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, Six Sigma is an example of Statistical Thinking.   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.

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.

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.

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.
   

The previous blog post describes an application of Statistical Thinking to increase customer satisfaction by examining the processes starting with the raw material supplier and ending with the customer use of the product.   This example illustrates important features of Statistical Thinking described by Britz, Emerling et al (2000).   These features include:

1. Reducing variation improves performance.   The team had training in Statistical Thinking so they understood the various types of variation.   One type is common-cause variation which is always present.   Another type is special-cause variation which is due to isolated events.   One way to reduce overall variation is to identify outcomes that have a significant special-cause variation component.  For those outcomes, we can analyze the circumstances causing the increased variation.    To reduce common-cause variation, we need to analyze the all outcomes not affected by special causes.   The team knew this so they collected data to help them identify outcomes due to special causes.    A control chart which is a statistical method is a common approach for identifying outcomes affected by special causes.
2. The team had management support.   An understanding of Statistical Thinking facilitates management support.   Management had to support the tactic of going to the customer and convincing them to collect usage data so the team could estimate defect rates.   The team explained the concepts of Statistical Thinking to the customer to gain their support.   Note that management and the customer did not have to have a detailed understanding of the statistical methods.  When the team discovered that the importance of raw material, they had to convince management to support designed experiments to reduce common-cause variation.   My experience is that management can be very reluctant to approve designed experiments unless they appreciate the principles of Statistical Thinking.
3. Reducing variation is often a sequential process.   The team went after special-cause variation and then discovered a potential contributor to common-cause variation.

References

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
   

Statistical Thinking gives a framework for learning and action to improve performance.  We initiate the application of Statistical Thinking by identifying, documenting and defining the business process.  The Monthly-Billing-Process Example began by flowcharting and defining the billing process.   The team in the Customer-Complaint Process recognized that the process included raw material suppliers, the OEM manufacturer, and their customers.   Statistical Thinking recognizes that reducing variation is the key to success.  Often reducing variation involves recognizing the different types of variation.   The team in the Customer-Complaint-Process Example recognized the difference between special-cause and common-cause variation.

Usually Statistical Thinking requires the collection and analysis of data to estimate and reduce variation.  Statistical Thinking is data-driven decision making.   However, we need to define the overall process including its customer before collecting and analyzing data.   Also, the process definition includes available subject matter knowledge.   In the Monthly-Billing-Process Example, the process definition created knowledge concerning the process that did not exist without the flowcharts.   In the Customer-Complaint-Process example, the team recognized that it had to collect usage rates in order to estimate variation and identify special-cause outcome.  This process definition allows us to collect the appropriate data and focus our analysis.

Britz, Emerling, et al (2000, p26) point out two key advantages of Statistical Thinking and data-driven decision making.

1. Managers react to the last outcome.   If it is satisfactory, everyone is pleased and satisfied that the system is performing well.   If it is unsatisfactory, the implication is that something needs correction.   Results from common-causes are treated as resulting from special causes.  The analysis to reduce common-cause variation is much more effective if results from multiple outcomes are used.  Trying to find a special cause when one does not exist leads to frustration.
2. The lack of data makes everyone an expert.   Individual opinions vary and conflict with each other.

The figure depicts the relationship among Statistical Thinking, data and statistical methods.   Effective application of statistical methods occurs after performing Statistical Thinking.   In the Customer Complaint Process Example, a control chart and designed experiments occur after Statistical Thinking.   Lynne Hare points out in the reference by Britz, Emerling, et al (2000, p27) that he was successful in getting increased use of statistical tools only after explaining Statistical Thinking to managers.   They would not permit employees to use tools when they did not understand their purpose.

1. Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.
   

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

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

1.     Britz, G. C., D. W. Emerling, et al. (2000). Improving Performance Through Statistical Thinking. Milwaukee, WI, ASQ Quality Press.