Technology

Mining operations

Oct 26 2011

Data Mining in Manufacturing versus the Web

Data mining, in general, is the retrieval of information from data collected for a different purpose, such as using sales transaction histories to infer what products tend to be bought together. By contrast, design of experiments  involves the collection of observations for the purpose of confirming or refuting hypotheses.

This perspective on data mining is consistent with the literature in expressing purpose, but most authors go further. They include in their definitions that data mining is done with computers, using large databases and specific analytical tools, which I think is too restrictive. The tools they list are the ones they have found useful in analyzing the behavior of millions of users of search engines or commerce websites, and they are not obviously applicable in other areas, such as manufacturing.

During World War II, British analysts used the serial numbers of captured or destroyed German tanks to estimate the numbers produced. Because serial numbers were not attached for this purpose, it was data mining. It used clever statistical models but, obviously, no computers.

Today, PhD-level data miners at Google, eBay, or Amazon sift through the  page views and click-throughs of millions of users for clues to patterns they can use. The data, automatically collected, is accurate and collected by the terabytes every day. This “big data” requires parallel processing on clusters of computers and lends itself to the most advanced analytical tools ever developed.

Compared to this fire hose of data, what manufacturing produces is a trickle. In a factory, the master data/technical specs, plans and schedules, status of operations and work in process, and the history of production over, say, 12 months, usually adds up to a few gigabytes. It doesn’t  fit on one spreadsheet, but it often does on a memory stick. On the other hand, much of it is still manually generated and therefore contains errors, and it is often structured in ways that make it difficult to work with.

Even if manufacturing companies could hire the data miners away from their current jobs, their experience with e-commerce or web search would not have prepared them well for the different challenges of manufacturing data mining.

There is an opportunity for data mining to contribute to competitiveness in manufacturing, but the approach must start from the needs. It must not be an e-commerce cure in search of manufacturing diseases.

By • Technology • 0 • Tags: , ,

Vilfredo_Pareto

Oct 14 2011

Revisiting Pareto

Revisiting Pareto is a paper about the application of the 80/20 law, also known as the law of the vital few and the trivial many and the Pareto principle. It presents new ways of applying it to manufacturing operations and is scheduled for publication in Industrial Engineer Magazine in January, 2012. As a preview, I am including here the following:

  1. The complete abstract of the paper as it will be published.
  2. A section on a simulation of a game leading to the emergence of a Pareto distribution of wealth among players, which was cut from the article because it is meant to stimulate thinking and does not contain actionable recommendations.

Abstract of the paper as scheduled for publication in 1/2012

The Pareto principle, so named by J.M. Juran in the 1940s, is also known as the 80/20 law, the law of the vital few and the trivial many, and ABC classification. It is a simple yet powerful idea, generally accepted but still underutilized in business. First recognized by Vilfredo Pareto in the distribution of farm land in Italy around 1900, it applies in various forms to city populations as counted in the 2010 census of the US, as well as to quality defects in manufacturing, the market demand for products, the consumption of components in production, and various metrics of item quantities in warehouses.

The key issues in making it useful are (1) to properly define quantities and categories, (2) to collect or retrieve the data needed, (3) to identify the actions to take as a result of its application and (4) to present the analysis and recommendations in a compelling way to decision makers.

In the classical Pareto analysis of quality problems, defect categories only partition the defectives if none has more than one type of defect. When multiple defects can be found on the same unit, the elimination of the tallest bar may  increase the height of its runner-up. With independent defect categories and an electronic spreadsheet, this is avoided by calculating the yield of every test in the sequence instead of simply counting occurrences, and multiplying these yields to obtain the yield of a sequence of tests. We can then plot a bar chart of the relative frequencies each defect in the population that is actually tested for it, and, as a cumulative chart, the probability of observing at least one of the preceding defects.

When analyzing warehouse content, there are usually too many different items to count physically, and we must rely on data in the plant’s databases.  The working capital tied up by each item is usually the most accessible. But physical characteristics like volume occupied, weight or part count are often scattered in multiple databases and sometimes not recorded. The challenge then is to extract, clean, and integrate the relevant data from these different sources.

