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Oct 4 2022

Strange Statements About Probability Models | Don Wheeler | Quality Digest

In his latest column in Quality Digest, Don Wheeler wrote the following blanket statements, free of any caveat:

  1. “Probability models are built on the assumption that the data can be thought of as observations from a set of random variables that are independent and identically distributed.”
  2. “In the end, which probability model you may fit to your data hardly matters. It is an exercise that serves no practical purpose.”

Source: Wheeler, D. (2022) Converting Capabilities, What difference does the probability model make? Quality Digest

Michel Baudin‘s comments:

Not all models assume i.i.d. variables

Wheeler’s first statement might have applied 100 years ago. Today, however, there are many models in probability that are not based on the assumption that data are “observations from a set of random variables that are independent and identically distributed”:

  • ARIMA models for time series are used, for example in forecasting beer sales.
  • Epidemiologists use models that assume existing infections cause new ones. Therefore counts for successive periods are not independent.
  • The spatial data analysis tools used in mining and oil exploration assume that an observation at any point informs you about its neighborhood. The analysts don’t assume that observations at different points are independent.
  • The probability models used to locate a wreck on the ocean floor, find a needle in a haystack, and other similar search problems have nothing to do with series of independent and identically distributed observations.

Probability Models Are Useful

In his second statement, Wheeler seems determined to deter engineers and managers from studying probability. If a prominent statistician tells them it serves no useful purpose, why bother? It is particularly odd when you consider that Wheeler’s beloved XmR/Process Behavior charts use control limits based on the model of observations as the sum of a constant and a Gaussian white noise.

Probability models have many useful purposes.  They can keep from pursuing special causes for mere fluctuations and help you find root causes of actual problems. They also help you plan your supply chain and dimension your production lines.

Histograms are Old-Hat; Use KDE Instead

As Wheeler also says, “Many people have been taught that the first step in the statistical inquisition of their data is to fit some probability model to the histogram.” It’s time to learn something new, that takes advantage of IT developments since Karl Pearson invented the histogram in 1891.

Fitting models to a sample of 250 points based on a histogram is old-hat. A small dataset today is more 30,000 points, and you visualize its distribution with kernel density estimation(KDE), not histograms.

#donwheeler, #probability, #quality

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Dec 25 2021

Always the Hurricanes Blowing

Atlantic hurricanes hurt people and destroy property around the Gulf of Mexico every year. Whether climate change is increasing their frequency is a serious question. Don Wheeler just had a column on this subject in the latest Quality Digest. It’s about Torturing the Data. He argues that we should be careful about not force-fitting models to arrive at pre-ordained conclusions.

His way of not torturing the history of hurricanes in the Atlantic is plotting yearly counts on, what else,  an XmR chart. It’s just as he would for hole diameters in metal plates coming off a production line in 1945. Hurricanes and holes in metal plates, however, have different backstories.

Continue reading…

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Oct 27 2021

Culture Change | MIT Sloan Management Review | Rose Hollister et al.

How the authors see it: “We define culture as a shared set of values (what we care about), beliefs (what we believe to be true), and norms of behavior (how we do things). […] We developed a set of culture transformation principles that maximize the likelihood of success:

  • Recognize that responsibility for culture can’t be delegated.
  • Start with the “why.”
  • Define the target cultural values and behaviors.
  • Engage and get input.
  • Build a bridge to the future desired culture.
  • Build a culture road map.
  • Reinforce the desired culture in all organizational systems.
  • Rapidly reward the emerging culture. “

Source: Hollister, R., Tecosky, K., Watkins, M, & Wolpert, C. (2021) Why Every Executive Should Be Focusing on Culture Change Now, MIT Sloan Management Review, Reprint 63137

Michel Baudin‘s comments: I define culture more simply as “the way we do things around here.” You don’t change it by making it the goal of a change program. To do it, first, you change the work, and then employees’ perceptions follow.

Redesign shop floor layouts to facilitate flow, develop multiskilled operators, hire employees for whole careers and retain them through thick and thin, engage them in solving problems,…

Over time, employees realize it’s not idle talk about lofty goals but concrete changes to their daily experience, including teamwork. Then it becomes “the way we do things around here,” in other words, a new culture.

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Jul 31 2021

Follett in 1924: Use Operators’ Knowledge

Mary Parker Follett

 

Almost 100 years ago, Mary Parker Follett wrote: “And our aim in the […] organization of industry should be […] so to organize the plant that the workmen’s experience can be added to that of the expert; we must see just where their experience will be a plus matter, and we must plan to have the workmen learn more and more of the industry as a whole.” 

Source: Follett, M. P. (2013 reprint). Creative Experience. United States: Martino Fine Books. (p. 20)

Michel Baudin‘s comments: Today, we would say “manufacturing” rather than “industry,” and “operator” rather than “workmen.” This is the earliest text I have seen that recommends engaging shop floor operators in improvement activities and training them to understand the broader picture. 

