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.

This posting gives two additional examples illustrating the Analyze Common-Cause Variation step, step 6, in the Hoerl-Snee process improvement strategy.   Refer to the posting on 5/18/2008 for a description of this step.   Both examples include disaggregation as a tool.

·        Disaggregation – Stratification.  The posting on 2/18/2008 describes statistical thinking by a Midwest manufacturing firm to reduce waiting times by customers.   The company’s goal was to have 95% of incoming customer calls answered by a customer service representative in less than 2 minutes.   Based on a process flowchart, team collected service time data for each step in the process.   That is disaggregation.   The team also collected data for estimating the distribution of incoming calls by time of the day.   That is stratification by the time of day.  They used these data as inputs to a simulation of the call answering process.  They used the simulation construct staffing levels by the hour of the day.   The construction and use of the simulation illustrates step 7, Study Cause & Effect.
·        Disaggregation – Regression Analysis.  The posting on 2/21/2008 describes statistical thinking by a manufacturer of automotive door frames.  The purpose was to eliminate a problem meeting dimensional specifications of the finished product.   Shop floor personnel thought that variations in the incoming raw material characteristics caused the problem meeting dimensional specifications.  The team defined important quality characteristics for each step in the process.   They included quality characteristics of the incoming material.   The manufacturer collected data listing the important quality characteristics as well as the final part dimensions.    A regression analysis showed no effect by the incoming material characteristics.    Moreover, it identified several quality characteristics having a significant effect on finished product dimensions.    The regression analysis also showed that the left and right door frames had significantly different variation for two quality characteristics.   These results motivated corrective action and eliminated the need for rework.   In this example, the team did not need to employ step 7, Study Cause & Effect.

Histogram – Stratification.   The posting on 3/25/2008 describes statistical thinking by a team at Ricoh’s Numazu plant.   The plant makes raw material used as ingredients for copy machine toner.  The team wanted to reduce variation in output quantity which indicated a lack of control of the underlying process.   After removing a special cause, the team constructed a histogram of the output quantity.   The histogram clearly displayed excessive variation and two peaks.   The process flow chart showed a split after phase 2 into 2 separate lines, i.e., line A and line B.   Separate histograms for the two lines showed the output from line B was consistently lower that line A.  Constructing separate histograms for the two lines illustrates stratification by line.  Next, the team conducted a brainstorming session to formulate their collective thinking about the causes of excessive variation and the differences between the two lines.   They documented the results with a cause and effect diagram.   The brainstorming session and the construction of a cause and effect diagram illustrate step 7, Study Cause & Effect.

Stratification requires identifying a stratification factor, such as time of the day, and the partitioning of this factor into logical categories.   What tools may we use to aid in the selection of a stratification factor?    The team in the example above noticed two peaks in a histogram.   Breyfogle (2003) provides some guidance for this question.

1. On page 220, Breyfogle states that patterns on a control chart may suggest the need for stratification.   A sequence of points with small up and down variation relative to the control limits may suggest that the sequence of points comes from a single strata.   The opposite situation where a sequence of points that do not have values near the center line may indicate the combination of two strata.
   
2. On page 385, Breyfogle suggests dividing the data into categories based on posing basic questions such as who, what, when and where.
   

Disaggregation may be aided by constructing a process map such as the one used in the posting on 2/21/08.    The process map (Breyfogle, 2003, p. 103) is a flowchart with key process input variables listed for each step in the process.

1.     Breyfogle, F. W. (2003). Implementing Six Sigma. Hoboken, New Jersey, John Wiley & Sons, Inc.