Ehie and Sheu (2005) report that the Axle Factory project improvements described in the Axle Factory Case Study Post - Phases 3 Through 6 post saved the manufacturer $200,000 per year.   This exceeded the average savings of a typical Six Sigma project at the plant.    The team and managers regarded the use of the integrated TOC/SS framework a success.   Managers appreciated the benefits of being able to select a project giving greater bottom-line performance due to the TOC concept. Six Sigma contributed statistical tools and engineering techniques for defining the process to be improved, identifying root causes and designing improvement actions.  

The X-bar chart shown in the Phases 3 Through 6 post does motivate questions concerning the implementation of the TOC/SS framework.   The chart shows the variation in the CSI which is the ratio between the number of products produced that meet customer specifications and peak capacity.  The difference between the UCL and the LCL does suggest a significant variation in the project performance measure, CSI, after the improvements were performed.   Was this variation thoroughly analyzed?    Even if the cutting phase is no longer a system constraint, reducing the CSI variation might lead to further improvement.  

This post continues the Case Study illustrating the application of an integrated Six Sigma and the Theory of Constraints (TOC) framework.  The Integrated Six Sigma and Theory of Constraints post describes this framework.   The application of this framework improved the performance of an axle factory.  The application of the first two phases are described in the previous post.   In the first phase of the framework,  the team identified the cutting phase as the primary bottleneck operation.   In the second phase, the team noticed that the cutter grinders caused 40% of cutting machine downtime and that the machine operators assigned lack of proper lubrication as the primary cause of grinder downtime.

Phase 3: Exploit the Constraint by Improving the Process
In this phase the project team identifies specific actions to remove root causes.  The product blades have a drive and coast side.  Based on operator input and observation, the team found that most of the cutting coolant was deflected when cutting the coast sides of the product.   The cutter blades became dull decreasing their life and the number of defects produced.   The solution involved:
1. Acquiring a muffler pipe that distributed an equal flow of coolant to both sides of the cutting operation.
2. Insure that filters were changed on a timely basis.
These changes increased the shelf life and yield of the blades, and the blades no longer needed to be re-ground.   The result was reduced cutter downtime and improved quality.

The primary performance measure was the CSI index or the ratio between the number of products produced that meet customer specifications and peak capacity.  It improved from 65% to more than 80%.

Phase 4: Subordinate the Systems to Sustain the Improvement
The purpose of this phase is to monitor the process to insure that the improvements are sustained.  The following figure shows an X-bar control chart of the CSI before and after the improvements were implemented.


Phase 5: Elevate the Constraints
The first four phases significantly improved the cutting process.   That result eliminated the need to further elevate the constraints further by methods such as purchasing additional cutting capacity.  If the benefits of additional throughput would exceed the cost of additional capacity, the constraints would be elevated.

Phase 6: Check for the Next Constraints
The cutting process improvement was completed in March 2003.   The axle production system was monitored, and the cutting process was no longer the bottleneck.   The monitoring also looked new constraints to determine if they would justify a new improvement project.

The next post will present the conclusions from this case study and the use of this version of an integrated Six Sigma and Theory of Constraints process improvement approach.

1. Ehie, Ike and Chwen Sheu (2005). "Integrating Six Sigma and Theory of Constraints for Continuous Improvement: A Case Study" Journal of Manufacturing Technology Management 16(5): 542-553.

Ehie and Sheu (2005) describe an application of their integrated framework for Six Sigma (SS) and the Theory of Constraints (TOC) by a company supplying vehicular components to automotive manufacturers.  The company has an Axle facility manufacturing axle products and related components.  The Axle facility formed a team with the goal of improving their production process to achieve savings of at least $175,000 per year.   The team decided to select a project that improved overall axle quality and system throughput.   The company had success in using SS, and they attended a few TOC seminars.  The project description is organized using the phases in the Ehie and Sheu framework presented in the previous posting.

Phase 1.  Identify the System Constraint

The team reviewed process maps to identify potential bottlenecks, conducted interviews and did in-depth process observations.  The figure gives an overview of the process flow.  The cutting process was identified as the primary bottleneck operation.   The cutting operation had large piles of inventory waiting to be cut.   Also, the following operation, lapping, was continually starved for work.  

