Statistical Thinking to Improve Quality

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.

References
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.

 

Posted by Gordon M. Clark at 02:52 PM | Permalink | Comments (0)

This posting starts presentation of an example application that illustrates the Hoerl-Sneel process improvement strategy.  We take the example from Britz et all (2000), and they reference Imai (1986).

Resin Output Variation Example (Part A)

Ricoh’s Numazu plant made raw material used as ingredients for copy machine toner.   The tolerances for the raw material ingredients were measured in ten-thousands of a gram.   They had a team which continually monitored the process to achieve continuous improvement.  The team noticed a problem with actual output results compared to theoretical output quantities.   The yield ratio frequently exceeded 1.0.   That is, the actual output quantity for a batch divided by the theoretical output quantity sometimes exceeded 1.0.   The following figure shows a run chart displaying these results.  These values were technically impossible, so the team attributed these results to undesirable variation somewhere in the process.   Their experience indicated that this variation would degrade finished product quality.   They wanted to know the source of the variation and how to eliminate it.

 

 

The figure on the left gives a flowchart of the process.  Notice that after the second phase the process splits into two lines supposedly with identical sub-processes.

The next step in their investigation was to examine the run chart for stability.   The time period in the middle of the run chart had the greatest concentration of values above 1.0.  Further analysis showed that a drop in air pressure was the root cause (special cause) for the excessive variations above 1.0.   They verified this conclusion, but removing this cause did not completed eliminate the outputs greater than theoretical predictions.

Notice that their first steps were to document (understand) the problem and look for special causes.

 

 

References

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
2. Imai, M. (1986). Kaizen, The Key to Japan’s Competitive Success.  New York: Random House Business Edition.
   

Posted by Gordon M. Clark at 11:33 AM | Permalink | Comments (0)

The previous post described Part A of the Distribution Center On-Time Delivery Example.   It illustrated Off-Target and Common-Cause Variation.   This part of the example illustrates Special-Cause and Structural variation.   The control chart in Figure 2 of Part A shows a Lower Control Limit (LCL) of about 88% on-time deliveries. This means that Common-Cause variation would rarely result in a weekly on-time delivery percentage lower than 88%.

Shawn formed a team to study the process and improve it.   While monitoring the process the weekly on-time delivery percentage fell to 73%.  Something had happened to increase the variation.   Figure 3 shows this drop in on-time delivery performance.  The team reviewed the distribution center activities and found that a division supplying the distribution center announced a price increase.   Customers responded by submitting additional orders to avoid the price increase.   This one-time increase in volume caused the distribution center to fall behind in filling orders because it was unprepared to handle the additional work.   Also, this one-time increase in volume is an example of Special-Cause variation.

Figure 3

The team responded by developing an improvement policy.   They determined that one could predict the weekly work load given the state of orders on Wednesday.   The improvement policy provided for overtime hours based on the orders received and remaining work on Wednesday.    Figure 4 shows the result.   The average on-time percentage rose to 98.5%.   The new LCL became 97%.   However, subsequent results  showed two weeks, Special-Cause weeks, where the volume was so heavy even the improvement policy could not handle the heavy demand.   These were end-of-quarter weeks.  Figure 4 shows them as weeks 39 and 52.

Figure 4

These end-of-quarter weeks shown in Figure 4 are examples of Structural variation.   Structural variation is a blend of common and predictable special causes.   Structural variation is due to causes that operate as an inherent part of the system as common causes do.   However, on a control chart, they appear to be due to special causes.  But their occurrence is predictable.

The four types of variation defined by Britz, Emerling et al (2000, p. 34) are:

·        Off-Target variation occurs when the process average is not equal to its target value.

·        Common-Cause variation is the variation exhibited by the process while operating in its best manner.

·        Special-Cause variation results from the intervention of causes that are unplanned and undesirable.

·        Structural variation is variation inherent in the system but appears to be due to special causes on a control chart.   However, the causes of Structural variation are predictable.

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

 

Posted by Gordon M. Clark at 08:51 PM | Permalink | Comments (0)

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.

References

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

Posted by Gordon M. Clark at 09:27 PM | Permalink | Comments (1)

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.

References

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

Posted by Gordon M. Clark at 04:56 PM | Permalink | Comments (0)

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.

References

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.
   

Posted by Gordon M. Clark at 04:46 PM | Permalink | Comments (0)