In both supply chain and in-plant logistics, the design of the system should start with an analysis of part consumption by a production line in terms of frequency of use, another quantity that is not additive across items. In this application, the classical Pareto chart is replaced by the S-curve, which plots the number of shippable product units as a function of the frequency ranks of the components used, and thus provides a business basis for grouping them into A-, B- and C-items, also known as runners, repeaters and strangers.

The presentation of the results should be focused on communication, not decoration,  and use graphics only to the extent that they serve this purpose.

Emergence of the Pareto distribution in a simulation

While the Pareto principle can be easily validated in many contexts, we are short on explanations as to why that is.  We do not provide one, but we show how, in a simulation of a multiple-round roulette game in which each player’s winnings at each round determine his odds in the next one, the distribution of chips among the players eventually comes close to the 80/20 rule. This happens even though it is a pure game of chance: players start out with equal numbers of chips and have no way to influence the outcome.

Assume we use a roulette wheel to allocate chips among players in multiple rounds, with the following rules:

  1. On the first round, the players all have equal wedges of the roulette wheel, and the roulette is spun once for each chip.
  2. On each following round, each player’s wedge is proportional to the amount he won on the preceding round.

This is a pure game of chance. There is nothing players can do to influence the outcome, and the players who do best in one round are set to do even better on the next one. It is also a zero-sum game, in that whatever a player wins comes out of the other players’ hands. There is no safety net: a player with no chips after any round is out of the game.  If you know the present state of the game –how many chips the player in each rank has– then the results of future rounds is independent of the path by which you arrived at the present state. Technically, it is a random walk and a Markov process. The concept of the game is shown in Figure 1.

Figure 1. Simulation concept

It could be viewed as a representing a simplified Oklahoma Land Rush, where farmers of equal talent are initially given identical plots of land. Even in the first round, some plots will have higher crop yields than others. If the average crop is needed to survive, the farmers with a surplus sell it to the farmers with a shortfall in exchange for land and start the next season with land in proportion to the crop they had on the previous one.  The players could also be functionally equivalent, similarly priced consumable products sold in the same channels, like toothpaste or soft drinks, and the chips would be the buyers of these products.

If we run this game through enough rounds, do we tend towards a distribution where 20% of the players hold 80% of the chips, or do all the chips end up in the hands of only one player? We simulated this game in software with 1 million chips to be divided among 1,000 players in 100,000 rounds, and the simulation takes about 2 minutes to run on a desktop PC.

The results show that the “wealth distribution” is stable, beyond 10,000 rounds, with 23% of the players collectively holding 80% of the chips Figure 2 shows the distribution after 100,000 rounds, which roughly satisfies the 80/20 law, but not recursively, because it takes the top 49% of the players to account for 96% of the chips, instead of 36%.

Figure 2. Chip distribution after 100,000 rounds

Figure 3 shows other indicators of the simulation results every 10,000 rounds. The proportion of the top players holding 80% of all the chips oscillates between 21.5% and 25%, with a very slow downward trend. The number of chips held by the top 10 players also varies, but is essentially flat.Figure 3. Indicators every 10,000 rounds

This pure game of chance, which favors at every round the winners of the previous round, does not rapidly concentrate all the chips in a few hands. Instead, it produces a distribution that is as close to Pareto’s as anything we can observe in demographics, quality, or production control. This suggests the following two conclusions:

  1. The reason the 80/20 law is so often verified with actual data that it does not require some categories to be “better” than others. A long random walk is sufficient to produce it, even when you start out with equal quantities assigned to each category. The products that are Runners are not necessarily better in any way than the Repeaters or the Strangers. From the point of view of Manufacturing, it does not matter why or how they became Runners: as long as they dominate the volume, they need dedicated resources.
  2. If some categories are intrinsically better able to attract the quantity to be distributed than others, we can expect the distribution to be more unequal than 80/20. If the players are farmers, differences in skill may skew the distribution further. If they are products competing for customers, the better products may take over the market, but it does not always happen.

The simulation has shown the limitations of the conclusions drawn from a Pareto chart. When a product is a Runner, by definition it deserves a dedicated production line. That is a direct consequence of its being at the top of the chart. It does not, however, imply that it is “better” in any way than that the other products. The simulation arrived at a near 80/20 distribution of the chips without assuming any difference in the players’ ability to acquire chips: the roulette wheel has no favorites, and the players can do nothing to influence the outcome.

