Autonomy in a Social Setting:

I have always been interested in the idea of autonomy in a social setting. In today’s post, I am looking at autonomy in a social setting such as an organization, from a Cybernetics viewpoint. I will lean on the ideas of Heinz von Foerster, and Stafford Beer.

Von Foerster came up with the notion of first order and second order cybernetics. First order cybernetics is the study of observed systems, and second order cybernetics is the study of observing systems.  Von Foerster would say that ethics cannot be articulated. He was influenced by the writings of his family friend and distant relative, Ludwig Wittgenstein. All systems are descriptions of some phenomenon and require a describer. All systems are human systems. We cannot ignore the human condition that sets the background and foreground for the systems. Every description is rich with possibilities; however, we cannot ignore the fact that they are constructions of an observer or observers. We cannot stipulate that only our version is the right one, and that the others are incorrect. I may choose to draw a boundary here, whereas you may choose to draw a boundary there. I may choose to include these 10 things, whereas you may choose to include the 10 things and add 20 more things on top of that. Even if our systems may look the same on a sheet of paper with nice boxes and arrows (sometimes curved arrows), what those mean could be entirely different. Von Foerster’s view was that there is no “I”, without the other. He came up with the ethical imperative – I shall always act so as to increase the number of choices. To me, this is his urging to always consider the other co-constructors. We should act to increase the possibilities so that the common good prevails. In a social realm, ethics is always involved. As noted earlier, ethics cannot be articulated, instead it must be based on action. This is where von Foerster’s ethical imperative comes in.

Stafford Beer created the Viable System Model (VSM) as a means to diagnose and study a social structure such as an organization. As the name suggests, VSM is a model, and therefore does not claim to be the most accurate representation. A system such as an organization is said to be viable if it is able to maintain its identity and survive in its environment. In order to sustain, it must be able to manage complexity. In cybernetics terms, it must be able to deal with the variety thrown at it. Variety is the measure of complexity. A key idea in VSM is recursion. In order to stay viable, an organization must deal with variety at multiple levels. This means that at every possible level, there must be “sub”-systems that are also viable. The organization should contain viable systems within viable systems in order to stay viable. A common description that is often used to explain this is that of the Russian nested dolls. An organization has multiple levels of recursion, and at each level of recursion, we can depict that viable system using the same structure that we used to depict the larger viable system. I welcome the reader to explore these ideas.

In order to ensure viability, each viable system should have maximum autonomy. This ensures that the variety thrown at it from the environment can be dealt with. However, this autonomy cannot be absolute. There has to be maximum autonomy without compromising the identity of the larger viable system it is part of. The larger viable system has to have means to ensure this to ensure its viability. It needs to ensure maximum autonomy of the sub-systems while not compromising its own viability. This is the case at each recursion level. An example of the levels of recursion is shown below. This is taken from Project Cybersyn.

At the smallest level, we have the operator who themselves are viable systems, and at the largest level we have the whole nation. The same viability model applies at all levels of recursion. Each level has to have the maximum autonomy possible without compromising the viability of the larger viable systems. Each larger viable system has to allow maximum autonomy of the lower viable systems in order to stay viable.

One can see a common theme emerging – one of interdependence and having a common identity. In this realm, ethics cannot be articulated. We must act to increase the number of choices. If you are to remain in a social realm, then to maintain its viability one must always act in the name of the common good.

I will finish with some wise words from one of my favorite philosophers, Simone de Beauvoir:

 And it is not true that the recognition of the freedom of others limits my own freedom: to be free is not to have the power to do anything you like; it is to be able to surpass the given toward an open future; the existence of others as a freedom defines my situation and is even the condition of my own freedom.

Always keep on learning…

My last post was Ppk, Capability Index and Tolerance Interval Relation:

Ppk, Capability Index and Tolerance Interval Relation:

In today’s post, I am looking at the relationship between capability index (Cpk or Ppk) and Tolerance Intervals. The capability index is tied to the specification limits, and tying this to the tolerance interval allows us to utilize the confidence/reliability statement allowed by the tolerance interval calculation.

Consider the scenario below:

A quality engineer is tasked with assessing the capability of a sealing process. The requirement the engineer is used to is that the process capability index, Ppk, must be greater than or equal to 1.33. The engineer is used to using 30 as the sample size.

But what does this really tell us about the process? Is 1.33 expected to be the population parameter? If so, does testing 30 samples provide us with this information? The capability index calculated from 30 samples is only the statistic and not the parameter.

We can utilize the tolerance interval calculation approach here and calculate the one-sided k-factor for a sample size of 30. Let us assume that we want to find the tolerance interval that will cover 99.9% of the population with 95% confidence. NIST provides us a handy reference to calculate this and we can utilize an Excel spreadsheet to do this for us. We see that the one-sided k-factor calculated is 4.006.

