Profound Implications of Minimum Variance Control

Author:  Pradeep B. Deshpande

Professor Emeritus of Chemical Engineering, University of Louisville, Visiting Professor of Management, Gatton College of Business & Economics, University of Kentucky, and President and CEO, Six Sigma and Advanced Controls, Inc.,

In control engineering, minimum variance refers to the state where the output of interest is influenced solely by uncontrollable/unknown random causes. In such a state the output response exhibits a zero mean in the deviation sense meaning that the response is at the desired steady state on average and its variance is constant with time. The control technology to achieve this state is Minimum Variance Control (MVC). MVC is a theoretical standard, better control cannot be achieved with any control law. Attempt to achieve minimum variance is fraught with problems. The control system becomes extremely sensitive to modeling errors, stability becomes a serious issue, and the cost of control escalates.

The various control laws in use today are all designed to keep the control system a safe distance away from the theoretical standard delivering a good compromise between stability, quality of dynamic response, and the cost of control. One among them is the process industry-standard Constrained Model Predictive Control (CMPC) strategy. A block diagram of the MVC scheme drawn in the form of an Internal Model Control (IMC) structure is depicted in Figure 1.

Figure 1. Minimum Variance Control for Servo Applications

The IMC structure is entirely consistent with the traditional feedback control structure control engineers are familiar with it. There are many textbooks on control and optimization of dynamic processes, one by the author is listed under Further Reading at the end of the chapter (Deshpande and Tantalean, 2015).

These ideas carry over to all repetitive human activities. The outcomes of interest in these processes too are influenced by uncontrollable/unknown random causes which statisticians refer to as common causes (unmeasurable disturbances in control jargon), measurement errors (accuracy, stability, linearity, repeatability, and reproducibility issues), and nonrandom causes that can be discovered (manipulated variables in control jargon).

The goal here is to minimize measurement errors and identify the discoverable nonrandom causes (assignable causes) with a disciplined, data-driven methodology and set them at the optimal values so that the outcome moves towards the natural state where it is influenced solely by common causes. Mikel Harry and the Late Bill Smith developed a five-phase, eleven-step methodology at Motorola in the late seventies and early eighties to return the outcomes of repetitive static manufacturing and transactions processes to their natural state and called it six sigma. By now over 40% of US corporations and a large number of corporations overseas have embraced six sigma programs for improving quality, reducing costs, and optimizing cycle times.

These objectives are not unfamiliar to control engineers. Transactional processes are abundant in manufacturing companies too where control engineers work. A great opportunity for control engineers is to examine all the transactional processes at work to assess if they are in the state of minimum variance. Figure 2 diagrammatically illustrates these ideas.

Figure 2Figure 2. Returning the Outcome to its Natural State

The diagram [Figure 2] applies to both static manufacturing and transactional applications. In process industries, the technology to achieve the desired state safely close to minimum variance is constrained model predictive control while in static manufacturing and transactional applications it is six sigma.

Six sigma and constrained model predictive control strategies are for achieving close to perfection in manufacturing and repetitive human processes. They constitute what the author refers to as the Scientific Framework for External Excellence. For several decades the author has been working on what he is referring to as the Scientific Framework for the Excellence of the Internal. If internal excellence had no bearing on external excellence, then this article has no place in control engineering literature and control professionals should have no interest in it.

Each of the 6 ½ billion of us humans have three components of the mindset S, R, and T that defines who we are. The two emotions, positive emotions and negative emotions, are in turn related to the three components. Positive emotions strongly and positively correlate with the S component while negative emotions strongly and positively correlate with the R and T components. The specific proportion of these components determines the level of internal excellence of an individual. These ideas are depicted in Figure 3.

Figure 3Figure 3. Level of Internal Excellence Explained

The noble ones among us are towards the top of the scale while the wicked ones are towards the bottom and the rest of us somewhere in between. So, how does one know where an individual is on the scale of internal excellence? If an individual possesses the capacity to remain centered in the face of the most challenging situations that are part of life, then he or she is doing well. If on the other hand, the internal condition goes haywire and remains disturbed for a long time, then that is not good.

