Statistical Thinking to Improve Quality

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.

Posted by Gordon M. Clark at 07:48 PM | Permalink | Comments (0)

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.

Posted by Gordon M. Clark at 12:17 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)

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)

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)

This post illustrates the Statistical Thinking tool, the flowchart or process map, using an example taken from the author’s consulting experience.   A flowchart of a process is sometimes referred to as a process map.   A manufacturer produced automotive door frames, depicted in the following figure.   The door frame consists of four parts which were joined by a welding operation.  The shape and finished product dimensions were important quality characteristics of the finished product.  However, they had a problem meeting dimensional specifications on the assembled final product.   As a result they did considerable rework to insure satisfactory quality for the finished product.  

The manufacturer formed a team to recommend corrective action to reduce rework costs and the time to meet shipment schedules.   Shop floor personnel thought that variations in incoming raw material caused the quality problems.   An analysis showed that the header was the primary quality problem.

The following figure gives the flowchart or process map for producing a header.  The roll mill takes sheet metal, cuts the input material to the proper length, forms the two parts for a header, and spot welds them together.   The bender bends the header to the proper shape punches two holes which will be used to position the part in subsequent operations.   The saw forms the proper angles at the two ends of the header.    The data on the flow chart below each operation specify important quality characteristics.   The symbols h₁, h₂, g, D1, D2, D3 and SC 4 through SC20 specify dimensions.

The manufacturer collected data for the team for relating the quality characteristics on the flowchart to finished part dimensions.   Collecting and analyzing data for individual steps in the flowchart is an example of disaggregation.  A regression analysis resulted in the following conclusions:

1. Variation in material characteristics has little effect on quality characteristics.
2. D1, D2 and D3 have considerable variation and affect finished product quality
3. The left and right headers have significantly different variation for D2 and D3.

The above conclusions motivated corrective action, and the manufacturer eliminated the need for rework.    This example reinforces the conclusion that data-driven decision making gives Statistical Thinking a significant advantage over expert opinion.

Posted by Gordon M. Clark at 10:02 PM | Permalink | Comments (0)

This post starts a series of posts to present the use of Statistical Thinking Tools in applying Statistical Thinking.   The Statistical Thinking Tool illustrated by this example is a flowchart.   We can have flowcharts for processes having service time objectives as well as processes processes producing a physical product.  Jeffries and Sells (2004) present this example and describe the use of “statistical tools” to meet company service time objectives.   We regard their use of statistical tools as an application of Statistical Thinking.

A Midwest manufacturing firm processes orders for its 6 manufacturing plants and 12 warehouses.   Originally, each plant and warehouse had its own order processing service staffed by a total of 36 customer service representatives.  To improve customer service and reduce costs, the company president directed a team to develop a centralized customer service center located at corporate headquarters.   The president made this decision after the team surveyed customers and found that they were adamant that they did not want to wait for a customer service representative to answer a phone call and they were not very interested in personalized service provided by a plant or warehouse representative.

The team established a goal where 95% of incoming calls would wait less than 2 minutes for a customer service representative.   The team acquired an Automatic Call Distribution (ACD) system to route customer calls to customer service representatives.  The call center would operate from 7:00 am to 7:30 pm Central Time.   The following figure gives a flowchart specifying the process of answering incoming customer calls.

The team collected data giving the distributions of incoming calls by time of day and the service times of the customer service representatives to answer the calls.  Recording and analyzing data for individual steps in the process flow chart is an example of disaggregation.   Classifying and analyzing data by a factor such as time of the day is an example of stratification.

The customer service center staffing levels by hour of the day is a crucial system design parameter.   Wait times will be long without adequate staff.  On two occasions in the past two months, I have had to wait more than an hour for technical service support personnel to answer my calls.   I know that this happens because the companies involved have allocated inadequate staffing to handle the incoming calls.

The team developed staffing levels throughout the day using a simulation of the process represented by the figure above.   Constructing a simulation requires a flowchart.  Refer to Jeffries and Sells (2004) for additional details.

The next post will illustrate the use of a flowchart for a process producing a physical product.

References

1. Jeffries, R. D. and P. R. Sells (2004). Managing Customer Service Using Statistical Tools: A Case Study. Annual Quality Congress Proceedings.
   

Posted by Gordon M. Clark at 09:32 PM | Permalink | Comments (0)