The relationship between the required Ppk and the one-sided k-factor is as follows:

Ppk_required = k₁/3

Similarly for a bilateral specification, the relationship between the required Ppk and the two-sided k-factor is:

Ppk_required = k₂/3

In our example, the required Ppk is 1.34. In other words, if we utilize a sample size of 30 and show that the calculated Ppk is 1.34 or above, we can make the following statement:

With 95% confidence, at least 99.9% of the population is conforming to the specifications. In other words, with 95% confidence, we can claim at least 99.9% reliability.

This approach is also utilized for variable sampling plans. However, please do note that the bilateral specification also requires an additional condition to be met for variable sample plans.

I have attached a spreadsheet that allows the reader to perform these calculations easily. I welcome your thoughts. Please note that the spreadsheet is provided as-is with no guarantees.

Final words:

I will finish with the history of the process capability indices from a great article by Roope M. Turunen and Gregory H. Watson. ^[1]

The concept of process capability originated in the same Bell Labs group where Walter A. Shewhart developed SPC. Bonnie B. Small led the editing team for the Western Electric Statistical Quality Control Handbook, but the contributor of the process capability concept is not identified. The handbook proposes two methods by which to calculate process capability: first, “as a distribution having a certain center, shape and spread,” and second, “as a percentage outside some specified limit.” These methods were combined to create a ratio of observed variation relative to standard deviation, which is expressed as a percentage. The handbook does not call the ratio an index; this terminology was introduced by two Japanese quality specialists in their 1956 conference paper delivered to the Japanese Society for Quality Control (JSQC). M. Kato and T. Otsu modified Bell Labs’ use of percentage and converted it to an index, and proposed using that as a Cp index to measure machine process capability. Subsequently, in a 1967 JSQC conference paper, T. Ishiyama proposed Cpb as a measurement index of bias in nonsymmetric distributions. This later was changed to Cpk, where “k” refers to the Japanese term katayori, which means “offset” or “bias.”

Always keep on learning…

My last post was All Communication is Miscommunication:

[1] Analyzing the capability of lean processes by Roope M. Turunen and Gregory H. Watson (Quality Progress Feb 2021)

All Communication is Miscommunication:

The title of this post is a nod to the French psychoanalyst, Jacques Lacan^[1]. In today’s post, I am looking at the idea of communication. The etymology of “communication” goes back to the Latin words, com and munus. The basic meaning of communication is to make something common. “Com” means “together” while “munus” means “service”, “gift” etc. A closely related word to “communication” is “information”. Similar to “communication”, the etymology of “information” also goes back to its Latin roots. The two Latin words are “in” and “formare”. Taken together, the meaning of “information” is something like – to give shape or form to something. In the context of “information”, this would be – to give shape or form to knowledge or a set of ideas.

In Cybernetics, a core concept is the idea of informational closure. This means that a system such as each one of us is informally closed. Information does not enter into the system. Instead, the system is perturbed by the external world, and based on its interpretative framework, the system finds the perturbation informative.

Informationally closed means that all we have access to is our internal states. For example, when we see a flower, the light hitting the retina of our eyes does not bring in the information that what we are seeing is a flower. Instead, our retinal cells undergo a change of state from the light hitting them. There is nothing qualitative about this interaction. Based on our past interactions and the stability of our experiential knowledge we see the perturbation as informative, and we represent that as “flower”.  The word is used to describe a sliver of our experiential reality.

Now this presents a fascinating idea – if we are informationally closed how does communication take place? There can be no direct transfer of information happening between two interacting agents. All that is happening is a relay of perturbations mainly.  In order to posit the possibility of communication, the interacting agents should have access to a common set of meanings. When a message is transmitted, both the transmitter and the receiver should be working with a set of possible messages that are contextual. This allows the receiver to choose the most meaningful messages from the set of possible messages. For example, if my friend says that he has a chocolate lab, and I take it to mean that he has a lab where he crafts delectable chocolate creations, then from my friend’s standpoint a miscommunication has occurred. A person more familiar with dogs would have immediately started talking about dogs.

Communication takes place in the form of verbal and nonverbal communication. This adds to the complexity of communication. All communication takes place in a social realm in the background of history of past interactions, cultural norms, language norms, inside jokes etc. Language, as Wittgenstein would say, lies in the public realm. In other words, our private experiences can only be described in terms of public language. Being informationally closed means that we have to indeed work hard at getting good at this communication business. Language is dynamic and ever evolving, and this makes communication even more challenging. Our communication will always be lacking.

I will finish with the wise words of William H. Whyte:

The great enemy of communication, we find, is the illusion of it… we have failed to concede the immense complexity of our society–and thus the great gaps between ourselves and those with whom we seek understanding.

Always keep on learning…

My last post was Absurdity in Systems Thinking

[1] The Democracy of the Objects, Levy Bryant

Absurdity in Systems Thinking

In today’s post, I am looking at absurdity in Systems Thinking. Absurdity is an official term used in the school of philosophy called existentialism. An existentialist believes that existence precedes essence. This means that our essence is not pregiven. Our meaning and purpose are that which we create. In existentialism, the notion of absurdity comes from the predicament that we are by nature meaning makers, and we are thrown into a world devoid of meaning. We do not have direct access to the external world; therefore, our cognitive framework has been tweaked by evolution to seek meaning in all perturbations we encounter. We are forever trying to make sense of a world devoid of any sense or meaning.