For example, if you stub your toe, or if someone cuts into your lane nearly causing an accident, what is your instant (reflux) reaction? If it is strong negative emotion that lingers on, then there is much progress to make. The lifelong objective of every individual should be to rise on this scale of internal excellence. The level of internal excellence is not static. It varies with time and the lower the level of internal excellence, the bigger the fluctuations. In the seminars the author has presented in several countries, no one has raised their hand wanting to go in the downward direction.

The link between external excellence and internal excellence is this. In the absence of an adequate level of internal excellence, external excellence programs such as six sigma or any other quality initiative will give suboptimal results. In other words, the state of minimum variance in Figure 2 is really not the true minimum variance state meaning that further improvement in performance is possible through internal excellence.  Figure 4 illustrates these ideas.

Figure 4Figure 4. Internal Excellence Boosts Performance

The precise mechanics of how rising levels on internal excellence improves performance is not well understood. It is easier to see this working in transactional applications but the reader could ask a perfectly reasonable question: How can rising levels of internal excellence possibly improve performance in a manufacturing environment? The answer is, the folks in manufacturing work for say eight hours day and how they lead their lives for the remainder of their 24-hour day has a bearing on their performance at work. It is possible to verify these claims with a six sigma project. The author has recently published a book on the scientific framework for internal excellence with a theoretical physicist turned medical doctor (Deshpande and Kowall, 2015).

There are two approaches to raising the level of internal excellence, a conscious approach and meditation which materializes the desired changes autonomically. Again, the mechanics of how exactly meditation brings about the positive changes in ourselves is not well understood although scientists have made progress in recent years.

Several US corporations have shown that embracing internal excellence programs delivers exemplary business performance (Cava, 2015, Gelles, 2015, Pinsker, 2015). Additionally, prestigious science publications such as Nature, Science, Proc. National Academy of Sciences-US, etc., (Adami, 2013, Condon, 2013, Bhasin, et al., 2013, Blackburn, 2012, Epel, et, al., 2004, Hagelin, 1999, Lutz, et al, 2004, Orme-Johnson, 1998, Wallace, 1970), business publications such as Forbes (Boyers, 2013), Time (Urist, 2014), and New York Times (Gelles, 2015), and medical publications such as JAMA (Goyal, 2014, Paul-Labrador, et al., 2006) and Neurology Now (Paturel 2012) have carried full-length articles on meditation and its benefits ranging from improvements in health and wellness, to exemplary performance, to better leadership decisions and interpersonal relationships, to less discord and violence.

Figure 5 [see below] depicts meditation as an IMC strategy. The controlled variable in Figure 5 must be measurable and reflect the autonomic state inaccessible to conscious adjustment. Some measurements which meet these constraints are heart rate and heart rate variability, respiration rate, and Gamma waves in the brain. Control engineers may find the control system rather strange in that the process and the controller are one and the same. This dilemma had led Max Planck to remark, ‘This problem is difficult because we are a part of the problem we are trying to solve’.

Figure 5Figure 5. Meditation in IMC Structure

Figure 6 [see below] depicts the heart rate variability of a subject under the influence of negative emotions (top) and positive emotions (bottom). If the controlled variable in Figure 5 is taken to be HRV then the target is to move towards positive emotional state as in the lower figure in Figure 6.

Figure 6Figure 6. Influence of Positive and Negative Emotionson Heart Rate Variability (Source, IHM (McCraty, 2001)

As additional evidence, Elizabeth Blackburn has shown that high levels of stress cause the length of our telomeres to dwindle and the telomerase enzyme levels in the cells to fall leading to accelerated aging. For this work she received the Nobel Prize in Physiology and Medicine in 2009. Cardiologists know well that negative emotions are a huge contributing factor for high levels of stress and AMA says that stress is a major contributing factor for 80% of all diseases. Blackburn has also shown that more than diet, exercises, and family support, meditation is the most effective intervention for restoring the length of telomeres potentially slowing aging (Blackburn, 2012, Epel, et al., 2004).

Finally, minimum variance can play a critical role to make this a better and more peaceful world. Take a group of people gathered in a hall for example. If these folks are hooked up to monitors, it will be found that their heart rates are varying. If these individuals were to begin a collective activity such as meditation, chanting, or prayer, their heart rates will be seen to synchronize in short order. Not only that, if the size of the group is sufficiently large, then the group activity has a positive influence on the people who are not even participating. This is what renowned quantum physicist and three-time presidential nominee, John Hagelin showed in 1993. He conducted an auditable experiment involving 4,000 participants meditating over eight weeks showing that the crime rate in the entire Washington DC area came down significantly. These claims too can be verified again with additional experimentation.

