Statistical Thinking to Improve Quality

This posting gives two examples illustrating the Analyze Common-Cause Variation step, step 6, in the Hoerl-Snee process improvement strategy.   Refer to the previous posting for a description of this step.

·         Stratification – Pareto Chart.  The posting on 2/25/2008 describes statistical thinking by a company experiencing a high rejection rate in one of its machine shops.   In order to determine the root cause of these rejections they stratified by classifying the rejections with respect to machine type causing the rejections.   Then they created a Pareto Chart ranking the frequency of rejections by machine type.   They found that 60% of the rejections were due to grinding problems.   This finding did not give them the root cause of the rejections, but it allowed them to focus on grinding operations.  Their next step was to construct a cause and effect diagram and then to design experiments to determine improved grinding procedures.   This next step illustrates the implementation of the Study Cause & Effect step, step 7 in the Hoerl-Snee process improvement strategy.
·         Regression Analysis – Stratification.  The posting on 3/4/2008 describes statistical thinking by Pease Industries to reduce the defect rate of decorative glass inserts for a wooden entry door.   The prevailing opinion was that humidity and temperature variations in the mold department were the root cause.  The team collected data and did a regression analysis using temperature and humidity as independent variables and the number of defects as the dependent variable.   The result was no correlation between the independent variables and the number of defects.  They collected more data and stratified the data by part type, month of occurrence and day of week.   They were surprised by the result showing day of the week strongly affecting the defect rate.   A Chi-Square test showed the day of the week was statistically significant.   The next step was to construct a Cause-and-Effect diagram and do a Is-Is Not analysis.   This step illustrates the Study Cause and Effect step, step 7.

In both of the above examples, the use Cause-and-Effect diagrams, designed experiments and the Is-Is Not analysis required the previous results from the Analyze Cause and Effect steps.   One needs to identify the effects prior to studying the effects.

Posted by Gordon M. Clark at 05:51 PM | Permalink | Comments (0)

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

Common-cause variation affects all of the data which distinguishes this step from the Address-Special-Causes step.  The purpose of the Analyze-Common-Cause-Variation step is to identify sources of variation.     Locating the sources of variation might also reveal its root cause without significant additional analysis.  On other occasions, knowing a source of common-cause variation might require further analysis to determine its root cause.   This additional analysis is performed in the next step, Study Cause and Effect.

Some of the tools we might use in this step are:

• Stratification.  Define a stratification factor such as the day of the week or machine.   Partition the factor into logical categories.  Compare the data for each category to highlight differences.
• Disaggregation.  Define quality measures for sub-processes or individual process steps.  Study the variation in the individual sub-processes.  How does it contribute to the overall process variation?
• Pareto Chart.  Classify defects into categories.  Highlight the categories having the most frequent occurrences.    
• Histogram.  Plot the distribution of quality measures.  One or more peaks might indicate the presence of categories that could be examined by stratification.
• Regression Analysis.   Existing opinion might suggest one or more input variables that influence the output quality measure.   A regression analysis might verify this opinion or indicate that these variables have negligible effect.

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 02:49 PM | Permalink | Comments (0)

We use Pareto Charts to rank problems or causes with respect to their frequency of occurrence.  The charts highlight those causes which result in the most quality problems.  

Pareto charts get their name from Vilfredo Pareto (1848 – 1923) who was an economist.   He analyzed and studied the unequal distribution of wealth.   Dr. Juran in the 1940s stated a principle of the “vital few” and the “trivial many” (see Juran and Godfrey (1999)).   That is, in many situations a few problem categories (about 20%) will produce the most problems (about 80%).  Juran called this principle “Pareto’s principle of unequal distribution.”

We illustrate the application of Pareto Charts using a case study taken from Gijo (2005).  A company was experiencing a high rejection rate in one of its machining shops.   They did not know the root causes of these rejections nor how to reduce their occurrence.   They started by examining existing records, and they classified the defects by the individual operations causing the defect.   The analysis of data by this classification is called stratification.   Using the results, they constructed a Pareto chart. The following figure presents the chart.  

The chart shows that 60% of the rejections were due to grinding problems.   Based on the Pareto Chart they started a study improve grinding operations.   This study resulted in designed experiments to determine improved grinding operating procedures.   The resulting analyses lead to operating procedures that significantly reducing rejections and rework due to grinding operations.  

References

1. Juran, J. M. and A. B. Godfrey (1999). Juran’s Quality Handbook, 5^th Edition, New York, McGraw-Hill.
2. Gijo, E. V. (2005). "Improving Process Capability of Manufacturing Process by Application of Statistical Techniques." Quality Engineering 17(2): 309-315.
   

Posted by Gordon M. Clark at 09:48 PM | Permalink | Comments (0)