We like to imagine that there is greater meaning to this all and that there is a “system” of objective truths in this world. In this framework, we all have access to an objective reality where we can use 2 x 2 matrices to solve complex problems. In the existentialist framework, we see that instead of a “system” of objective truths, we have multiplicity of subjective truths. Soren Kierkegaard, one of the pioneers of existentialism, viewed subjective truth as the highest truth attainable.

When we talk about a “system” we are generally talking about a collection of interrelated phenomena that serves a purpose. From the existentialism standpoint, every “system” is a construction by someone to make sense of something. For example, when I talk about the healthcare system, I have a specific purpose in mind – one that I constructed. The parts of this system serve the purpose of working together for a goal. However, this is my version and my construction. I cannot act as if everyone has the same perspective as me. I could be viewing this as a patient, while someone else, say a doctor, could see an entirely different “system” from their viewpoint. Systems have meaning only from the perspective of a participant or an observer. We are talking about systems as if they have an inherent meaning that is grasped by all. When we talk about fixing “systems”, we again treat a conceptual framework as if they are real things in the world like a machine.  The notion of absurdity makes sense here. The first framework is like what Maurice Merleau-Ponty, another existential philosopher, called “high-altitude thinking”.  Existentialism rejects this framework. In existentialism, we see that all “systems” are human systems – conceptual frameworks unique to everyone who constructed them based on their worldviews and living experiences. Each “system” is thus highly rich from all aspects of the human condition.

Kevin Aho wrote about this beautifully in the essay, “Existentialism”:

By practicing what Merleau-Ponty disparagingly calls, “high-altitude thinking”, the philosopher adopts a perspective that is detached and impersonal, a “God’s eye view” or “view from nowhere” uncorrupted by the contingencies of our emotions, our embodiment, or the prejudices of our time and place. In this way the philosopher can grasp the “reality” behind the flux of “appearances,” the essential and timeless nature of things “under the perspective of eternity” (sub specie aeternitatis). Existentialism offers a thoroughgoing rejection of this view, arguing that we cannot look down on the human condition from a detached, third-person perspective because we are already thrown into the self-interpreting event or activity of existing, an activity that is always embodied, felt, and historically situated. 

We are each thrown here into the world devoid of any meaning, and we try to make meaning. In the act of making sense and meaning, we tend to believe that our version of world and systems are real. We often forget to see the world from others’ viewpoints.

Every post about Systems Thinking must contain the wonderful quote from West Churchman – the systems approach begins when first you see the world through the eyes of another. This beautifully captures the essence of Systems Thinking. Existentialism teaches us to realize the absurdity of seeking meaning in a world devoid of any meaning, while at the same time realizing that the act of seeking meaning itself is meaningful for us.

Always keep on learning!

References:

[1] Aho, Kevin, “Existentialism”, The Stanford Encyclopedia of Philosophy (Summer 2023 Edition), Edward N. Zalta & Uri Nodelman (eds.), URL = <https://plato.stanford.edu/archives/sum2023/entries/existentialism/&gt;.

Utilizing Stress/Strength Analysis to Reduce Sample Size:

Art by NightCafe

In today’s post, I am looking at some practical suggestions for reducing sample sizes for attribute testing. A sample is chosen to represent a population. The sample size should be sufficient enough to represent the population parameters such as mean, standard deviation etc. Here, we are looking at attribute testing, where a test results in either a pass or a fail. The common way to select an appropriate sample size using reliability and confidence level is based on success run theorem. The often-used sample sizes are shown below. The assumptions for using binomial distribution holds true here.

The formula for the Success Run Theorem is given as:

n = ln(1 – C)/ ln(R), where n is the sample size, ln is the natural logarithm, C is the confidence level and R is reliability.

Selecting a sample size must be based on risk involved. The specific combinations of reliability and confidence level should be tied to the risk involved. Testing for higher risk profile attributes require higher sample sizes. For example, for a high-risk attribute, one can test 299 samples and if there were no rejects found, then claim that at 95% confidence, the product lot is at least 99% conforming or that the process that produced the product is at least 99% reliable.

Often time, due to several constraints such as material availability, resource constraints, unforeseen circumstances etc., one may not be able to utilize required sample sizes needed. I am proposing here that we can utilize the stress/strength relationship to appropriately justify the use of a smaller sample size while at the same time not compromise on the desired reliability/confidence level combination.

A common depiction of a stress/strength relationship is shown below for a product. We can see that as long as the stress distribution does not overlap with the strength distribution, the product should function with no issues. The space between the two distributions is referred to as the margin of safety. Often, the product manufacturer defines the normal operating parameters based on this. The specifications for the product are also based on this and some value of margin of safety is incorporated in the specifications.