Swedish medical researchers have provided additional evidence (Vickhoff, et al., 2013). Figure 7 [see below] depicts the heart rate variability, heart rates, and respiration rates of five participants who were singing choir music, humming, or chanting a mantra. The HRV of participants is seen to increase during the practices while the respiration rates and heart rates of participants may be seen to be synchronizing. In other words, the variation of the variance of heart rates and respiration rates has diminished.

Figure 7

Figure 7. HRV of 5 Participants (Left) increased and their Heart Rates and Respirations Rates (Right) Synchronize

The YouTube video at the link listed under Further Reading provides additional visual information.


Control engineering and six sigma are systemic approaches meaning that they are based solely on the analysis of input-output data. Fundamental approaches to problem solving should always be preferred but when sufficiently detailed knowledge of the system under scrutiny is unavailable, systemic approaches are used. Such is the case with modern manufacturing and transactional processes. It is also the case with human systems.

Control engineers and six sigma professionals are best equipped to understand the concepts presented in this paper and take advantage of them. They understand that uncontrollable/unknown causes introduce an unexplained variation in the outcomes of all processes. Science on the other hand demands that the results of every experiment are repeatable and reproducible no matter who does the experiment, where, when, or how many times and that is the way it should be. Each of the 6 ½ billion of us is a multivariable, nonlinear, self-regulated, and evolving (meaning that we will never be what we are today) entity with a unique common cause variability that we inherit from our ancestors and how we live from birth to the present age. Therefore, experiments involving internal excellence produce outcomes that have inherent variability. Nikola Tesla is reported to have remarked, The day science begins to study non-physical phenomena, it will make more progress in one decade than in all the previous centuries of its existence. What is required for progress is an openness of mind and a willingness try new and nontraditional approaches.

Eminent scientists and world leaders have issued a warning urging people across the world that there is an urgent need for change if the human race is to survive and thrive (Deshpande, online blog, 2015). The framework for internal and external excellence is the pathway to meet this challenge.


The author thanks Vasant B. Waikar, Professor Emeritus of Statistics, Miami University for his review and comments on the article. Upon seeing the diagram, Figure 4, Mikel Harry, Co-Creator of Six Sigma, National Best Selling Author, and Consultant to the World’s Top Executives remarked, Pradeep – Very, very basic and to the point. Technically correct.  I assume the graphic is associated with a larger body of information.  Nonetheless, standing on its own merits, it’s a nice description that virtually everyone can understand.  Great work and I love your thorough documentation of the underpinning sources of information – very professional. The author also thanks his former doctoral scholars who have taken the time to review and comment on the article. The author always thanks his Guruji Gurumahan Paranjothiar for his blessings and inspiration.

To Conclude

A new perspective on the importance of minimum variance control has been presented. No matter what the process is, static or dynamic, linear or nonlinear, manufacturing or transactional or it involves a group of individuals, a technology around the notion of minimum variance can be configured which can take the system toward perfection. These concepts present a unique opportunity to control engineers to improve their health & wellness, performance in all walks of life, and make them better leaders and human beings. They also present corporate leaders with a new opportunity to improve their corporate performance. Taken together the scientific framework for external and internal excellence can make this a better and more peaceful world.

Further Reading

Scientific Framework of External Excellence

  • Deshpande, Pradeep B. and Tantalean, Roberto Z., Process Control and Optimization, Six Sigma and Advanced Controls, Inc., August 2015 (will be available on amazon).
  • Deshpande, P. B., Six Sigma for Karma Capitalism, Six Sigma and Advanced Controls, Inc., 2015 (Available on amazon).
  • Harry, J. Mikel and Lawson, J. R., Six Sigma Productivity Analysis and Process Characterization, Motorola Press, 1992.