Taylor wanted to control operators so that they couldn’t collude to curtail output. The Gilbreths wanted to make their work easier. Follett wants to tap into their knowledge and combine it with the experts’ in order to achieve better outcomes. And she also believes in their ability to learn.

In these few words, she showed more respect for the humanity of the operators than I recall seeing from her immediate precursors and contemporaries. 

 

#maryparkerfollett, #respectforhumanity, #traceyrichardson

 

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Aug 3 2020

Process Behavior Charts and Covid-19 | Donald J. Wheeler | Quality Digest

Daily number of COVID-19 deaths in the US

“Many schemes, ranging from simple to complex, using process behavior charts with Covid data have been tried. But regardless of their complexity, they all come up against the fact that epidemiological data do not represent a steady-state system where we need to discover if assignable causes are present. Process behavior charts simply ask the wrong questions here. When dealing with data from a dynamic system where the causes are well understood, the data will create a running record that can be interpreted at face value. The long-term changes will be sufficiently clear so that further data analysis becomes moot.

So, while specialists may use epidemiological models, when it comes to data analysis by nonspecialists we do not need more analysis, but less. We need to draw the graphs that let the data speak for themselves, and then get out of the way. As always, the best analysis is the simplest analysis that provides the needed insight.”

Sourced : Quality Digest

Michel Baudin‘s comments: Don Wheeler is correct that process behavior charts are not a fit for data about the pandemic. Non-specialists, however, cannot ignore epidemiological models for several reasons:

  1. Their key concepts have found their way into news media and political speeches. The German chancellor discusses R_{0} on TV, the British Prime Minister talks about "herd immunity," and everybody in the US wants to "flatten the curve." As citizens, we need to know what they mean and notice when our leaders don't.
  2. The epidemiological models are useful to anticipate what happens when organizations resume operations after a pandemic-induced shutdown.

That's why I took a stab at learning and sharing about them in a few recent posts:

#covid19, #coronavirus, #epidemiology, #pandemic

 

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May 28 2020

“Herd Immunity” Varies With The Herd

New York Times article presents herd immunity as independent of population

In today’s New York Times, N. Popovitch and M. Sanger-Katz wrote an article about how The World Is Still Far From Herd Immunity for Coronavirus, in which they treat herd immunity as if it were a characteristic of the disease only, achieved when 60% of the population has antibodies.

The CDC On Herd Immunity

The US CDC website defines herd immunity it as “a situation in which a sufficient proportion of a population is immune to an infectious disease (through vaccination and/or prior illness) to make its spread from person to person unlikely.”

The CDC  makes it clear is that the “sufficient proportion” depends on both the disease and the population in which it spreads. In other words, for a given disease herd immunity varies with the herd. The same proportion of immune individuals will not achieve it in populations with different lifestyles. It is higher if they commute in crowded buses to work shoulder-to-shoulder on assembly lines; lower, if they move in individual cars and work in private offices.

The CDC’s definition fails to say what they mean by unlikely. To reopen factories without making them COVID-19 hot spots, we need the workforce to have herd immunity. It means that its members must be unlikely to infect each other, not that 60% of them must have immunity.

Herd Immunity In The SIR Model

Two of the charts from my previous post on this subject can clarify the issues. The first one shows the generic pattern of an epidemic over time in a population, in the classic SIR model.

The key parameter often mentioned today by people like Angela Merkel is R_{0} , pronounced “are-nought,” which can be interpreted as the expected number of people an infected person would transmit the disease to while infectious in a population where no one else is infected. In a population of size N The number of infected people peaks when the number S of susceptible individuals drops enough to have R_{0} = N/S . Some authors call the ratio r = 1- S/N of recovered people to the entire population at the peak of the epidemic the “herd immunity threshold.” Past this point, the epidemic ebbs, but infection can still be likely.

At the right side of the curve, where the number of infected people drops to 0 , the limit r_{\infty} of r varies between 0% and 100% depending on R_{0} . r_{\infty} describes the proportion of the population with acquired immunity that is necessary to confer herd immunity on the entire population. You don’t have to say how unlikely transmission is.

r_{\infty} is a final score directly observable only when the epidemic is over. R_{0} , on the other hand, can be estimated early on, albeit with wide margins of error. With a model of the epidemic,  r_{\infty} can then be inferred from R_{0} .  The second chart plots s_{\infty}  = 1- r_{\infty} as a function of R_{0} in the basic SIR model, with the ranges of R_{0} estimates published for the seasonal flu and COVID-1.

When The Population Is The Workforce Of A Factory

All the practices introduced into a factory to prevent contagion at work lower the R_{0} of the disease within the workforce while working, which lowers both the herd immunity threshold and the level of actual immunity required to achieve herd immunity in the long run, and this is quantifiable.

Of course, outside of work, the employees of the factory are within society at large. They are subject to its contagion dynamics. The main problem of today, however, is factories turning into epidemic hot spots.

#herdimmunity, #covid19, #factoryreopening, #factoryhotspots

 

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