Technology

Mar 23 2015

Tradition, Tradition, Data Visualization, and Pareto Charts

Some of the standard charts used in manufacturing for decades don’t meet today’s criteria for effective visualization. But using them is now a tradition; they are taught in school and their value is unchallenged, but it is time to challenge it. If we were to see these charts for the first time in 2015, would we consider the information they provide useful, and would we want to use the classical formats? This post suggests answers in the case of the venerable Pareto chart.

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Mar 16 2015

Lean Engineering Case Study | Pascal Chaloyard (PDF)

“Potain, a manufacturer and supplier of tower cranes in La Clayette, France, where it made all the mechanical and electrical systems, safety devices and cabs for cranes manufactured in Europe. The diversity of components manufactured was wide and production was in small runs, indeed in single units.

The factory, on a hill, had a handicap in terms of flow as, each time the business grew, a new building had to be built at a different altitude from the others. The organisation was by trade, which penalized production flows.

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Feb 7 2015

One-piece Flow for Information Products?

Organizations that produce documents — whether they are publications for sale, standard tests for schools, legal templates, or work instructions for production — face challenges that differ from manufacturing, because data and materials don’t flow the same way. The production of a document by a team is a process of collaborative editing, not a fixed sequence of standardized operations.

With electronic documents, you need a revision management system to prevent inconsistent updates, you need to cap the number of documents in process to control lead time, and you may need to improve the work flow or increase the team size if saturated.

Tools like 5S are irrelevant in this context, because the work takes place inside a computer network, not in the physical office, and setting up an effective network — with the right software properly configured — requires information systems professionals at the state of the art. What looks like rework in this context is a collaborative editing process that must be managed, not eliminated.

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Gauss with bell shape banknote

Aug 23 2014

The bell curve: “Normal” or “Gaussian”?

Most discussions of statistical quality refer to the “Normal distribution,” but “Normal” is a loaded word. If we talk about the “Normal distribution,” it implies that all other distributions are, in some way, abnormal. The “Normal distribution” is also called “Gaussian,” after the discoverer of many of its properties, and I prefer it as a more neutral term. Before Germany adopted the Euro, its last 10-Mark note featured the bell curve next to Gauss’s face.

The Gaussian distribution is widely used, and abused, because its math is simple, well known, and wonderful. Here are a few of its remarkable properties:

  1. It applies to a broad class of measurement errors. John Herschel arrived at the Gaussian distribution for measurement errors in the position of bodies in the sky simply from the fact that the errors in x and y should be independent and that the probability of a given error should depend only on the distance from the true point.
  2. It is stable. If you add Gaussian variables, or take any linear combination of them, the result is also Gaussian.
  3. Many sums of variables converge to it.  The Central Limit Theorem (CLT) says that, if you add variables that are independent, identically distributed, with a distribution that has a mean and a standard deviation, they sum converges towards a Gaussian. It makes it an attractive model, for example, for order quantities for a product coming independently from a large number of customers.
  4. Mint syrup diffusion in water
    Mint syrup diffusion in water

    It solves the equation of diffusion. The concentration of, say, a dye introduced into clear water through a pinpoint is a Gaussian that spreads overt time. You can experience it in your kitchen: fill a white plate with about 1/8 in of water, and drop the smallest amount of mint syrup you can in the center. After a few seconds, the syrup in the water forms a cloud that looks very much like a two-dimensional Gaussian bell shape for concentration, as shown on the right. And it fact it is, because the Gaussian density function solves the diffusion equation, with a standard deviation that rises with time. It also happens in gases, but too quickly to observe in your kitchen, and in solids, but too slowly.

  5. It solves the equation of heat transfer by conduction. Likewise, when heat spreads by conduction from a point source in a solid, the temperature profile is Gaussian… The equation is the same as for diffusion.
  6. Unique filter. A time-series of raw data — for temperatures, order quantities, stock prices,… — usually has fluctuations that you want to smooth out in order to bring to light the trends or cycles your are looking for. A common way of doing this is replacing each point with a moving average of its neighbors, taken over windows of varying lengths, often with weights that decrease with distance, so that a point that is 30 minutes in the past counts for less than the point of 1 second ago. And you would like to set these weights so that, whenever you enlarge the window, the peaks in your signal are eroded and the valleys fill up. A surprising, and recent discovery (1986) is that the only weighting function that does this is the Gaussian bell curve, with its standard deviation as the scale parameter.
  7. Own transform. This is mostly of interest to mathematicians, but the Gaussian bell curve is its own Laplace transform, which drastically simplifies calculations.
  8. …

For all these reasons, the Gaussian distribution deserves attention, but it doesn’t mean that there aren’t other models that do too. For example, when you pool the output of independent series of events, like failures of different types on a machine, you tend towards a Poisson process, characterized by independent numbers of events in disjoint time intervals, and a constant occurrence rate over time. It is also quite useful but it doesn’t command the same level of attention as the gaussian.

The most egregious misuse of the gaussian distribution is in the rank-and-yank approach to human resources, which forces bosses to rate their subordinates “on a curve.” Measuring several dimensions of people performance and examining their distributions might make sense, but mandating that grades be “normally distributed” is absurd.

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Aug 8 2014

The meaning(s) of “random”

Random and seq. access“That was random!” is my younger son’s response to the many things I say that sound strange to him, and my computer has Random Access Memory (RAM), meaning that access to all memory locations is equally fast, as opposed to sequential access, as on a tape, where you have to go through a sequence of locations to reach the one you want.

In this sense, a side-loading truck provides random access to its load, while a back-loading truck provides sequential access.

While  these uses of random are common, they have nothing to do with probability or statistics, and it’s no problem as long as the context is clear. In discussion of quality management or production control, on the other hand, randomness is connected with the application of models from probability and statistics, and misunderstanding it as a technical term leads to mistakes.

