Statistical Thinking to Improve Quality

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)

The principal performance measure in the Monthly Billing Time Example was the total cycle time to prepare customer bills at the end of a month.   How important is variation in systems that have a flow-time or cycle-time performance measure?  Assume we have a process that consists of a number of stations that must be performed in series.   That is, a work item must be processed by station 1 and then after completing station 1, it must be processed by station 2, and so on.    Also, assume the each station has a single server which can only process a single work item at a time.   For example, in the billing time example, a work item might be a single task the corporation performed for a customer in the previous month.  A station might determine the hours expended on that task and calculate its cost.  Assume a clerk determines the hours and calculates its cost.

Reducing the mean time for the clerk to determine the hours expended and calculate a cost will reduce the mean flow time.   What if we reduce the variation in the time a clerk takes to calculate a cost for a work item?    For illustrative purposes, assume the mean time expended by the clerk is 9 minutes to calculate the cost of a work item.  Also, assume the work item arrivals have a mean inter-arrival time of 10 minutes.

The first figure depicts the case where inter-arrival times and service times are constant, i.e., there is no variation.   The number in the system is the number of work items being served and waiting for service.  In this case no work items have to wait.   Therefore, their time at the clerk’s station is a constant 9 minutes.

The second figure illustrates the case where inter-arrival times and service times have variation.   For the five arrivals, their inter-arrival times are:  8, 7, 10, 12 and 13 minutes, for an average of 10 minutes.   Their service times are: 12, 11, 9, 7 and 6 minutes, for an average of 9 minutes.  Now the times at the work station are 12, 16, 15, 10 and 6 minutes for an average of 11.8 minutes.  The variation in inter-arrival and service times increased the time at the work station by 31%.   Thus, variation can have a significant effect on system performance when the performance measure is a flow time or cycle time.

The two figures illustrate a manual simulation for calculating the system time increase due to variation.   When analyzing an actual system, one can predict the system time using a discrete-event simulation.   Inputs to the simulation would include a flow diagram, service time distributions and system inter-arrival time distributions.   Arrival times at the individual work stations would be calculated by the simulation.

Posted by Gordon M. Clark at 09:19 PM | Permalink | Comments (0)

The previous blog post illustrates several key features of Statistical Thinking. One of these features is that Statistical Thinking is a philosophy of learning and action.   That is, learning how to best obtain information which forms the basis of effective action.   In the example, an important first step was to create a systems map and flow chart.   Next the team collected cycle-time observations.   Statistical Thinking evaluates a process by collecting data in addition to past experiences and perceptions.   These data may be numerical (cycle-time measurements) or simply process documentation.   The systems map and the flowcharts are process documentation.  Once we have this documentation, we can ask why we operate in that manner and how we can improve the system.   These data allow us to advance beyond personal opinions expressed by individuals.  Recall that the departments involved thought that the other departments caused the lengthy billing time.  Snee (1986) points out that “Good Decisions are based on facts, not opinions and emotions. … without data everyone is an expert.”

One guideline for effective application of Statistical Thinking is to always flowchart the process.   The flowchart shows the relationships among different people and functions.  Examining the flowchart suggests opportunities for improvement and areas for further examination and data collection.

The acronym SIPOC depicts our systems view of a process.   The following figure depicts the SIPOC components which are Suppliers, Inputs, Process, Outputs and Customers.   One motivation in the Monthly Billing-Time Example was to satisfy customer interests.   

 References

1. Snee, R. D. (1986). "In Pursuit of Total Quality." Quality Progress 20(8): 25-31.

Posted by Gordon M. Clark at 03:35 PM | Permalink | Comments (0)

Britz et al (1996, p4), Britz et al (2000, p7), and Hoerl and Snee (2002, p3) all describe the same example of an actual application of Statistical Thinking at a large corporation.   The corporation wanted to decrease the average monthly billing cycle time of about 17 days to the corporation target of 10 days.   A shorter time would improve the corporation’s cash flow and satisfy customer needs to more rapidly close monthly books.  Customers had complained that other competing corporations were not as tardy in submitting bills.

The initial review of the process revealed that three separate departments constituted the billing process.   Each department worked independently to perform their billing functions.   No one understood the entire billing process flow.   The corporation did not have a standard bill process operating procedure.  Members of three departments claimed that the billing time delays were due to the other departments. 

The initial step to improve the billing system was to develop both a systems map and a flow chart.   The systems map identified responsible groups and the information flow among the groups.   The flow allowed the construction of a production schedule for the monthly billing cycle.   The schedule:

·        listed the specific activities that had to be performed

·        identified the responsible group for each activity

·        specified due dates for each activity

The next step involved creating cross-functional teams to improve the performance of individual activities.   They recorded cycle times, and these cycle times highlighted problem areas. They developed solutions to minimize variations in the problem areas.  They documented the entire process and the procedures.   The documented process procedures helped reduce variation in the problem areas.  The documentation also helped in training new employees.

The corporation assigned a process owner to insure that they continued to realize the performance improvements.     

The result was a reduction in billing cycle time in a 5 month period from 17 day to 9-10 days.   That was almost a 50% reduction.   This result satisfied customers and generated annual savings of $2.5 million.

This example illustrates key features of Statistical Thinking.