By • Technology • 4 • Tags: , , ,

Mar 3 2011

A factory can always be improved

Based on an NWLEAN post entitled: Laws of Nature – Pareto efficiency and Pareto improvements, from 3/3/2011 

In manufacturing, Italian economist Vilfredo Pareto is mostly known for the Pareto diagrams and the 80/20 law, but  in economics, he is also known for the unrelated concept of Pareto efficiency, or Pareto optimality, which is also relevant to Lean. A basic tenet of Lean is that a factory can always be improved, and that, once you have achieved any level of performance, it is just the starting point for the next round of improvement. Perfection is something you never achieve but always pursue and, if you dig deep enough, you always find opportunities. This is the vocabulary you use when discussing the matter with fellow production people. If, however, you are taking college courses on the side, you might score more points with your instructor by saying, as an empirical law of nature, that a business system is never Pareto-efficient. It means the same thing, but our problem is that this way of thinking is taught neither in Engineering nor in Business school, and that few managers practice it.

A system is Pareto-efficient if you cannot improve any aspect of its performance without making something else worse. Managers who believe their factories to be Pareto-efficient think, for example, that you cannot improve quality without lengthening lead times and increasing costs, which is exactly what Lean does. In fact, eliminating waste is synonymous with making improvements in some dimensions of performance without degrading anything else, or taking advantage of the lack of Pareto-efficiency in the plant.

When we say that a factory can always be improved it is a postulate, an assumption you start from when you walk through the gates. The overwhelming empirical evidence is that, if you make that assumption, you find improvement opportunities. Obviously, if you don’t make that assumption, you won’t find any, because you won’t be trying.

This is not a minor issue. Writing in the Harvard Business Review back in 1991 about Activity-Based Costing, Robert Kaplan stated that all the possible shop floor improvements had already been made over the previous 50 years. He was teaching his MBA students that factories were Pareto-efficient and that it was therefore pointless to try and improve them. They would do better to focus on financial engineering and outsource production.

The idea that improving factories is futile and a distraction from more “strategic” pursuits dies hard. It is expressed repeatedly in a variety of ways. The diminishing returns argument is that, as you keep reaching for fruits that hang ever higher, the effort requires starts being excessive with respect to the benefits, but there are two things to consider:

  • As you make improvements, you enhance not only performance but your own skills as well, so that some of what was out of reach before no longer is.
  • Competition is constantly raising the bar. If your competitors keep improving and you don’t, you lose.

Another argument is that the focus on waste elimination discourages activities like R&D that do not have an immediate impact on sales. The improvement effort, however,  isn’t about what we do but how we do it. Nobody in his right mind would call R&D waste, even on projects that fail. Waste in R&D comes in the form of researchers waiting for test equipment, sitting through badly organized meetings, or filling out administrative paperwork.

In manufacturing itself, some see the pursuit of improvement as a deterrent to investment in new technology. While it is clear that the improvement mindset does not lead to solving every problem by buying new machines,  the  practitioners of continuous improvement are in fact better informed, savvier buyers of new technology. On one side of the shop floor, you see a cell with old machines on which incremental improvements over several years have reduced staffing requirements from 5 operators to 1. On the other side of the aisle, you see a brand new, fully automatic line with a design that incorporates the lessons learned on the old one.

Others have argued that a society that pursues improvement will be slower to develop and adopt new, disruptive technology. But does the machinist improving a fixture deter the founder of the next Facebook? There is no connection. If the machinist were not making improvements, his creativity would most likely be untapped. And his improvement work does not siphon off the venture capital needed for disruptive technology.

By • Laws of nature • 14 • Tags: , , , , ,

Feb 11 2011

Comparative advantage in the allocation of work among machines

Another NWLEAN post in response to Mike Thelen’s query on Laws of Nature, posted on 2/11/2011

On several occasions, I ran into the problem of allocating work among machines of different generations with overlapping capabilities. There were several products that could be processed to the same levels of quality in both the new and the old machines. The machines worked differently. For example, the old machines would process parts in batches while the new ones supported one-piece flow. But the resulting time per part was shorter on the new machines for all products. In other words, the new machines had a higher capacity for everything.