For example, let’s say that the maximum force that the glue joint of a medical device would see during normal use is 0.50 pound-force, and the specification is set as 1.5 pound-force to account for a margin of safety. It is estimated that a maximum of 1% can likely fail at 1.5 pound-force. This refers to 99% reliability. As part of design verification, we could test 299 samples at 1.5 pound-force and if we do not have any failures, claim that the process is at least 99% reliable at 95% confidence level. If the glue joint is tested at 0.50 pound-force, we should be expecting no product to fail. This is after all, the reason to include the margin of safety.

Following this logic, if we increase the testing stress, we will also increase the likelihood for failures. For example, by increasing the stress five-fold (7.5 pound-force), we are also increasing the likelihood of failure by five-fold (5%) or more. Therefore, if we test 60 parts (one-fifth of 299 from the original study) at 7.5 pound-force and see no failures, this would equate to 99% reliability at 95% confidence at 1.5 pound-force. We can claim at least 99% reliability of performance at 95% confidence level during normal use of product. We were able to reduce the sample size needed to demonstrate the required 99% reliability at 95% confidence level by increasing the stress test condition.

Similarly, if we are to test the glue joint at 3 pound-force (two-fold), we will need 150 samples (half of 299 from the original study) with no failures to claim the same 99% reliability at 95% confidence level during the normal use of product. The rule of thumb is that when aiming for a testing margin of safety of ‘x,’ we can reduce the sample size by a factor of ‘1/x’ while maintaining the same level of reliability and confidence. The exact number can be found by using the success run theorem. In our example, we estimate at least 95% reliability based on the 5% failures while using 5X stress test conditions, when compared to the original 1% failures. Using the equation ln(1-C)/ln(R), where C = 0.95 and R = 0.95, this equates to 59 samples. Similarly for 2X stress conditions, we estimate 2% failures, and here R = 0.98. Using C = 0.95 in the equation, we get the sample size required as 149.

If we had started with a 95% reliability (5% failures utmost) and 95% confidence at the 1X stress conditions, and we go to 2X stress conditions, then we need to calculate the reduced sample size based on 10% failures (2 x 5%). This means that the reliability is estimated to be 90% at 2X stress conditions. Using 0.95 for confidence and 0.90 reliability, this equates to a reduced sample size of 29.

A good resource to follow up on this is Dr. Wayne Taylor’s book, “Statistical Procedures for the Medical Device Industry”. Dr. Taylor notes that:

An attribute stress test results in a pass/fail result. However, the unit is exposed to higher stresses than are typical under normal conditions. As a result, the stress test is expected to produce more failures than will occur under normal conditions. This allows the number of units tested to be reduced. Stress testing requires identifying the appropriate stressor, including time, temperature, force, humidity and voltage. Examples of stress tests include dropping a product from a higher height, exposing a product to more cycles and exposing a product to a wider range of operating conditions.

Many test methods contained in standards are in fact stress tests designed to provide a safety margin. For example, the ASTM packaging standards provide for conditioning units by repeated temperature/humidity cycles and dropping of units from heights that are more extreme and at intervals that are more frequent than most products would typically see during shipping. As a result, it is common practice to test smaller sample sizes. The ASTM packaging conditioning tests are shown… to be five-times stress tests.

It should be apparent that if the product is failing at the elevated stress level, we cannot claim the margin of safety, we were going for. We need to clearly understand how the product will be used in the field and what the normal performance conditions are. We need a good understanding of the safety margins involved. With this approach, if we are able to improve the product design to maximize the safety margins for the specific attributes, we can then utilize a smaller sample size than what is noted in the table above.

Always keep on learning. In case you are interested, my last post was Deriving the Success Run Theorem:

Note:

1) It’s commonly used to depict a distribution using +/-3 standard deviations (σ). This is a practical way to visualize a distribution.

2) The most prevalent representation of a distribution often resembles a symmetrical bell curve. However, this is a simplified sketch and not intended to accurately represent the true data distribution, which may exhibit various distribution shapes with varying degrees of fit.

Deriving the Success Run Theorem:

Art by NightCafe

In today’s post, I am explaining how to derive the Success Run Theorem using some basic assumptions. Success Run theorem is one of the most common statistical rational for sample sizes used for attribute data. It goes in the form of:

Having zero failures out of 22 samples, we can be 90% confident that the process is at least 90% reliable (or at least 90% of the population is conforming).

Or

Having zero failures out of 59 samples, we can be 95% confident that the process is at least 95% reliable (or at least of 95% of the population is conforming).

The formula for the Success Run Theorem is given as:

n = ln(1 – C)/ ln(R), where n is the sample size, nl is the natural logarithm, C is the confidence level and R is reliability.

The derivation is fairly straightforward and we can use the multiplication rule of probability to do so. Let’s assume that we have a lot of infinite size and we are testing random samples out of the lot. The infinite size of the lot ensures independence of the samples. If the lot was finite and small then the probability of finding good (conforming) or bad (nonconforming) parts will change from sample to sample, if we are not replacing the tested sample back into the lot.

Let’s assume that q is the conforming rate (probability of finding a good part).

