Content By Donald J. Wheeler

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By: Donald J. Wheeler

This article tracks the progression of Covid-19 over the past six months on a state-by-state basis and provides a framework for interpreting these curves by including curves for seven other countries. While 52 states and territories are covered here, it turns out that there are just three basic stories told by the curves.

The world

In order to have a frame of reference for understanding the progression of Covid-19 within the United States we will begin with graphs showing the progression in some other countries. The values plotted for each country are the cumulative number of confirmed cases of Covid-19 per thousand population. These values were computed at the end of each calendar week. When these weekly per capita values are plotted for each of the 26 weeks between March 1 and August 29 we end up with the running records shown in figure 1. These curves allow us to compare levels between countries and also to see how these levels are changing over time. In this way we can see where the pandemic is growing rapidly and where it has been slowed down.

Donald J. Wheeler’s picture

By: Donald J. Wheeler

In past articles I have used graphs to provide perspective on how the Covid-19 pandemic is progressing around the world. In this article I shall update some of those graphs and use these historical data to make projections on what may be expected in the United States in the fall.

The worldwide pandemic

Figures 1 and 2 contain the weekly total number of new confirmed cases of Covid-19 worldwide reported by the European CDC. There we can see the first wave of the epidemic as it spread in and around Hubei Province in China. Next we see the second wave as this epidemic turned into a pandemic spreading rapidly through South Korea, Japan, Australia, Iran, Turkey, Western Europe, and the United States. Then starting in mid-May we see the third wave as Covid-19 began to show up in large numbers in other countries around the globe.


Figure 1: Weekly total numbers of new cases worldwide

Donald J. Wheeler’s picture

By: Donald J. Wheeler

Since the start of the Covid pandemic I have received many questions about how to analyze the Covid numbers using process behavior charts. Various schemes have been proposed and used. This column will discuss appropriate ways of analyzing data from epidemics and pandemics.

Now to be clear, in this article the term “data analysis” is distinct from mathematical modeling. Epidemiological models incorporate subject-matter knowledge to create mathematical models that are useful for understanding and predicting the course of an epidemic. These models allow the experts to evaluate different treatment approaches. While these models are generally refined and updated using the collected data, this is not the same as what I call data analysis. Data analysis can be carried out by non-epidemiologists. This occurs when people try to use the data to tell the story of what is happening. This article is about the analysis of the existing data by non-epidemiologists. Nothing in what follows should be construed as a critique of epidemiological models.

Donald J. Wheeler’s picture

By: Donald J. Wheeler

With data that come along one number at a time, it is easy to get lost in the details. To see the big picture, it helps to use a time-series graph that will draw your eye in the direction that your mind wants to go. These simple graphs reveal how the values are changing over time and thereby place each value in context, making them more easily understood. Here we will look at some time-series that provide a global perspective on the Covid-19 pandemic.

Comparable numbers

With 329 million people, the United States is the third largest country in the world. China and India have more than four times the population of the United States, and fourth-place Indonesia has only 82 percent of the population of the United States. These size differences make direct comparisons misleading, which is why data are often normalized and expressed as rates per million population. While these rates provide an equitable basis for making comparisons, the per-capita rates are one step removed from the original values. A conversion is required to turn these rates into values we can expect to see in practice. This conversion is not complicated, but it nevertheless creates an obstacle for readers to either hurdle or stumble over.

Donald J. Wheeler’s picture

By: Donald J. Wheeler

In May 2019, James Beagle and I published an article that contained tables for the analysis of mean moving ranges or ANOMmR (pronounced a-nom-m-r). By request of those using this technique, I have expanded these tables. This article contains these expanded tables and repeats the illustrative example from the earlier paper.

Say you have m measurement devices and you wish to know if these devices have equivalent amounts of measurement error. Also assume that each of these devices is used to repeatedly measure a standard item k times. When repeated measurements of a standard are placed on an XmR chart the resulting chart is known as a consistency chart. 



