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)

The previous post described Part A of the Distribution Center On-Time Delivery Example.   It illustrated Off-Target and Common-Cause Variation.   This part of the example illustrates Special-Cause and Structural variation.   The control chart in Figure 2 of Part A shows a Lower Control Limit (LCL) of about 88% on-time deliveries. This means that Common-Cause variation would rarely result in a weekly on-time delivery percentage lower than 88%.

Shawn formed a team to study the process and improve it.   While monitoring the process the weekly on-time delivery percentage fell to 73%.  Something had happened to increase the variation.   Figure 3 shows this drop in on-time delivery performance.  The team reviewed the distribution center activities and found that a division supplying the distribution center announced a price increase.   Customers responded by submitting additional orders to avoid the price increase.   This one-time increase in volume caused the distribution center to fall behind in filling orders because it was unprepared to handle the additional work.   Also, this one-time increase in volume is an example of Special-Cause variation.

Figure 3

The team responded by developing an improvement policy.   They determined that one could predict the weekly work load given the state of orders on Wednesday.   The improvement policy provided for overtime hours based on the orders received and remaining work on Wednesday.    Figure 4 shows the result.   The average on-time percentage rose to 98.5%.   The new LCL became 97%.   However, subsequent results  showed two weeks, Special-Cause weeks, where the volume was so heavy even the improvement policy could not handle the heavy demand.   These were end-of-quarter weeks.  Figure 4 shows them as weeks 39 and 52.

Figure 4

These end-of-quarter weeks shown in Figure 4 are examples of Structural variation.   Structural variation is a blend of common and predictable special causes.   Structural variation is due to causes that operate as an inherent part of the system as common causes do.   However, on a control chart, they appear to be due to special causes.  But their occurrence is predictable.

The four types of variation defined by Britz, Emerling et al (2000, p. 34) are:

·        Off-Target variation occurs when the process average is not equal to its target value.

·        Common-Cause variation is the variation exhibited by the process while operating in its best manner.

·        Special-Cause variation results from the intervention of causes that are unplanned and undesirable.

·        Structural variation is variation inherent in the system but appears to be due to special causes on a control chart.   However, the causes of Structural variation are predictable.

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 08:51 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)