Statistical Thinking to Improve Quality

The purpose of Exploratory Data Analysis (EDA) is to generate hypotheses or clues that guide us in improving quality or process performance.  Breyfogle (2003, pgs. 10-11) views Six Sigma as a murder mystery where we use a structured approach to uncover clues that lead us to improve process outputs.   These clues are Key Process Input Variables (KPIVS) and process improvement strategies.  As an example, he considers the process of traveling to work where the Key Process Output Variable (KPOV) is the arrival time.   Examples of KPIVs are the setting of our alarm clock and our departure time.   An alternative process improvement strategy might be a different travel route that is less subject to variation during congested time periods.   Then, the route selected is another KPIV, and the travel time along that route is a function of both the route and departure time.   Exploratory Data Analysis helps us identify these KPIVs.

De Mast and Trip (2007) state that the purpose of EDA from a quality improvement project viewpoint is to identify the dependent (Y) and independent (X) variables that may help understand or solve the quality problem.   The dependent Y variables are KPOVs, and the independent X variables are KPIVs.  Leitnaker (2000) gives an example of EDA to identify KPIVs.  The example is a molding operation where:

• Yields are erratic
• Parts are produced that do not meet specifications
• Shipment schedules are not consistently met

A team studied a molding operation supplying plastic switches to industrial customers for use in assembled control pads.   The operation has eight machines, each machine has two molds, and each mold has four cavities.  To investigate the process capability, the team took a sample of size 5 from the output of one machine every 4 hours.   The following control chart displays the results for a critical dimension.

The process is in control, and the range chart supported this conclusion.  But the variation is large.  Next the team investigated the effect of the cavities and molds on the measured dimension.   To do this, they sampled one part from each of the four cavities of the two molds on one machine.   Breaking down the data by cavities and molds is an example of stratification.  Control charts for the individual cavities and molds showed that all cavities and molds appear to be in control. However, mold 2 cavities have larger averages than mold 1 cavities, and the averages for the cavities increases with cavity number.  The following figure clearly shows this pattern.

The figure leads us to identify mold and cavities numbers as KPIVs.   The team can proceed to reduce the variability in the measured dimension by reducing the differences in averages for the molds and cavities.

 

 

 

 

References

1. Breyfogle, F. W. (2003). Implementing Six Sigma. Hoboken, New Jersey, John Wiley & Sons, Inc.
2. de Mast, Jeroen and Albert Trip (2007). “Exploratory Data Analysis in Quality-Improvement Projects”, Journal of Quality Technology, 39(4): 301-311.
3. Leitnaker, M. G. (2000). Using the Power of Statistical Thinking, Special Publication of the ASQ Statistics Division, Summer 2000.
   

Posted by Gordon M. Clark at 11:47 AM | Permalink | Comments (1)

This posting describes the final phase of the resin output variation example that illustrates 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 stated that the next step for the team was to investigate the weighing processes.

The overall process had two weighing processes.  The first was an in-process manual method, and the second method was a final, automatic scale.   The manual method had individuals reading a line on a scale.  They observed that individuals of different heights read the line from different viewpoints.  Thus, they produced different readings.   The team changed the presentation of the line so people of different heights had the same view point.   This change reduced in-process measurement variation.

Next the team investigated the automatic scale and found significant measurement errors.   They reduced these errors by:

1.     Redesigning the scales protective cover.

2.     Establishing procedures for checking the alignment on a periodic basis.

The following figure presents a control chart showing the results for this project.  The difference between the final upper and lower control limits was less than the team objective of ± 5 kg.  However, the resulting average was 4292 kg which is less than the original target of 4300 kg.   Given the reduction in output variability, management regarded the results as more than adequate.   The improvement also resulted in reduction in the variation of resin viscosity.   This verified the team’s motivation to reduce variation of finished product quality by reducing the output quantity variation. To maintain the results, the team created procedure manuals and established a schedule adjusting the automatic weighing process.

The overall improvement process consisted of four Plan-Do-Check-Act (PDCA) cycles.   This posting describes the last one, the previous post describes two of them and the posting on March 21 (Hoerl-Snee Example) describes the first one.   That one focused on finding and correcting special causes.   This process is different than that suggested by a serial DMAIC process.   Our next posting will present the Hoerl-Snee process improvement strategy which has an overall PDCA approach.

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 01:50 PM | Permalink | Comments (0)

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)

The Customer-Complaint-Process Example illustrated two types of variation, i.e., special and common cause.   The example, taken from Britz, Emerling, et (2000, p. 29), in this post illustrates four types of variation, i.e.,

·        Off-target

·        Common Cause

·        Special Cause

·        Structural.

Off-target variation occurs when the process average does not meet the organization’s desired target.  Structural variation occurs when causes occur in a predictable manner.    For example, the waiting line for a table at a restaurant might be longer on Saturday evenings than on other days.

Distribution Center On-Time Delivery Example

Shawn was perplexed when she examined Figure 1 showing a plot of weekly on-time deliver percentages at her distribution center.  The corporation’s goal was to deliver 97.5% of orders each week in a timely manner.  During the past quarter, the center had only met that goal twice.   In addition, a review to the center’s activities during the two satisfactory weeks did not reveal any unusual behavior.

The overall average of weekly on-time delivery percentages was 94% which was significantly below the corporate goal of 97.5%.    The average of weekly on-time percentages must be greater than 97.5% in order for the center to consistently meet its goal of 97.5%.   If the average of all weekly on-time delivery percentages exactly equaled 97.5% then about half of the weeks would have on-time delivery percentages less than the goal of 97.5%.   Assume that a target of 99% on-time deliveries would permit the center to consistently meet the goal of 97.5% for each week.   This gap between the target (99%) and the weekly averages of 94% is Off-target variation.

 

Figure 1

Figure 2 suggests that the variation in on-time delivery percentages is due to common-cause variation.   One reason is that all of the plotted points are less than the Upper Control Limit (UCL) and greater than the Lower Control Limit (LCL).   Factors contributing to Common-Cause Variation are:

·        Number and complexity of orders in each week

·        Truck schedules

·        Personnel availability

The conclusion is that an analysis of the actions during the two weeks where the center met the goal of 97.5% would be an inefficient approach to improving the system.   Analyzing all of the weeks where the same common-causes are active would be more effective in identifying process improvements.

The next post will illustrate special-cause and structural variation.

Figure 2

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 09:13 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)