Given that the products were components going into the same assemblies, they were to be made in matching quantities per the assembly bill of materials and the demand was such that the plant had to make as many matching sets as possible. The question then is: how do you allocate the work among the machines?

When I first saw this problem, I thought it was unique, but, in fact, many machine shops keep multiple generations of machines on their floors and make parts in matching sets for their customers, and it is in fact quite common. The solution that maximizes the total output is to apply the law of comparative advantage from classical economics. Adapted to this context, it says that the key is the ratio of performance between the old and the new machines on each product. For example, if the new machine can do product X 30% faster than the old machine and product Y ten times faster, then the old machine is said to have a comparative advantage on product X, and you should run as much as possible of product X on the old machine.

It is a bit surprising at first, but easy to apply. What is more surprising is that so few plants do. The logic that is actually most commonly used is to load up the new machine with as much work as possible, on the grounds that it has a high depreciation and needs to “earn its keep.” What many managers have a difficult time coming to terms with is that what you paid for a machine and when you paid it is irrelevant when allocating work, because it is in the past and nothing you do will change it. You produce today with the machines you have, and the only thing that matters is what they can do, now and in the future.

The law of comparative advantage is taught in economics, not manufacturing or industrial engineering, and pertains to the benefits of free trade between countries, not work allocation among machines. The similarity is not obvious. This law is attributed to David Ricardo who published in 1817, based on an analysis of the production of wine and cloth in England and Portugal. Trade was free because, at the time, Portugal was under British occupation. Both wine and cloth were cheaper to produce in Portugal, but wine was much cheaper and cloth only slightly cheaper. England had therefore a comparative advantage on cloth, and the total output of wine and cloth was maximized by specializing England on cloth and Portugal on wine. You transplant that reasoning to your machine shop by mapping the countries to machines and costs to process times.

This simple approach works in a specific context. It is not general, but is of value because that context occurs in reality. The literature on operations research is full of more complicated ways to arrive at solutions in different situations. There is an article from IE Magazine in July, 2006 that I wrote about this entitled “Not-so-basic equipment: the pitfalls to avoid when allocating work among machines.” It used to be available on line for free on the magazine’s web site. Now you have to buy it on Amazon to download it.

By • Laws of nature • 0 • Tags: , ,

Jan 21 2011

Learning or experience curves

The following is a revision of a posting on NWLEAN in January, 2011 in response to Mike Thelen’s call for “Laws of nature” in manufacturing.

Learning curves are often mentioned informally, as in “there is a learning curve on this tool,” just to say that it takes learning and practice to get proficient at it. There is, however, a formal version expressing costs as a function of cumulative production volume during the life of a manufactured product. T. P. Wright first introduced the learning curve concept  in the US aircraft industry in 1936, about  labor costs; Bruce Henderson generalized in the experience curve, to include all costs ,  particularly those of purchased components.

The key idea is to look at cumulative volume. After all, how many units of a product you have made since you started is your experience, and it stands to reason that, the more you have already made of a product, the easier and cheaper it becomes for you to build one more. The x-axis of the experience curve is defined clearly and easily. The y-axis, on the other hand, is the cost per unit of the product, one of the characteristics that are commonly discussed as if they were well-defined, intrinsic properties like weight and color.  They really are a function of current production volume, and contain allocations that can be calculated in different ways for shared resources and resources used over time. The classic reference on the subject, Bruce Henderson’s Perpectives on Experience (1972), glosses over these difficulties and presents empirical evidence about prices rather than costs.

Assuming an unambiguous and meaningful definition of unit costs, it is reasonable to assume that they would decline as experience in making the product accumulates. But what might be the shape of the cost decline curve?  Engineers like to plot quantities and look for straight lines on various kinds of graph paper. Even before looking at empirical data, we can reflect on the logic of the most common types of models:

  1. In a plot of unit cost versus cumulative volume in regular, Cartesian coordinates, a straight line means a linear cost decline, which makes no sense because you would end up with negative costs for a sufficiently large volume.
  2. In a semi-logarithmic plot, a straight line would mean an exponential cost decline, which makes no sense either, because you could make an infinite volume at a finite cost.
  3. If you try a log-log plot, a straight line means an inverse-power cost decline, meaning, for example, the unit cost drops by 20% every time the cumulative volume doubles. This approach has none of the above problems. It represents a smooth decline as long as production continues, slow enough that the cumulative costs keeps growing to infinity with the volume.