Figure 1: Consistency charts for instruments 1, 2, 3, and 4

 

With a consistency chart the moving ranges provide a measure of measurement error, and the average moving range may be used to estimate measurement error for each device. In the example used here we shall have m = 8 consistency charts, each based on k = 10 measurements of a standard.   

Donald J. Wheeler’s picture

By: Donald J. Wheeler

The daily Covid-19 pandemic values tell us how things have changed from yesterday, and give us the current totals, but they are difficult to understand simply because they are only a small piece of the puzzle. This article will present a global perspective on the pandemic and show where the United States stands in relation to the rest of the world at the end of the third week in June.

Here we will consider 27 countries that are home to 5 billion people (67% of the world's population). According to the European CDC database, which is the source for all of the data reported here, these 27 countries had more than 75 percent of the world’s confirmed Covid-19 cases and 86 percent of the Covid deaths as of June 20, 2020. So they should provide a reasonable perspective on the worldwide pandemic. Figure 1 lists these countries by region and gives the relevant Covid-19 counts and rates as of June 20, 2020.


Figure 1: Countries used for global summary

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By: Donald J. Wheeler

Setting the process aim is a key element in the short production runs that characterize the lean production of multiple products. Last month in part one we looked at how to use a target-centered XmR chart to reliably set the aim. This column will describe aim-setting plans that use the average of multiple measurements.

The necessity of process predictability

All effective aim-setting procedures will be built upon the notion of a process standard deviation. Some estimate of this process dispersion parameter will be used in determining the decision rules for adjusting or not adjusting the process aim. When a process is operated predictably this idea of a single dispersion parameter makes sense.


Figure 1: When statistics serve as estimates

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By: Donald J. Wheeler

Lean production of multiple products is built on the assumption that the process aim can be properly set for each short production run. This article will describe how to set the process aim so that your short production runs can be on target.

In a lean production environment, without a bank of in-process inventory to cushion the impact, and without adequate lead time to allow for reworking or refabricating the product, a single off-target run can shut down an assembly operation and create a massive pile of unintended, in-process inventory. (I once saw 25 jumbo jets parked outside their assembly building. When I asked why they were parked there, I was told that they were all waiting for parts—a billion dollar pile of in-process inventory!)

Aim vs. consistency

A plant had three suppliers for a piece of wire. When a shipment arrived they collected a sample of five pieces and measured their lengths. These five values were subgrouped together and placed on an average and range chart. The charts for each of the three suppliers, drawn to the same vertical scale, are shown in figure 1.

Donald J. Wheeler
By: Donald J. Wheeler, Al Pfadt

Each day we receive data that seek to quantify the Covid-19 pandemic. These daily values tell us how things have changed from yesterday, and give us the current totals, but they are difficult to understand simply because they are only a small piece of the puzzle. And like pieces of a puzzle, data only begin to make sense when they are placed in context. And the best way to place data in context is with an appropriate graph.

When using epidemiological models to evaluate different scenarios it is common to see graphs that portray the number of new cases, or the demand for services, each day.1 Typically, these graphs look something like the curves in figure 1.


Figure 1: Epidemiological models produce curves of new cases under different scenarios in order to compare peak demands over time. (Click image for larger view.)

Donald J. Wheeler
By: Donald J. Wheeler, Al Pfadt, Kathryn J. Whyte

This article is an update to “Tracking Covid-19” that Al Pfadt, Kathryn Whyte, and I wrote last week. In that article we summarized what is known about Covid-19, what has already happened, and what is to be expected based on the analysis of the data and the epidemiological models.

Over the past week the curve of Covid-19 infections in the United States has slightly flattened. Here are updated graphs of the actual data and new projections for what we can expect in the next few weeks.

Figure 1 shows the number of confirmed cases of Covid-19 in the United States as of 7 a.m. each day. These are the values posted by the European CDC at noon London time, and so they are slightly smaller than some other values that are reported later each day.



Figure 1: Number of confirmed Covid-19 cases in the United States