Scientific Framework of Internal Excellence

  • Deshpande, Pradeep B. and Kowall, James P., The Nature of Ultimate Reality and How it can Transform our World: Evidence from Modern Physics; Wisdom of YODA, Six Sigma and Advanced Controls, Inc., January 2015 (Available from amazon).
  • Deshpande, P., Audacity of Tolerance, Online Blog (, 2015.
  • Kulkarni, B. D. and Deshpande, P. B., Brahma Uncertainty Principle, Journal of Consciousness Explorations and Research 3, 2, February 2012.

Science of the Heart

  • McCraty, R., Atkinson, M., and Tomasino, D., Science of the Heart, HeartMath Research Center, Publication No. 01-001, Institute for HeartMath, Boulder Creek, CA 2001.
  • Vickhoff, Bjorn, et al., Music Structure Determines Heart Rate Variability of Singers, Frontiers, July 14, 2013.
  • Vickhoff, Bjorn, et a., YouTube Video, Music Synchronizes Heart Rates, University of Gothenburg, Sweden, 2013

Meditation in Science Publications

  • Adami, C. and Hintze, A., Selfish Traits Not Supported by Evolution, Nature Communications, August 1, 2013.
  • Bhasin, Manoj K., et al., Relaxation Response Induces Temporal Trasncriptome Changes in Energy Metabolism, Insulin Secretion, and Inflammatory Pathways, PLOS One, 8, 5, May 2013. pp. 1 – 13.
  • Blackburn, Elizabeth and Epel, Elissa, Telomere and Adversity – Too Toxic to Ignore, Nature, 490, 11 October 2012 pp. 169-171.
  • Condon, Paul, et al., Meditation Increases Compassionate Responses to Suffering, Psychological Science Online First, August 21, 2013. (Also see, DeSteno, David, The Morality of Meditation, Op Ed Column, NY Times, July 5, 2013.
  • Epel, Elissa, et al., Accelerated Telomere Shortening in Response to Life Stress, Proceedings of the National Academy of Sciences, 101, 49, December 2004. pp. 17312-17315.
  • Hagelin, John S., et al., Effects of Group Practice of the Transcendental Meditation Program on Preventing Violent Crime in Washington, DC: Results of the National Demonstration Project, June-July 1993, Social Indicators Research, 47, 2, 153-201, 1999.
  • Lutz, Antoine, et al., Long-Term Meditators self-induce high amplitude Gamma-Wave Synchrony during Mental Practice, Proc. Nat. Acad. Sciences, Nov. 16, 2004.
  • Orme-Johnson, David W., et al., The Effects of the Maharishi Technology of the United Field, Journal of Conflict Resolution, 32, 4, 1988.
  • Wallace, R. K., Physiological Effects of Transcendental Meditation, Science, Vol. 167, No. 3926, 1970.

Sampling of Meditation Articles in Medical Journals and Popular Media

Internal Excellence Programs Boosts Business Performance

  • Cava, Marco della, Benioff: USA Needs Compassionate Capitalism, USA Today, April 4, 2015
  • Gelles, David, At Aetna, a CEO’s Management by Mantra, The International New York Times, 27 February 2015.
  • Pinsker, Joe, Corporations’ Newest Productivity Hack: Meditation, The Atlantic, March 10, 2015.

Business Publications on Meditation

  • Boyers, J., Why Empathy is the Force that Moves a Business Forward, Forbes, May 30, 2013.
  • Fryer, Bronwyn, The Rise of Compassionate Management (Finally), HBR Blog Network, September 18, 2013.


About Mikel Harry

Dr. Harry has been widely recognized in many of today's notable publications as the Co-Creator of Six Sigma and the world's leading authority within this field. His book entitled Six Sigma: The Breakthrough Management Strategy Revolutionizing the World’s Top Corporations has been on the best seller list of the Wall Street Journal, New York Times, Business Week, and He has been a consultant to many of the world’s top senior executives, such as Jack Welch, former CEO and Chairman of General Electric Corporation. Dr. Harry has also been a featured guest on popular television programs, such as the premier NBC show "Power Lunch." He is often quoted in newspapers like USA Today and interviewed by the media, such as The Economic Times. In addition, Dr. Harry has received many distinguished awards in recognition of his contributions to industry and society. At the present time, Dr. Harry is Chairman of the Six Sigma Management Institute and CEO of The Great Discovery, LLC.
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