From the AMS blog (2012)
From the AMS blog (2012)

In factories, the only example I ever saw of Control Charts used as recommended in the literature was in a ceramics plant  that was firing thin rectangular plates for use as electronic substrates in batches of 5,000 in a tunnel kiln. They took dimensional measurements on plates prior to firing, as a control on the stamping machine used to cut them, and they made adjustments to the machine settings if control limits were crossed. They did not measure every one of the 5,000 plates on a wagon. The operator explained to us that he took measurements on a “random sample.”

“And how do you take random samples?” I asked.

“Oh! I just pick here and there,” the operator said, pointing to a kiln wagon.

That was the end of the conversation. One of the first things I remember learning when studying statistics was that picking “here and there” did not generate a random sample. A random sample is one in which every unit in the population has an equal probability of being selected, and it doesn’t happen with humans acting arbitrarily.

A common human pattern, for example, is to refrain from picking two neighboring units in succession. A true random sampler does not know where the previous pick took place and selects the unit next to it with the same probability as any other. This is done by having a system select a location based on a random number generator, and direct the operator to it.

This meaning of the word “random” does not carry over to other uses even in probability theory. A mistake that is frequently encountered in discussions of quality is the idea that a random variable is one for which all values are equally likely.  What makes a variable random is that probabilities can be attached to values or sets of values in some fashion;  it does not have to be uniform. One value can have a 90% probability while all other values share the remaining 10%, and it is still a random variable.

When you say of a phenomenon that it is random, technically, it means that it is amenable to modeling using probability theory. Some real phenomena do not need it, because they are deterministic:  you insert the key into the lock and it opens, or you turn on a kettle and you have boiling water. Based on your input, you know what the outcome will be. There is no need to consider multiple outcomes and assign them probabilities.

There are other phenomena that vary so much, or on which you know so little, that you can’t use probability theory. They are called by a variety of names; I use uncertain.  Earthquakes, financial crises, or wars can be generically expected to happen but cannot be specifically predicted. You apply earthquake engineering to construction in Japan or California, but you don’t leave Fukushima or San Francisco based on a prediction that an earthquake will hit tomorrow, because no one knows how to make such a prediction.

Between the two extremes of deterministic and uncertain phenomena is the domain of randomness, where you can apply probabilistic models to estimate the most likely outcome, predict a range of outcomes, or detect when a system has shifted. It includes fluctuations in the critical dimensions of a product or in its daily demand.

The boundaries between the deterministic, random and uncertain domains are fuzzy. Which perspective you apply to a particular phenomenon is a judgement call, and depends on your needs. According to Nate Silver, over the past 20 years, daily weather has transitioned from uncertain to random, and forecasters could give you accurate probabilities that it will rain today. On the air, they overstate the probability of rain, because a wrong rain forecast elicits fewer viewer complaints than a wrong fair weather forecast. In manufacturing, the length of a rod is deterministic from the assembler’s point of view but random from the perspective of an engineer trying to improve the capability of a cutting machine.

Rods for assemblers vs. engineers

Claude Shannon
Claude Shannon

This categorization suggests that that a phenomenon that is almost deterministic is, in some way, “less random” than one that is near uncertainty. But we need a metric of randomness to give a meaning to an expression like “less random.”  Shannon’s entropy does the job. It is not defined for every probabilistic model but, where you can calculate it, it works. It is zero for a deterministic phenomenon, and rises to a maximum where all outcomes are equally likely. This brings us back to random sampling.  We could more accurately  call it “maximum randomness sampling” or “maximum entropy sampling,” but it would take too long.

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Apr 8 2014

Preventing Errors in Food Delivery by Natural Mapping at Benihana

Restaurant waiters who deliver food to tables of five or more customers rarely remember who ordered what, and have to ask.

Generic restaurant order form
Generic restaurant order form

Most restaurants still use paper order forms, and the most common are not much help, because they tell the waiter what was ordered at each table, but not which customer ordered it. The row of titles on the top, with “APPT- SOUP/SAL-…” is intended as a series of column headers to record each customer’s choice in each category.

 

 

Order form with table layouts and numbered positionsSome form suppliers, like National Checking with their WaitRpad, have addressed this problem by providing table maps at the top of the form. These sketches include the following:

  1. The shape of the table.
  2. Where the waiter is to stand when delivering food.
  3. A clockwise numbered position for each customer.

The waiter arrives with a tray carrying the dishes laid out clockwise to match the customer positions.  National Checking posted the following video to highlight the advantages of this form:

Benihana table
Benihana table

Benihana, however, goes one step further and takes advantage of the special characteristics of their service. It is a chain of Japanese restaurants in the US, with a single 8-seat table layout and a chef at each table cooking on a hot plate in front of the customers, from ingredients in a cart. The work done away from the table is limited to kitting the ingredients to match the customers’ orders.

 

 

Benihana order form
Benihana order form

The order form is a map of the table, which is possible only because the tables are all identical, and the form can be filled out with abbreviations because the orders are all for full-course meals: “DIA” for “Diablo,” “SM” for “Splash-and-Meadow,” etc., with a few options, such as fried rice versus steamed rice.

While this is effective at ensuring that customers receive exactly what they ordered, it is not mistake-proofing/poka-yoke. It does not physically prevent mistakes, nor does it have a mechanism to signal any error that may happen. A disorganized chef could still get it wrong, and customers could confuse any chef by switching seats.

It is instead an application of the usability engineering principle of natural mapping. An order form that is a map of the table makes it easy for the chef to know which dishes to give to which customers and thereby reduces the likelihood of errors. Mistake-proofing would be better, if someone could find a way to do it.

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