Let us calculate the probability of finding 22 conforming products in a row. In other words, we are testing 22 random samples and we want to find out the probability of finding 22 good parts. This is also the probability of NOT finding any bad product in the 22 random samples. For ease of explanation, let us assume that q = 0.9 or 90%. This rate of conforming product can also be notated as the reliability, R.

Using the multiplication rule of probability:

p(22 conforming products in a row) = 0.9 x 0.9 x 0.9 …… x 0.9 = 0.9 ^22

            = 0.10

            = 10%

If we find zero rejects in the 22 samples, we are also going to accept the lot. Therefore, this is also the probability of accepting the lot.

The complement of this is the probability of NOT finding 22 conforming products in a row, or the probability of finding at least one nonconforming product in the 22 samples. This is also the probability of rejecting the lot.

p(rejecting the lot) = 1 – p(22 conforming products in a row)

            = 1 – 0.10 = 0.90

            = 90%

This can be also stated as the CONFIDENCE that if the lot is passing our inspection (if we found zero rejects), then the lot is at least 90% conforming.

In other words, C = 1 – R^n

Or R^n = 1 – C

Taking logarithms of both sides,

n * ln(R) = ln(1 – C)

Or n = ln(1 – C)/ln(R)

Using the example, if we tested 22 samples from a lot, and there were zero rejects then we can with 90% confidence say that the lot is at least 90% conforming. This is also a form of LTPD sampling in Acceptance Sampling. We can get the same results using an OC Curve.

Using a similar approach, we can derive a one-sided nonparametric tolerance interval. If we test 22 samples, then we can say with 90% confidence level that at least 90% of the population is above the smallest value of the samples tested.

Any statistic we calculate should reflect our lack of knowledge of the parameter of the population. The use of confidence/reliability statement is one such way of doing it. I am calling this the epistemic humility dictum:

Any statistical statement we make should reflect our lack of knowledge of the “true” value/nature of the parameter we are interested in.

Always keep on learning. In case you missed it, my last post was An Existentialist’s View of Complexity:

An Existentialist’s View of Complexity:

Art by NightCafe

In my post today, I am looking at the idea of complexity from an existentialist’s viewpoint. An existentialist believes that we, humans, create meanings for ourselves. There is no meaning out there that we do not create. An existentialist would say, from this viewpoint, that complexity is entirely dependent upon an observer, a meaning maker.

We are meaning makers, and we assign meanings to things or situations in terms of possibilities. In other words, the what-is is defined by an observer in terms of what-it-can-be. For example, a door is described by an observer in terms of what it can be used for, in relation to other things in its environment. The door’s meaning is generated in terms of its possibilities. For example, it is something for me to enter or exit a building. The door makes sense to me when it has possibilities in terms of action or relation to other things. This is very similar to the ideas of Gibson, in terms of “affordances”.

In existentialism, there are two concepts that go hand in hand that are relevant here. These are “facticity” and “transcendence”. Facticity refers to the constraints a subject is subjected to. For example, I am a middle-aged male living in the 21^st century. I could very well blame my facticity for pretty much any situation in life. Transcendence is realizing that I have freedom to make choices to stand up for myself to transcend my facticity and make meaning of my own existence. We exist in terms of facticity and transcendence. We are thrown into this world and we find ourselves situated amidst the temporal, physical, cultural and social constraints. We could very well say that we have a purpose in this world, one that is prescribed to us as part of facticity or we can refer to ourselves to enable us to transcend our facticity and create our own purposes in the world.

In the context of the post, I am using “facticity” to refer to the constraints and “transcendence” to refer to the possibilities. Going back to complexity and an observer, managing complexity is making sense of “what-is” as the constraints, in terms of “what-it-can-be” as the possibilities. We describe a situation in terms of complexity, when we have to make meaning out of it. We do so to manage the situation – to get something out of it. This is a subject-object relationship in many regards. What the object is, is entirely dependent on what the subject can afford. When one person calls something as complex, they are indicating that the variety of the situation is manifold than what they can absorb. Another subject (observer) can describe the same object as something simple. That subject may choose to focus on only certain attributes of the situation, the attributes that the subject is familiar with. Anything can be called as complex or simple from this regard. As I have noted before, a box of air can be as complex as it can get when one considers the motion of an air particle inside, or as simple as it can get when one considers it as a box of “nothing”. In other words, complexity has no meaning without an observer because the meaning of the situation is introduced by the observer.

A social realm obviously adds more nuance to this simply because there are other meaning-makers involved. Going back to existentialism, we are the subject and at the same time objects for the others in the social realm. Something that has a specific meaning to us can have an entirely different meaning to another person. When we draw a box and call that as a “system”, another person can draw a different box that includes only a portion of my box, and call that as the same “system”. In the social realm, meaning-making should be a social activity as well. It will be a wrong approach to use a prescribed framework to make sense because each of us have different facticities and what possibilities lie within a situation are influenced by these facticities. The essence of these situations cannot be prescribed simply because the essence is brought forth in the social realm by different social beings. A situation is as-is with no complexity inherent to it. It is us who interact with it, and utilize our freedom to assign meaning to it. I will finish off with a great quote from Sartre:

Human reality everywhere encounters resistance and obstacles which it has not created, but these resistances and obstacles have meaning only in and through the free choice which human reality is.

