistical Methods

Statistical Thinking gives a framework for learning and action to improve performance.  We initiate the application of Statistical Thinking by identifying, documenting and defining the business process.  The Monthly-Billing-Process Example began by flowcharting and defining the billing process.   The team in the Customer-Complaint Process recognized that the process included raw material suppliers, the OEM manufacturer, and their customers.   Statistical Thinking recognizes that reducing variation is the key to success.  Often reducing variation involves recognizing the different types of variation.   The team in the Customer-Complaint-Process Example recognized the difference between special-cause and common-cause variation.

Usually Statistical Thinking requires the collection and analysis of data to estimate and reduce variation.  Statistical Thinking is data-driven decision making.   However, we need to define the overall process including its customer before collecting and analyzing data.   Also, the process definition includes available subject matter knowledge.   In the Monthly-Billing-Process Example, the process definition created knowledge concerning the process that did not exist without the flowcharts.   In the Customer-Complaint-Process example, the team recognized that it had to collect usage rates in order to estimate variation and identify special-cause outcome.  This process definition allows us to collect the appropriate data and focus our analysis.

Britz, Emerling, et al (2000, p26) point out two key advantages of Statistical Thinking and data-driven decision making.

  1. Managers react to the last outcome.   If it is satisfactory, everyone is pleased and satisfied that the system is performing well.   If it is unsatisfactory, the implication is that something needs correction.   Results from common-causes are treated as resulting from special causes.  The analysis to reduce common-cause variation is much more effective if results from multiple outcomes are used.  Trying to find a special cause when one does not exist leads to frustration.
  2. The lack of data makes everyone an expert.   Individual opinions vary and conflict with each other.

The figure depicts the relationship among Statistical Thinking, data and statistical methods.   Effective application of statistical methods occurs after performing Statistical Thinking.   In the Customer Complaint Process Example, a control chart and designed experiments occur after Statistical Thinking.   Lynne Hare points out in the reference by Britz, Emerling, et al (2000, p27) that he was successful in getting increased use of statistical tools only after explaining Statistical Thinking to managers.   They would not permit employees to use tools when they did not understand their purpose.

  1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.

February 04, 2008

Observations Based on the Customer-Complaint-Process Example

The previous blog post describes an application of Statistical Thinking to increase customer satisfaction by examining the processes starting with the raw material supplier and ending with the customer use of the product.   This example illustrates important features of Statistical Thinking described by Britz, Emerling et al (2000).   These features include:

  1. Reducing variation improves performance.   The team had training in Statistical Thinking so they understood the various types of variation.   One type is common-cause variation which is always present.   Another type is special-cause variation which is due to isolated events.   One way to reduce overall variation is to identify outcomes that have a significant special-cause variation component.  For those outcomes, we can analyze the circumstances causing the increased variation.    To reduce common-cause variation, we need to analyze the all outcomes not affected by special causes.   The team knew this so they collected data to help them identify outcomes due to special causes.    A control chart which is a statistical method is a common approach for identifying outcomes affected by special causes.
  2. The team had management support.   An understanding of Statistical Thinking facilitates management support.   Management had to support the tactic of going to the customer and convincing them to collect usage data so the team could estimate defect rates.   The team explained the concepts of Statistical Thinking to the customer to gain their support.   Note that management and the customer did not have to have a detailed understanding of the statistical methods.  When the team discovered that the importance of raw material, they had to convince management to support designed experiments to reduce common-cause variation.   My experience is that management can be very reluctant to approve designed experiments unless they appreciate the principles of Statistical Thinking.
  3. Reducing variation is often a sequential process.   The team went after special-cause variation and then discovered a potential contributor to common-cause variation.


  1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.

January 30, 2008

Customer Complaint Process Example

Britz, Emerling et al (2000, p52) describe an application of Statistical Thinking that illustrates the following: the first principle, “All work consists of interconnected processes”, two types of variation, and shows the application of statistical methods to improve quality.   An OEM manufacturer responded to customer complaints by regarding them as isolated events.   Their corrective action did little to improve quality for future products.   They received training in Statistical Thinking and formed a team to improve the complaint handling process.   The team wanted to analyze each complaint to determine if it was the result of an isolated event (a special cause) or if it resulted from a process that needed improvement (a common cause).   Shewhart (1931) developed these terms which are basic to Statistical Quality Control.  Common-cause variation is the natural variation of a process when it is operating in a stable manner, and special-cause variation is due to an unpredicable special event.   Examples of special causes in manufacturing are improperly maintained machines, operator errors or defective raw material.

In order to categorize the causes, the company asked the customer for usage data so the team could calculate defect rates.   The company explained Statistical Thinking concepts to their customers to convince them to supply usage data.  The team plotted using the control chart shown in the following figure.   The high defect rate in October 91 indicated a special cause.  An investigation led to raw material.   The raw material supplier used the wrong material.  However, discussions with the supplier and within the team motivated further analysis of the raw material.  The supplier and the company conducted a series of designed experiments which identified an improved raw material composition.   They changed their standard operating procedure to use this new raw material specification.   The control chart shows a defect rate improvement from .023% to .004%.   








The significant reduction in the complaint rate required recognition of a process involving raw material suppliers, the OEM manufacturer, and their customers. The team also used two statistical methods: Statistical Process Control (SPC) and Designed Experiments.  The team used SPC to identify the special cause, and they used Designed Experiments to reduce the common-cause variation.


  1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
  2. Shewhart, W. A. (1931), Economic Control of Quality of Manufactured Product, Milwaukee, WI, American Society for Quality.