I don’t know of any deeper theoretical justification for using inverse-power laws in learning or experience curves. Henderson, investigated the prices of various industrial products. I remember in particular his analysis of the Ford Model T, which showed prices from 1908 to 1927 that were consistent with a fixed percentage drop in unit costs for each doubling of the cumulative volume. The prices followed an obvious straight line on a log-log plot, suggesting that the costs did the same below.

Today, you don’t hear much about experience curves in the car industry, but you do in Electronics, where products have much shorter lives and this curve is a key factor in planning. When working in semiconductors, I remember a proposal from a Japanese electronics manufacturer that was designing one of our chips into a product. Out of curiosity, I plotted the declining prices they were offering to pay  for increasing quantities on log-log scales, and found that they were perfectly aligned. There was no doubt that this was how they had come up with the numbers.

The slope of your own curve is a function of your improvement abilities. Your market share then determines where you are on the x-axis. The higher your market share the faster your cumulative production volume grows. Being first lets you to grab market share early; being farther along the curve than your competitors allows you to retain it.

By • Laws of nature • 0

Little's Law concept

Jan 13 2011

Lead times, work sampling, and Little’s Law

On 1/11/2011, Michael Thelen asked in the NWLEAN forum about “laws of nature” as they related to Lean. This is based on one of my answers. 

Lead time is a key performance indicator of manufacturing operations, but how do you measure it? It is not a quantity that you can directly observe by walking through a plant. To measure it directly you need to retrieve start and finish timestamps from historical data, assuming they are available and accurate. Or you could put tracers on a sample of parts, which means that it would take you at least six weeks to measure a six-week lead time. In most plants, however, a quick and rough estimate is more useful than a precise one that takes extensive time and effort to achieve.

That is where work sampling and Little’s Law come in handy. The key idea of work sampling, which the Wikipedia article fails to make clear, is that lets you infer a breakdown of each entity’s status over time from snapshots of the status of multiple identical entities. If, every time you go to the shop floor, you see 2 out  of 10 operators walking the aisle, you infer that, on the average, each operator spends 20% of the time walking the aisle.

There are obviously necessary conditions for such an inference to be valid. For example, you want to take snapshots during normal operations, not during startup orshutdown, and the group you are measuring must be homogeneous: if it is comprised of two materials handlers and eight production operators, the 20% average is not interesting, even if it is accurate. Work sampling is usually described as applied to people, but the same logic is applicable to machines and to work pieces, and that is what makes it possible to infer lead times from snapshots of inventory and throughput rates.

On the shop floor, you can count parts, bins or pallets, and observe the pace at which they are being consumed. Let us assume we are in the context shown in Figure 1, and want to estimate how long we take to turn a blank into a finished good.


Figure 1. Context of Little’s Law

Little’s Law, then, says that on the average,  in steady state, within one process or process segment,

Inventory = Lead time X Throughput

The reason this is true is best explained graphically, as in Figure 2, in the simple case of constant throughput and lead time. The cumulative count of blanks in is a straight line going up over time, and so is the count of finished goods out, offset by the lead time.  The vertical distance between the curves is the number of blanks that have come in but not yet made it out as products, and represents therefore the inventory. The slope of each curve is the throughput, and it is clearly the ratio of the inventory to the lead time.

Figure 2. Little’s Law with constant throughput and lead time

What is interesting about Little’s Law is that it remains valid about averages when both rates of arrivals of blanks and departures of finished goods are allowed to fluctuate randomly about an average. This is probably the best known and most useful general result of queueing theory.

Since we can count inventory and measure throughput, we can infer average lead times from just this data. One snapshot will not give you an accurate estimate, but it is still considerably easier to take a few snapshots of a production line to get a more accurate estimate than it is to research history. The point is to get close to an answer that would take much longer to get if you actually had to be accurate.

By • Laws of nature • 2 • Tags: , , , , ,

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