Statistical Thinking to Improve Quality

This posting continues the resin output variation example described to illustrate the Hoerl-Snee process improvement strategy.   This example appears in Britz et al (2000) and in Hoerl and Snee (2002).   The Ricoh team is focusing on reducing the variability in resin output quantity.   The previous post ended with a description of cause & effect diagram the team constructed to list potential sources of variability.
Based this diagram the team regarded the following potential causes as most likely to be the largest contributors to output variation:

1. The procedure for dividing the resin after phase 2 (potentially the cause of differences between line A and B).
   
2. The solvent feed ratio.
   
3. The weighing process, i.e., final (automatic) and in-process (manual).
   

After attacking the first potential cause, the team found that some resin remained in the reaction tank after sending the materials to the two lines.  That meant that line B had less input and therefore less output.   After changing the dividing procedure, the team found no significant difference between the outputs of the two lines.

The output quantities still had too much variation.   The team turned to the second potential cause, i.e., the solvent feed ratio.  The following figure shows a scatter plot indicating that increasing solvent feed ratio is correlated with increasing output.   In calculating the regression line the team regarded the high output occurring at a feed ratio slightly less than 1, as an outlier.   This correlation violated the team’s knowledge of the underlying process.   They investigated the measurement of the feed ratio, and they found that the ratio measurement was affected by the length of time the solvent was in the tank.   They changed the procedure to insure that the solvent had stabilized prior to measurement.   They collected more data to measure the impact of this change and found less variation in the measured feed ratio and no correlation between the measured feed ratio and the output quantity.

The output variation still did not meet their targets shown in the previous posting.   The next posting will present their analysis of the weighing process.   This posting shows two cycles of PDCA which differs from the sequential process suggested by DMAIC.   From a DMAIC viewpoint the team went through two cycles of Analyze-Improve.

References

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
   
2. Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxbury.
   

Posted by Gordon M. Clark at 10:17 AM | Permalink | Comments (0)

This posting continues the resin output variation example described to illustrate the Hoerl-Snee process improvement strategy.   We take this example from Britz et al (2000).   It also appears in Hoerl and Snee (2002).

Having removed the special cause, the Ricoh team focused on output quantity variability.   A histogram displays this variability, and the following figure shows recent output data.  This histogram displays an unexpected pattern indicating a combination of two underlying distributions for the output quantity.   Notice the peaks at 4284 and 4308 kg.

The process flowchart appearing in the previous posting suggested that these two component distributions were due to the split after phase 2 into two separate lines, i.e., lines A and B.   The following histograms shown below confirmed this difference.   The output from line B was consistently lower than line A.   Based on the needs of their customers, the team established the limits shown in the histograms, i.e., 4300 kg ± 5 kg.

Clearly, the variation in output quantity is excessive.   Next the team conducted a brainstorming session to document their collective thinking on potential causes of excessive variation and differences between the two lines.   The following cause and effect diagram shows the result of this session.

The next posting will describe the investigation based on the potential causes shown above.  
Note that the improvement process is iterative. Gather data, identify special cause, gather more data, notice differences, and then conduct brainstorming session.   This improvement strategy looks more like Shewhart’s Plan-Do-Check-Act (PDCA) than the DMAIC steps recommended for Six-Sigma projects.   Also, the team didn’t adopt a specified target until after two data analysis steps.   That is, their Define step occurred in their second PDCA cycle.

References

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
   
2. Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxbury.
   

Posted by Gordon M. Clark at 02:06 PM | Permalink | Comments (2)

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)

A set of fundamental principles define Statistical Thinking, and these principles appear above in the introductory statements to this blog.    A number of different approaches exist for applying Statistical Thinking to improve quality.   Call these approaches Process Improvement Strategies.    The Statistics Division has promoted one originally defined by Hoerl and Snee (1995).    This is the same process improvement strategy described in detail by Britz, Emerling, et al (2000) and Hoerl and Snee (2002).   Call this process improvement strategy the Hoerl-Snee strategy.  

Six Sigma has another process improvement strategy.    Six Sigma uses the DMAIC steps which are Define, Measure, Analyze, Improve and Control.  The DMAIC steps differ from the Hoerl-Snee process improvement strategy.   Our blog posting on January 13, 2008 points out that Statistical Thinking is a crucial concept in Six Sigma.   Clearly Six Sigma regards work as a system of interconnected processes, looks for variation in all processes, and regards understanding and reducing variation as keys to success.

Each element in the Hoerl-Snee strategy maps to an element in the DMAIC strategy.   However, the author thinks that the Hoerl-Snee strategy is more explicit and easier to understand.

The Shainin System^TM or Statistical Engineering has another approach to quality improvement.   See Shainin (1995) for an overview or Steiner and MacKay (2005) for improvements to Statistical Engineering.   Statistical Engineering does use Statistical Thinking.   Its process improvement strategy places more emphasis on finding and eliminating a dominant cause (The Red X) than the Hoerl-Snee and Six Sigma strategies.  Statistical Engineering does not differentiate between special and common causes.   Also, it places less emphasis on advance planning prior to data gathering.   In addition, Statistical Engineering does not explicitly separate special causes from common causes so that it more effectively identifies the causes and eliminates them.