Stay safe and always keep on learning…

In case you missed it, my last post was Plurality of Variety:

Plurality of Variety:

Art by NightCafe

In my post today, I am looking further at the idea of variety in Cybernetics. Cybernetics, as Ross Ashby, put is interested in all of the possibilities of a phenomenon as in what all it can do, rather than what the phenomenon actually is. Here, the possibilities align with the number of possible states of the phenomenon. This would mean that Cybernetics is based on distinctions and these distinctions are based on an observer. Stafford Beer explained variety as the measure of complexity of a situation or phenomenon. The more distinctions an observer can make, the higher the perceived complexity. In order to manage a complex situation, the observer has to be able to come up with enough variety to match the variety of the situation. This is also known as Ashby’s Law of Requisite Variety (LRV), a key principle in Cybernetics. LRV simply put states that only variety can absorb variety.

One of the main premises of LRV is that the external world always has a much higher variety than the controller. Here, controller refers to the person(s) trying to manage the situation. The controller has to be able to counter the variety thrown at them by the situation. The term “requisite” refers to quality that allows a controller to stay viable by managing the variety. Let’s take the example of a department store (one of the examples that Stafford Beer uses). Here, the department store manager has to be able to counter the variety thrown at them by the customers. There may be 100 customers in the store looking to buy anything from a comb to a grill. There may be customers who are rude and customers being unruly. No one person will be able to manage all the excess variety thrown at them. From a Cybernetics standpoint, the manager has to attenuate or dampen the extra variety and amplify their internal variety to absorb the excess variety so that the two (external and internal variety) are somewhat balanced or kept within a tolerable level.

There are several ways this can be achieved. This can include several approaches such as employing security guards, installing security cameras, hiring more staff etc. There are ways to attenuate the variety coming in such as only allowing a certain number of people in the store or keeping the stores open during only selected hours. There are ways to amplify the internal variety such as the use of security guards as I noted above or making it known that the store is being recorded at all times etc.

A constraint is a term that is used in conjunction with variety. If variety stands for the number of possible states, then a constraint is said to exist when the resultant variety is less than the number of all possible variety. Let’s take the example of the store again. There are 24 hours to a day. A customer therefore could come to the store during any of the 24 hours. However, if the store is kept open only for 18 of those hours, then a constraint is said to exist. The store manager was able to apply a constraint that reduced the variety from 24 to 18. Constraints are utilized to achieve requisite variety. Constraints can be used for attenuation of external variety as in the case of the use of specific store hours or they can be used for amplifying internal variety. In the case of security guards, they can be used to ensure that unruly customers behave. It is important to note that a constraint can function as both sometimes or at all times. For example, the use of security guards can act as an amplifier to attract more customers who might come with the assumption that the store is safe to shop in.

One should not misunderstand that adding variety for the sake of variety will result in requisite variety. For example, adding more parts can result in an increase of possible states (variety), but it does not mean that requisite variety can be achieved. One should also take into consideration the interaction that could result between the parts. I am talking about this strictly from a first order Cybernetics standpoint. For example, Stafford Beer warned us that use of computers can result in proliferation of variety, often or always in the wrong side. Often, the first impulse to manage variety is to use automation or a new computer product. But if these are not used effectively, they can lead to more issues.

I want to look more at the idea of interaction. When there is only aggregation of parts, they do not add up to much (no pun intended). However, when there is interaction between the parts, they always lead to emergence of self-organization. With time, a hierarchical structure emerges. This often follows a power law distribution. For example, a leader naturally emerges within a group. The power structure shows that majority of the power within the group is with the leader. Going back to constraints, a constraint is self-applied by the group when there is an interaction. When there are so many parts, there will be a specific quantitative variety. But when the parts are able to interact with each other, there is additional variety. Not all parts are meant to interact with each other and some parts interact with each other better than the others. Some combinations lead to more better combinations that enable tremendous amplification of variety, whereas some combinations lead to tremendous attenuation of variety.

Understanding the interaction between the employees is important for a manager. The emphasis to generate potential variety is on diversity and not on just adding more parts. A diversity of parts allows for a generation of new parts that did not exist before. These new parts can further combine with other parts to generate even more parts. A review of progress that we have made in terms of computer applications shows this relation really well. Humans have been around for 300,000 years or so. Charles Babbage invented the first mechanical computer in 1822. A lot of other technological advances were made within the last 200-300 years. The progress we have made within in a short amount of time is more than exponential. If all the parts were similar then there is only so much amplification that could be generated from them. When there is diversity amongst the parts, that opens up lot more possibilities to connect with each other to generate new and more diverse ideas. If there is no diversity then the result is an echo chamber where the same ideas get amplified while everything else gets drowned out.  

I will finish with a fantastic quote from Stafford Beer:

The lethal variety attenuator is sheer ignorance.

Stay safe and always keep on learning…

In case you missed it, my last post was How Blank is Your Paper?