·        Regarding the system as a process

·        Reducing variation

·        Using data to determine improvements for the system

References

1. Britz, G., D. Emerling,  et al. (1996). Statistical Thinking, ASQ Statistics Division Special Publication
   
2. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
   
3. Hoerl, R. and R. D. Snee (2002). Statistical Thinking - Improving Business Performance. Pacific Grove, CA, Duxburry.
   

Posted by Gordon M. Clark at 05:01 PM | Permalink | Comments (0)

Britz et al (1996) assign Deming’s Theory of Profound Knowledge as the original source of our definition of Statistical Thinking.   Profound Knowledge has 4 parts:

1. Appreciation for a system
2. Knowledge about variation
3. Theory of knowledge
4. Psychology

The first Statistical-Thinking principle “All work occurs in a system of interconnected processes” follows from Profound Knowledge part 1.   The second and third Statistical-Thinking principles, “Variation exists in all processes” and “Understanding and reducing variation are keys to success”, come from Profound Knowledge part 2.

However, Ron Snee (1986 and 1990) used the term Statistical Thinking with the same meaning (other than wording changes) prior to the Statistics Division’s adoption of the term.   Snee states on page 27 (Snee 1986): “…, statistical thinking is used to describe the thought processes that acknowledge the ubiquitous nature of variation and that its identification, characterization, quantification, control, and reduction provide a unique opportunity for improvement.   ….Every enterprise is made up of a collection of interconnected processes whose input, control variable, and output are subject to variation.   This leads to the conclusion that statistical thinking must be used routinely at all levels of the organization.”   Later, Snee defines Statistical Thinking (Snee 1900, page 118): “I define statistical thinking as thought processes, which recognize that variation is all around us and present in everything we do, all work is a series of interconnected processes, and identifying, characterizing, quantifying, controlling, and reducing variation provide opportunities for improvement.  This definition is essentially the same as the Statistics Division definition published in 1996.

My conclusion is that the basic ideas in our definition of Statistical Thinking date back to Deming.    Ron Snee in 1986 and 1990 made the first use of the term Statistical Thinking giving it the meaning we are currently using.   If anyone has further information to contribute to this topic, please make your comments known.

Compare the Statistical-Thinking history with Six Sigma.  Breyfogle (2003 on page 5) credits Bill Smith at Motorola with the initial use of the term Six Sigma.  Like Statistical Thinking, the original ideas come from quality pioneers such as Deming.    In 1998, Motorola received the Malcom Baldridge National Quality Award in part due to their Six Sigma program.    Motorola University (http://www.motorola.com/content.jsp?globalObjectId=3079) states that Bill Smith introduced the term Six Sigma in 1986.   Thus, the initial definitions of the terms Six Sigma and Statistical Thinking occurred at about the same time.

References

1. Britz, G. et al. (1996). Statistical Thinking, ASQ Statistics Division Special Publication.
2. Snee, R. D. (1986). "In Pursuit of Total Quality." Quality Progress 20(8): 25-31.
3. Snee, R. D. (1990). "Statistical Thinking and Its Contribution to Total Quality." The American Statistician 44(2): 116-121.
4. Breyfogle, F. W. (2003). Implementing Six Sigma. Hoboken, New Jersey, John Wiley & Sons, Inc.
   

Posted by Gordon M. Clark at 11:04 AM | Permalink | Comments (0)

In January 1994, the Statistics Division (Britz et al, 1996) adopted a tactical plan to Enable Broad Application of Statistical Thinking.   The division developed a definition of Statistical Thinking which was published by Quality Press in 1996.   That definition is identical to the principles listed above as the basis for Statistical Thinking.  As the Past Chair of the division, I am motivated to promote the use of Statistical Thinking.

Why does the Statistics Division assign such a high priority to Statistical Thinking?   Why doesn’t the Statistics Division simply emphasize statistical methods such as SPC, DOE and regression analysis?  The answer is that the benefits of statistical methods are significantly improved by their use in the context of Statistical Thinking. 

Brtiz el (2000) point out that Statistical Thinking incorporates key concepts from several improvement methodologies such as Six Sigma, Total Quality Management (TQM) and systems thinking.   These key concepts include:

• A holistic approach to improving the system
• Viewing work as a process
• Using data to guide decisions
• Recognizing and responding wisely to variation

Clearly, Six Sigma uses Statistical Thinking.   Benbow and Kubiak (2005) state on page 2:

• “Understanding and improving processes is a key part of every Six Sigma project.”
•  “Six Sigma focuses on reducing process variation and enhancing process control, ”

Six Sigma uses a measure of variation, illustrated in the figure, as its overall measure of project success.  That is, for the distribution of the key quality characteristic, the distance from its mean to the closest specification limit (LSL or USL) measured in standard deviation (sigma) units.

In my opinion, Statistical Thinking is a crucial concept in Six Sigma.   We will see later that a customer focus is inherent in Statistical Thinking because a process includes its customer.

References

1. Britz, G. et al. (1996). Statistical Thinking, ASQ Statistics Division Special Publication.
2. Britz, G. et al. (2000). Improving Performance Through Statistical Thinking, ASQ Quality Press.
3. Benbow, D. W. and T. M. Kubiak (2005). The Certified Six Sigma Black Belt Handbook. Milwaukee, Wisconsin, ASQ Quality Press.
   

Posted by Gordon M. Clark at 06:14 PM | Permalink | Comments (0)