Approach in Subsequent Postings

First, we will specify the Hoerl-Snee strategy.   This strategy will be illustrated by example applications which we will present next.   After that we will discuss the differences between the three strategies mentioned above.   Case studies will illustrate the differences. 

References

1. Hoerl, R. W. and R. D. Snee (1995). Redesigning the Introductory Statistics Course. Madison, Wisconsin, University of Wisconsin, Center for Quality and Productivity Improvement.
   
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. Shainin, R. D. (1995). A Common Sense Approach to Quality Management. 49th Annual Quality Congress Proceedings.
   
5. Steiner, S. H. and R. J. MacKay (2005). Statistical Engineering: An Algorithm for Reducing Variation in Manufacturing Processes. Milwaukee, Wisconsin, ASQ Quality Press.
   

Posted by Gordon M. Clark at 10:37 AM | Permalink | Comments (0)

A major benefit of the Is-Is Not Analysis is its documentation of circumstances leading to the problem as well as those not associated with the problem.   In the  Pease Industries example, the Is-Is Not Analysis allowed the team to eliminate potential causes in the Cause-and-Effect Diagram.   Hoerl and Snee (2002, p 204) suggest that the results of the analysis be displayed in a table also showing possible causes and further action.

We illustrate that display of the analysis results using knowledge gained by the author’s consulting experience.  

Peach Pit Example

Packers located in the vicinity of peach farms purchase raw peaches and process them for use as ingredients in food products.   Their processing includes removal of the skin and pits.    They use high-speed machines to remove the pits.   We will call these machines pitters.  However, the best pitters leave some pits and pit fragments.    Some packers use inspectors downstream of the pitters to remove pits and pit fragments left by the pitters.   The picture on the left shows inspectors removing pits and pit fragments.

The following figure shows the processing sequence.

 

The following table shows the results of the Is-Is not analysis.

References

1. Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxburry
   

Posted by Gordon M. Clark at 09:11 PM | Permalink | Comments (0)

Britz, Emerling, et al (2000, p 118) and Hoerl and Snee (2002, p 203) describe the Is–Is Not Analysis which helps narrow the search for a root cause.    It does that by documenting the problem.   The analysis documents where, what, when and who are associated with the problem.    In addition, the analysis documents where, what, when and who are not associated with the problem symptoms.  This documentation suggests further action to discover the root cause.

Pease Industries Example

Smith and Adams (2001) give an example of Is-Is Not analysis being important in identifying a root cause when other approaches failed.   Pease Industries is a large Midwestern manufacturer of residential entry doors.  This was done as part of a Lean Six Sigma project.   A line that was placing rosin and glass inserts for more expensive residential entry doors had a 16% defect rate.  They formed a team consisting of operators, managers, and consultants.   The work flow used a batch processing system.   The team reduced non value-added activity, eliminated batch processing, and re-assigned operators who were no longer needed.   The line now had one-piece flow.   The defect rate decreased to 11% from 16%.   In addition, line productivity increased by 62%.  

This improvement still left an 11% defect rate in the decorative glass inserts for a wooden entry door.   The defect was a consistent hairline imperfection where liquid resin should have met the edge.   They called this defect a “shrink line.”   Engineers and managers felt that humidity and temperature variations in the mold department were the root cause.    The team collected data and did a regression analysis.   The dependent variable was the number of defects and the independent variables were temperature, humidity, and an interaction term involving both temperature and humidity.   (I hope they used Poisson regression rather than ordinary least squares.)   The result was no correlation between the independent variables and the number of defects.

 

Team members including engineers, quality managers, an operator, and a consultant went to the shop floor to personally collect data.   Using recorded data, they examined defect occurrence by the following factors: part type, monthly occurrence, and day of the week.   Stratification is the analysis of data by these factors.   To their surprise the following figure shows that defect occurrence was highest on Monday and declined through the week.   A Chi-Square test showed the day of week was statistically significant.

Next, the team constructed a Cause-and-Effect diagram giving all possible causes of the defect.   Then the team performed an Is-Is Not analysis.   The used the data they collected to do the analysis.   Their statistical analysis of the data supported not only what circumstances were associated with the defect but the circumstances that were not associated with the defect.   For example, resin, swirls, bad resin mixes and laminations were not problems.   They examined what the problem was versus what it was not, when it happened and when it did not, and where it happened versus where it did not.   They went back to the Cause-and-Effect diagram and eliminated possible causes.

Their conclusion was that they had dirty molds.  Molds were cleaned on certain days.  After implementing controls, they estimated the annual savings to be $1,050,000.

The example illustrates the potential benefits of using an Is-Is Not analysis.   However, a strict application of Statistical Thinking would have employed the Is-Is Not analysis prior to doing regression analyses.

References

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
2. Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxburry.
3. Smith, B. and E. Adams (2001). LeanSigma: Advanced Quality. Annual Quality Congress.
   

Posted by Gordon M. Clark at 04:25 AM | Permalink | Comments (0)