How Blank is Your Paper?

Art by NightCafe

In today’s post, I am looking at the idea of constructivism in Cybernetics. The title of the post is a nod to the famous philosopher John Locke’s idea of “Tabula Rasa” or “blank slate”. Locke believed that we are born with blank slates and that our experiences in the world lead to knowledge of the world. Constructivism in Cybernetics does not align with the idea of a blank slate, but it does align with the idea of our experiences in the world leading to knowledge of the world. From the time of enlightenment, the belief became dominant that we have access to an objective world and the knowledge of this world can set us free. Constructivism starts with the idea that we construct knowledge of our world, but we do not have access to the objective reality. We are not born with a blank slate. We are born with gene patterns that were passed on from our ancestors through evolution. For example, when we are born, we already know how to grip or reach out to warmth etc. We are also born with an operationally closed framework for learning. Similar to what Immanuel Kant would say about categories of understanding, we have a framework that we use to “see” the world. This framework is similar to other humans, but different enough to make them unique to us. How we experience the world becomes unique to us.

One of the main impedances to understanding this viewpoint is the notion that we have access to an objective world. Another notion that I would like to slightly challenge is the idea that we have representations of the world. Similar to Martin Heidegger’s ideas, our default mode of us is as beings in the world. This means that the world itself is our representation. We act in the world without first creating a representation. When we walk around, open doors, hold things etc., our body conforms to the environment naturally. We are situated in the world as a part of the world itself. When we open a door, our hand conforms to the shape of the door knob without us having to create a representation of the door knob. This does not mean that we cannot make representations, if needed. We can of course think in concepts, but this is not our default mode of being in the world.

From a constructivism standpoint, we have an embodied mind. This means that the mind is not separate from the body, and the body is not separate from the mind. We are ultimately meaning makers. We cannot ignore the “we” in this view. Rene Descartes famously said, “I think, therefore I am.” A fallacy that is often overlooked in this, is that he started the sentence with an “I”. He already snuck in the “I” before trying to demonstrate the existence of the “I”. It’s like asking “who created the universe?”. By asking “who”, one is already sneaking in a creator and therefore starting with a bias. In cybernetics, the emphasis is on the stable correlations that we establish in a social realm. What we construct is reinforced and often corrected by the others in the social realm. In order for this to be effective, we need repeat interactions. The more we interact with a phenomenon in a social realm, the more “real” it becomes to us. In addition to other people, the social realm also includes the language, the script and other societal aspects such as culture, moral implications etc. We are creatures of habit and our times.

A great example to understand how we construct stable correlations without having access to the objective world comes from Lynn Hoffman. I have slightly modified it for our purposes. Imagine rubbing a crayon on a piece of paper over a coin. The first time you rub, you may not be able to make out the coin, but the more you rub the crayon back and forth, the better the coin gets visible on the paper. What we have is the paper and we do not see the coin. The coin becomes “real” to us as what we constructed on the paper with the repeat interactions. The differences on the surface of the coin stand out to us as we interact more with it. This helps us construct the coin based on what we know already without a direct access to the coin. Traditionally, in philosophy there is a tendency to separate ontology (study of what exists) and epistemology (study of knowledge). Cybernetics is not about the world itself (what exists?); it is about us in the world, in the social realm, and how we make sense of it. In this worldview, ontology feeds epistemology as much as epistemology feeds ontology.

Stay safe and always keep on learning… In case you missed it, my last post was OC Curve and Reliability/Confidence Sample Sizes:

OC Curve and Reliability/Confidence Sample Sizes:

_{“Reliability” as dreamt by Dream by WOMBO}

In today’s post, I am looking at a topic in Statistics. I have had a lot of feedback on one of my earlier posts on OC curves and how one can use it to generate a reliability/confidence statement based on sample size, n and rejects, c. I provided an Excel spreadsheet that calculates the reliability/confidence based on sample size and rejects. I have been asked how we can utilize Minitab to generate the same results. So, this post is mostly geared towards giving an overview of using OC curves to generate reliability/confidence values and using Minitab to do the same.

The basic premise is that a Type B OC curve can be drawn for samples tested, n and rejects found, c. On the OC curve, the line represents various combinations of reliability and confidence. The OC curve is a plot between percent nonconforming, and probability of acceptance. The lower the percent nonconforming, the higher the probability of acceptance. The probability can be calculated using binomial, hypergeometric or Poisson distributions. The binomial OC curves are called as “Type B” OC curve and do not utilize lot sizes, generally represented as N. The hypergeometric OC curves utilizes lot sizes and are called as “Type A” OC curve. When the ratio n/N is small and n >= 15, the binomial distribution closely matches the hypergeometric distribution. Therefore, the Type B OC curve is used quite often.