Focusing on the bottleneck, the team considered purchasing additional cutting capacity.  The existing cutter used a solvent-cutting device where the cutting head was lubricated to increase cutting blade shelf life.   Newer machines used dry cutting which increased blade life and thus increasing capacity.   Because of capital constraints, the team focused on increasing quality and throughput without additional capital expenditures.

Phase 2.  Measure Current Performance and Identify Root Cause

The team created a Customer Specification Index (CSI) to measure the cutting operation output performance.  The CSI is the ratio between the number of products produced that meet customer specifications and peak capacity.   Peak capacity is the maximum output rate the operation can achieve under ideal conditions.  Over a two month period, the CSI was 65%.   The company wanted to achieve 80% which they felt was a standard for "world-class" performance. 

The team focused on the causes of poor CSI performance.   They did a Pareto Analysis of cutting machine downtime.  They discovered that the cutter grinder caused 40% of the cutting machines downtime.   They interviewed operators about the causes of cutter grinders causing cutting machine downtime.   The operators stated that the lack of proper lubrication on the cutter blades caused cutting heads to not achieve their maximum life.   When dull blades were removed for sharpening, the cutter grinders became idle.   Also, dull blades contributed to defects such as rough finish.   The team concluded that the root cause of poor CSI was blade inefficiency. 

The next posting will present the results of improving the process by exploiting the constraint.  Note that SS provided the tool, i.e., Pareto Analysis, for identifying the root cause limiting productivity and quality.

References
1. Ehie, Ike and Chwen Sheu (2005). "Integrating Six Sigma and Theory of Constraints for Continuous Improvement: A Case Study" Journal of Manufacturing Technology Management 16(5): 542-553.

Ehie and Sheu (2005) describe an approach to Continuous Improvement (CI) using an integration  of the Theory of Constraints (TOC) and Six Sigma (SS).   This posting summarizes that approach to CI.   The next posting presents an application  of their approach to improve the performance of a manufacturing system.   The TOC serves as a framework for their CI approach.  The integrated framework has six phases.  They are shown in the following table.   Five of the phases have names corresponding to the five steps outlined in the posting outlining the steps for applying the TOC. The second phase, Measure current performance and identify root cause, involves the SS Measure and Analyze phases.   SS provides statistical tools and engineering techniques used in the integrated CI framework.  

Integrated TOC & SS Framework

Phase	Purpose	Relation to TOC and SS
1	Identify the constraint and determine the process to be improved	TOC step 1 SS Define phase
2	Measure current performance and identify root cause	SS Measure and Analyze phases TOC step 2
3	Exploit the constraint by improving the process	TOC step 2 SS Improve phase Use SS statistical and engineering techniques
4	Subordinate the systems to sustain the improvement	TOC step 3 SS Control phase
5	Elevate the constraints	TOC step 4 SS Improve phase*
6	Check for next constraints	TOC step 5 SS Define phase*

* Not mentioned by Ehie and Sheu (2005)

The principal objective of the framework in the table is to remove a constraint or constraints limiting system performance.   This is consistent with the TOC.   In SS, the Define phase specifies a system performance objective or objectives and reduces its (their) variation.

This posting continues the description of an application of the Theory of Constraints to improve the capacity of the 366th Medical Group, an Air Force unit providing inpatient and outpatient services.  Physicians, dentists and nurses are providers.    This posting addresses the Patient-Provider Encounter process.   The team expected the availability of providers are the principal constraint effecting throughput since the providers are the most expensive resource.  

Step 1.  Identify the System Constraint
The team discovered that the availability of medical technician support was the constraint.   Flowcharts of the process flow showed multiple decision points asking whether everything was ready for the next step.  If everything was ready, the next step was implemented.   If not, the next step became "Find a medical technician".  If one was not available, the providers had to perform tasks normally done by medical technicians.

Step 2.  Improve or Exploit Its Capability
The team tried to find tasks that could be removed from the technician work load so that providers could have uninterrupted technician support.   The team found that few tasks could be removed from the technician work load.  

Step 3. Subordinate Other Links to the Constraint
The team reversed their emphasis by adjusting the schedule for providers.   If a technician was unavailable to support a provider, the provider switched to other necessary tasks such as completing records.   This approach had limited success.

Step 4. Strengthen the weak link or elevate it.
To significantly improve capacity, the team concluded that they had to elevate the constraint and add technicians.   Each provider had a dedicated medical technician.   The ratio of technicians to providers went from one-to-six to one-to-one.   As a result, the providers only performed tasks which required a provider.   They no longer performed tasks which a technician could do.   Routine appointments used to last 20 minutes with only 12 minutes spent with the patient.   After the change, many appointments lasted 15 minutes with no drop in time with the patients.  Implementation of the changes started in December.   The figure shows the dramatic reduction in waiting times for a routine appointment.   The objective was to schedule all routine appointments no more than seven days after a request.

Potential Application of Statistical Thinking or Statistical Engineering

The figure indicates a higher average waiting time in July which is slightly larger than the standard.   Is this result statistically significant?   Is there a special cause acting to give the larger result?   If so, does the special cause result in another constraint?

Womack and Flowers (1999) present a case study involving the application of the Theory of Constraints (TOC) to improve throughput at the 366th Medical Group, an Air Force unit located in Idaho that provided inpatient and outpatient services.   The patients involved were guaranteed access within specified time limits: 24 hours for acute appointments, seven days for routine appointments, and four weeks for health maintenance exams, i.e., HME appointments.    The medical group was failing to meet the routine appointment time limit, and the ease of obtaining an appointment was the primary customer satisfaction complaint.   Wait times for routine appointments had been as high as 24 days.  Wait times for the acute and HME appointments were almost always less than the relevant standards. The medical group formed a team with the mission of increasing available appointments and providing care to more individuals without increasing costs. The team received instruction in the TOC.

The team flowcharted key processes and identified the constraint in each process.    The Scheduling Process and the Patient-Provider Encounter Process  had important constraints.  

Scheduling Process

Step 1.  Identify the System Constraint
The availability of routine appointments was the constraint.   The schedules were managed as if the proportions of appointments in each category (acute, routine and HME) were constant.   That is, the scheduler used a template where the availability in each time period for each appointment type was governed by the expected average number of appointments.  This affected routine appointments more than the other two categories.

Step 2. Improve or Exploit Its Capability
Patients perceived difficulty in getting routine appointments.   This perception resulted in a high no-show rate for routine appointments.   The team designed interventions to decrease the no-show rate.

Step 3. Subordinate Other Links to the Constraint
An Appointment Manager was designated and given the responsibility to adjust proportions of appointments dedicated to the three appointment categories on a daily basis.   Womack and Flowers (1999) stated that "Idle, nonconstraint time dedicated to acute and HME appointments was switched to routine appointment time."   This only took about 15 minutes per day.   Not only did this help to alleviate the routine appointment constraint but it prevented creating another constraint for the other appointment types.

Step 4. Strengthen the weak link or elevate it.
With the current level of available patients, steps 1, 2 and 3 prevented available routine appointments from being a constraint.

Step 5. Repeat the Improvement Process
The team had the objective of providing care to increased numbers of patients.   That objective motivated the team to examine the constraints in the Patient-Provider Encounter Process.   The next posting will address that process.

Potential Application of Statistical Thinking and Engineering

Womack and Flowers do not describe any statistical analysis of patient demand data.   The team may have done that to help the Appointment Manager and create an improved template and to assist appointment schedulers.  Clearly, the demand process for appointments could be analyzed.   What about categorizing routine and HME appointments into subcategories to more accurately predict time requirements?   Does the patient demand vary with time?

References
1. Womack, D. E. and S. Flowers (1999). "Improving System Performance: A Case Study in the Application of the Theory of Constraints." Journal of Healthcare Management 44(5): 397-407.

Dettmer (1997) views the Theory of Constraints (TOC) as a System Improvement Strategy.    This system viewpoint is the reason why Goldratt chose the term constraint rather than bottleneck.   Goldratt (1997) on page 139 defines a bottleneck as any resource whose capacity is equal to or less than the demand placed on it.   On page 301, Goldratt addresses the potential of a material release system and marketing as limiting system performance.  To do that he recommends the use of the more general term constraint rather than bottleneck.  In a manufacturing process, the machine station that is the most overloaded might be the weakest link, and places a constraint on the throughput of the entire process.  In a hospital, nurses of a particular specialty might be a weak link causing long waiting times and be a system constraint.   They are also bottlenecks.

Goldratt specifies five steps to improving system performance using the TOC.   They are:
1. Identify the weak link or constraint.  A machine with capacity less than the plant output rate objective.
2. Improve or exploit its capability.  Operate the machine during lunch breaks.    Eliminate defective machine output.
3. Subordinate other links to the constraint.  Synchronize the output rate of upstream machines with the output rate of the constraint    machine to avoid unnecessary work-in-process.
4. Strengthen the weak link or elevate it.  Install a faster machine or multiple machines.
5. Repeat the improvement process. Once the weak link is strengthened, another weak link likely becomes the new constraint.  That new   constraint may no longer be the production process.  It might be in marketing so the next step will be to strengthen marketing.
2. Goldratt, Eliyahu and Cox, Jeff (1992). The Goal: A Process of Ongoing Improvement, Second Revised Edition, Great Barrington, MA, North River Press, Inc.

The posting on June 27, 2011 introduces Statistical Engineering, and the article by Anderson-Cook et al (2012) discusses the definition of Statistical Engineering proposed by Hoerl and Snee (2010).  That is, the study of how to use known statistical principles and tools to solve high-impact problems for the benefit of mankind.   The posting on June 27 gives two examples of Statistical Engineering.  They are Lean Six Sigma (LSS) and the Hoerl-Snee process improvement strategy discussed at length in this blog starting with the posting of March 18, 2008.    The Theory of Constraints (TOC) is another example of Statistical Engineering, and this is mentioned by the author of this blog in the article by Anderson-Cook et al (2012). 

Dettmer (1997) distinguishes between Goldratt's Theory of Constraints (TOC) and a Process Improvement Strategy.   He states that the TOC is a System Improvement Philosophy rather than a Process Improvement strategy.  Goldratt's viewpoint is that organizations achieve their goals as systems not as processes.   The interaction among component processes determines how well the system performs.    Goldratt views the system as a chain or a network of chains.   The network of chains has a weakest link that limits system performance.    The weakest link is the system constraint.  One has to improve the weakest link or constraint in order to improve the system.  On page 8, Stein (1997) states the following important principle employed by the TOC.  "In any chain of events there can only be one weakest link, and if improvement is to occur only the weakest link needs to be strengthened."

Stein (1997) specifies that the first step in applying the Theory of Constraints is to select a method of measurement for system performance.  This measurement method must be agreeable to management and all involved parties.   A measurement commonly used in TOC publications is Throughput.   One example given by Stein for throughput is the rate at which the system generates money through sales.  Creasy (2009) calls this performance measurement the Capstone Metric.

Why connect TOC with Statistical Engineering?   Creasy (2009) and Nave (2002) recommend using the Theory of Constraints (TOC) with LSS to generate more effective system improvements.   Also, Stein states on page 9: "Not only the physical resources but also the individual functions of a corporation are subject to the laws governing probability and statistical fluctuation."

References
1. Anderson-Cook, C.M., Lu, L., Clark, G., DeHart, S.P., Hoerl, R., Jones, B., MacKay, R.J., Montgomery, D.C., Parker, P.A., Simpson, J., Snee, R., Steiner, S., Van Mullekom, J., Vining, G.G., Wilson, A.G.  (2012). “Statistical Engineering – Forming the Foundations”, Quality Engineering, 24(2), pages 110-132.
2. Creasy, T. (2009) "Pyramid Power", Quality Progress 42(6): 40-45.
3. Dettmer, H. William (1997). Goldratt's Theory of Constraints: A Systems Approach to Continuous Improvement, ASQC Quality Press, Milwaukee, Wisconsin.
4. Nave, D. (2002). "How to Compare Six Sigma, Lean and the Theory of Constraint." Quality Progress 35(3): 73-78.
5. Stein, R. E. (1997) The Theory of Constraints: Second Edition. New York, Marcel Dekker, Inc.

Hello,

My company performs cross-team internal audits, between our global mfg. sites.

I am seeking out scoring mediums used to produce an ISO 9001:2008 (QMS) Maturity report; such as by using a Radar chart.

Could you help to provide direction to what you have found to be the most effective scoring technique/check list/self-assessment?

Thank you!
Jesse Kryger

Gordon Clark,

A couple of thoughts:

Objectives are simply what the user of the technology wants to improve – coupled with the explicit parameters he/she does not want to sacrifice (constraints). 

I liked your continuing blog assuring that ‘statistical engineering’ is more than a study, but something to ‘use’.  Perhaps we can talk about ‘applied statistical engineering’ and some of its toolsets.

I would like to propose as one example ‘sequential empirical optimization (SEO)’.  SEO is used for maximizing performance of a system by making the best quantitative adjustment decisions when evidence of the outcomes of decisions is obtained sequentially – and which can be dynamic as important uncontrolled inputs (conditions) change.  Of course, this technology is more than statistics, and it fits your “with other relevant tools”.  BTW, I see this from the point of view of an industrial engineer. 

Please see www.ultramax.com, including examples, and technical details in http://www.ultramax.com/downloadlogin.asp > Blue Book.  

Kindly let me know whether this fits well with your intellectual position. 

Carlos
Carlos.moreno@ultramax.com

Using the definition of Statistical Engineering proposed in the previous posting, the following figure illustrates the use of statistical engineering in a project. That figure will appear in Anderson-Cook et al (2012).   Note the feedback loop between statistical engineering methods and operational methods, i.e., statistical and non-statistical methods and tools.  Results generated by the operational methods are evaluated by the statistical engineering methods.   The evaluation may determine that the project objectives have been achieved or generate new instructions for the operational methods.  



References
1. Anderson-Cook, C.M., Lu, L., Clark, G., DeHart, S.P., Hoerl, R., Jones, B., MacKay, R.J., Montgomery, D.C., Parker, P.A., Simpson, J., Snee, R., Steiner, S., Van Mullekom, J., Vining, G.G., Wilson, A.G.  (2012) “Statistical Engineering – Forming the Foundations” Quality Engineering (in press)

The posting on June 27 introduces the Statistical Engineering paradigm.   The posting quotes Hoerl and Snee (2010) defining Statistical Engineering as "as the study of how to best use statistical concepts, methods and tools, and integrate them with IT and other relevant sciences to generate improved results.”  The improved results are with respect to the concepts of Statistical Thinking.   That means understanding and reducing variation.   Hoerl and Snee (2010) do not refer to objectives other than reducing variation.    In the article by Anderson-Cook et al (2012), a panel addresses the definition of Statistical Engineering.

As a panelist,  I address the question: " What are improved results?  We need project objectives in order to evaluate results.  Successful implementation of statistical engineering will highlight the criteria for improved results.   Johnson (2009) reviewed the results of a survey polling nearly 200 Six Sigma practitioners to determine the primary reasons Six Sigma projects fail.  The two top reasons were the lack of management support and project goals were not linked to finances.   Having explicit project objectives and criteria for improved results will help gain management support.
  
Snee and Hoerl (2007) point out that improvement methods need an ultimate objective in order to succeed.  Consider Lean Six Sigma (LSS).  From a Lean viewpoint the ultimate objective would emphasize reducing waste and cycle time.  Activities that do not contribute to customer value are wasteful.  Reducing waste, e.g., reducing excessive work-in-process and customer wait time, can force quality improvement.  From the Six Sigma viewpoint the ultimate objective would emphasize reducing variation.  Excessive variation can degrade quality and increase cost.   So both the Lean and Six Sigma view points can lead to improved quality and reduced cost.   For a LSS project, Snee and Hoerl (2007) recommend a holistic approach where the ultimate objective includes both the Lean and Six Sigma viewpoints.   The statistical engineering methodology used to achieve the ultimate objective would be an integrated approach with respect to the Lean and Six Sigma viewpoints.

The first step in a LSS project is to define the project objectives in a more detailed manner than just reducing waste and variation.    Those objectives must be meaningful to management.   Consider two example LSS projects.  One is developing a new production line and the other is reducing the patient wait times in a hospital emergency department.   What are the specific conditions where the production and the emergency room will be operated?   What are the constraints under which these systems will be operated?   For example, the costs of adding new machines or doctors may limit other options.   Reducing waste and variation may be conflicting objectives where some alternatives reducing one may increase the other.    
 
In the article, I propose the following definition for statistical engineering.   Statistical engineering is the study of how to best use statistical concepts, methods and tools along with other relevant tools to generate improved results with respect to reducing variation and other system objectives.
       

References
1. Hoerl, R. W. and R. D. Snee (2010). "Statistics Roundtable: Closing the Gap." Quality Progress 43(5): 52-53.
2. Snee, R. D. and R. W. Hoerl (2007). "Integrating Lean and Six Sigma - A Holistic Approach." Six Sigma Forum Magazine 6(3): 15-21.
3. Anderson-Cook, C.M., Lu, L., Clark, G., DeHart, S.P., Hoerl, R., Jones, B., MacKay, R.J., Montgomery, D.C., Parker, P.A., Simpson, J., Snee, R., Steiner, S., Van Mullekom, J., Vining, G.G., Wilson, A.G.  (2012) “Statistical Engineering – Forming the Foundations” Quality Engineering (in press)

Hoerl and Snee (2010) propose a general paradigm for linking statistical thinking with statistical methods and tools to improve quality.   They call this paradigm statistical engineering.   They define statistical engineering “as the study of how to best use statistical concepts, methods and tools, and integrate them with IT and other relevant sciences to generate improved results.”   The following figure, taken from Hoerl and Snee (2010), depicts the relationship among statistical thinking, statistical engineering, and statistical methods and tools.  .   Statistical thinking is a philosophy of learning and action, and The History of Statistical-Thinking Definition posting specifies its fundamental principles.   They are:
1. All work occurs in a system of interconnected processes.
2. Variation exists in all processes.
3. Understanding and reducing variation are keys to success.

The Hoerl-Snee Process Improvement Strategy is an example of statistical engineering.  Postings in this blog describes it in detail.  The process improvement strategy tells us how to use, integrate and deploy methodologies and tools to perform statistical thinking and improve system performance.  These methodologies and tools include but are not limited to statistical methods and tools.  

Hoerl and Snee (2010) cite Lean Six Sigma (LSS) as an example of statistical engineering.   LSS using the DMAIC and lean process improvement strategies.   

Two features of the Hoerl-Snee Process Improvement Strategy that differ from LSS are:

• Improvement occurs in iterative sequential steps similar to Plan-Do-Check-Act (PDCA) approach.
• One of the first steps is to remove special-cause sources of variation.
Stauffer (2008) recommends that the DMAIC process improvement strategy be modified to remove special-causes in the Define phase.


References
1. Hoerl, R. W. and R. D. Snee (2010). "Statistics Roundtable: Closing the Gap." Quality Progress 43(5): 52-53.
2. Stauffer, R. (2008). "A DMAIC Makeover." Quality Progress 41(12): 54-59.

I will present a webinar this April 14 at 3 pm EDT on the topic of Continual Improvement Using Simulation and Lean Six Sigma. Register for the webinar by visiting https://www1.gotomeeting.com/register/851692968.

The blog posting on January 20 mentions the lack of emphasis on simulation in Six Sigma and by ASQ. Simulation, Six Sigma, Lean and Statistical Thinking all view the system as a process. When refer to simulation, we mean Discrete-Event Simulation (DES). By DES, we mean that the system changes state at discrete points in time. The simulation is a model of the system. We can analyze the model implementing designed experiments with much less cost than we can with the real system. DES models are used to improve performance in systems such as manufacturing, healthcare, computer-communications, transportation, and call centers. Why not use simulation in Six Sigma and Lean Six Sigma? Case Studies will illustrate the use and benefit of simulation in Lean Six Sigma. The DMAIC process aides the development of simulation models, and simulation improves the effectiveness of the DMAIC process.

Hello,

Can I know how to justify a reason whether to use the SPC Xbar-R chart subgroup size 5 instead of 3 statistically?

Thank you.