The most commonly used standard for attribute sample plans is MIL 105E. The sample plans in MIL 105E are identical to the Z1.4 standard plans. The sampling plans provided as part of the tables do utilize lot sizes. These sampling plans were “tweaked” to include lot sizes because there was a push for including economic considerations of accepting a large lot that may contain rejects. The sample sizes for larger lots were made larger due to this. The OC curves shown in the standards however are Type B OC curves that do not use lot sizes. Hypergeometric distribution considers the fact that there is no replacement for the samples tested. Each test sample removed will impact the subsequent testing since the number of samples is now less. However, as noted above, when the ratio n/N is small, the issue of not replacing samples is not a concern. For the binomial distribution, lot size is not considered since the samples are assumed to be taken from lots of infinite lot size.

With this background, let’s look at a Type B OC curve. The OC Curve is a plot between % Nonconforming, and Probability of Acceptance. Lower the % Nonconforming, the higher the Probability of Acceptance. The OC Curve shown is for n = 59 with 0 rejects calculated using Binomial Distribution.

The producer’s risk is the risk of good product getting rejected. The acceptance quality limit (AQL) is generally defined as the percent of defectives that the plan will accept 95 percent of the time (i.e., in the long run). Lots that are at or better than the AQL will be accepted 95 percent of the time (in the long run). If the lot fails, we can say with 95-percent confidence that the lot quality level is worse than the AQL. Likewise, we can say that a lot at the AQL that is acceptable has a 5-percent chance of being rejected. In the example, the AQL is 0.09 percent.

The consumer’s risk, on the other hand, is the risk of accepting bad product. The lot tolerance percent defective (LTPD) is generally defined as percent of defective product that the plan will reject 90 percent of the time (in the long run). We can say that a lot at or worse than the LTPD will be rejected 90 percent of the time (in the long run). If the lot passes, we can say with 90-percent confidence that the lot quality is better than the LTPD (i.e., the percent nonconforming is less than the LTPD value). We could also say that a lot at the LTPD that is defective has a 10-percent chance of being accepted.

The vertical axis (y axis) of the OC curve goes from 0 percent to 100 percent probability of acceptance. Alternatively, we can say that the y axis corresponds to 100 percent to 0 percent probability of rejection. Let’s call this confidence. This is also the probability of rejecting the lot. The horizontal axis (x axis) of the OC curve goes from 0 percent to 100 percent for percent nonconforming. Alternatively, we can say that the x axis corresponds to 100 percent to 0 percent for percent conforming. Let’s call this reliability.

We can easily invert the y axis so that it aligns with a 0 to 100-percent confidence level. In addition, we can also invert the x axis so that it aligns with a 0 to 100-percent reliability level. This is shown below.

The OC Curve line is a combination of reliability and confidence values. Therefore, for any sample size and rejects combination, we can find the required combination of reliability and confidence values. If we know the sample size and rejects, then we can find the confidence value for any reliability value or vice-versa. Let us look at a problem to detail this further:

In the wonderful book Acceptance Sampling in Quality Control by Edward Schilling and Dean Neubauer, the authors discuss a problem that would be of interest here. They posed:

consider an example given by Mann et al. rephrased as follows: Suppose that n = 20 and the observed number of failures is x = 1. What is the reliability π of the units sampled with 90% confidence? Here π is unknown and γ is to be .90. 

One of the solutions given was to find the reliability or the confidence desired directly from the OC curve.

They gave the following relation:

π = 1 – p, where π is the reliability and p is the nonconforming rate.

γ = 1 – P_a, where γ is the confidence and P_a is the probability of acceptance.

This is the same relation that was explained above.

In my spreadsheet, when we enter the values as shown below, we see that the reliability value is 81.91% based on LTPD value of 18.10%. This is the same result documented in the book.

We can use Minitab to get the same result. However, it will be slightly backwards. As I noted above, drawing the OC curve requires only two inputs – the sample size and the number of rejects allowed or acceptance number. Once the OC curve is drawn, we can then look at the different reliability and confidence combinations. We can also calculate the confidence, if we provide the reliability. The reliability is also 1 – p. In Minitab, we can input the sample size, number of rejects and p, and the software will provide us the P_a. For the purpose of reliability and confidence, the p value will be the LTPD value and the confidence value will be 1 – P_a.

I am using Minitab 18 here. Go to Acceptance Sampling by Attributes as shown below:

Choose “Compare User Defined Sampling Plans” from the dropdown and enter the different values as shown. Please note that the acceptance number is the maximum number of rejects allowed. Here we are entering the LTPD value because we know the value to be 18.10. In the spreadsheet, we have to enter the confidence level we want to calculate the reliability, while in Minitab we have to enter the LTPD value (1 – reliability) to calculate the confidence. In the example below, we are going to show that entering the LTPD as 18.10 will yield the P_a as 0.10 and thus the confidence as 0.90 or 90%.

Minitab yields the following result:

One can use the combination of sample size, acceptance number and required LTPD value to calculate the confidence value. The spreadsheet is available here. I will finish with one of the oldest statistical quotes attributed to the famous sixteenth century Spanish writer, Miguel de Cervantes Saavedra that is apt here:

“The proof of the pudding is in the eating. By a small sample we may judge of the whole piece.”

Stay safe and always keep on learning…

In case you missed it, my last post was Second Order Variety: