SPC Outside of Manufacturing | Quality Digest

Figure 11: Peak flow data 

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By characterizing the system as predictable up to Week 50, we learn that any single week having up to, and including, 14 requests is “normal.” This insight debunks the idea that two people can satisfactorily handle all requests in each and every week of the year (assuming, as stated above, that one person can be expected to successfully manage up to four or five requests in a given week).

The daily values—morning values at around 7 a.m.—are shown in Figure 11 in the postscript. To allow for fair and valid comparison, the values from Week 28 onward came from measurements before use of the inhaler.

Health Care

SPC Outside of Manufacturing

Part 7 of our series on statistical process control in the digital era

Using the phrase “voice of the process,” what is Figure 2 trying to tell us?

A key question was: Is there a difference in peak flow when using the inhaler? As with most data, these can be looked at and analyzed in different ways (for example, as individual daily values or grouped by week). The thinking process alluded to at the start of this article focused on finding the simplest way to best answer the question of interest, with emphasis on an effective communication of the outcome. This points us in the direction of a “good graph.”

Example 3:
Peak flow data: Weeks 14 to 27 show peak flow without use of an inhaler. Weeks 28 and on show peak flow with the daily use of an inhaler.

What can be learned by listening to the voice of the process?

Figure 9: Illustration of successive values being equal

• Another reason why so much was being made when Scott got involved was because the manager liked to make one prediction in the morning, make the product, clean the equipment, and that was it. 
• Question: Similar to the situation described in Example 1, how would you go about deciding whether “things stay the same” during the weeks and months ahead? Also, why were the limits narrower in Figure 4?

Example 3: Asthma management

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Important context is that we have close to 500 data values and are looking back over one and one-half years. With so many data, we decided to group them by calendar week and use the weekly averages as individual values. The control chart using this approach is shown below in Figure 10. If we’d had less data, it’s unlikely we’d have taken this route, which again illustrates the importance of context and the need for careful thought.

Our questions

We also see that, about half the time, weeks will be “easy” with five or fewer requests to be expected.

You take over a new group and would like to plan your team’s resources for the next year to most effectively respond to technical support requests. How many of your group’s resources should be assigned weekly to ensure high-quality support? If too few people are assigned, you likely won’t fulfill the customers’ support needs. If too many people are assigned, you risk leaving some resources sitting idle.

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This example is courtesy of Allen Scott, and it uses data on the daily sales of a meat product. Scott’s focus was on daily planning, i.e., How many units are needed on a daily basis? The aim was to plan better to minimize waste.

While the voice of the process tells us that up to 101 units can be needed on a given “normal day,” the approach taken by Scott prefers running low on items and perhaps on the occasional day in the year even running out (see Part 3 of the empirical rule discussed in Example 1). Scott’s safeguard was a guy on duty until closing who had access to a small, easy-to-clean grinder to make the odd unit as needed.

Figure 6: Annotated average and range chart with limits based exclusively on the “no inhaler” data

So far in this series our focus has remained on statistical process control (SPC) in manufacturing. We’ve alternated between more traditional uses of SPC that remain relevant in this digital era and discussing uses of SPC and its related techniques that are enabled by the marvels of modern technology.

We can’t predict an exact number of sales per day but rather a range of possible sales. With a view to estimating this range, daily sales for close to one and one-half months were plotted on a control chart of individual values, as seen in Figure 3.

In a first discussion you’re told 1) to expect about five requests per week; and 2) that one person can manage up to four or five requests in a given week. Naturally, you wonder whether one person on duty per week might be sufficient. Nonetheless, you decide to take a look at some data before moving toward any final decision. You request data from the last calendar year, which are shown in Figure 1. (No requests were handled in weeks 1 and 52.)

Listening to the voice of the process provides a lot more than “statistics,” which to some might seem of little consequence when it comes to what really matters in business. This voice provides insight to enable smarter work, not harder work.

As Scott told us, the workers had no idea of how many packages to produce daily. One of the workers who’d been there for 30 years routinely made more than 300 packages per day, yet, as we see in Figure 4, we can scarcely expect to sell more than 100 packages on one day unless something out of the ordinary happens (such as a special order, which is something nonroutine to specially plan for).

For the signals in weeks 7 and 15, some explanations were put forward—a holiday in Week 15, which is something nonroutine—but explanations as definitive as Covid-19 or a heart attack weren’t forthcoming. One weakness in the data around the time of the signals in weeks 7 and 15 was missing data. Another weakness was the long time lag—trying to find causes for events that happened close to one year earlier—which helps to explain the first rule of thumb mentioned above.

One “watch out” for the Fitbit data is therefore the occurrence of many consecutive plot points having identical values, which brings into scope the problem of “chunky data.” An example of a simple way to create chunky data would be to measure different people’s height to the nearest yard. In doing so, we’d mistakenly think many people were the same height, e.g., two yards. The resolution here would be to measure height to the nearest inch.

Figure 7: Histograms of the with- and without-inhaler peak flow data

In this example we’ve seen that SPC techniques can play a useful role in healthcare, contributing to better decisions while also involving the patient in the treatment process. For those wishing to learn more, one of many examples that discuss SPC techniques in healthcare is a paper by Boggs, P. B. et al., “Using Statistical Process Control Charts for the Continual Improvement of Asthma Care in the Journal on Quality Improvement (Vol. 25(4), pp. 163–181, 1999).

Example 4: Fitbit data

Figure 1 adds more insight to the “about five requests per week” because the occurrence of requests as high as seven and eight during weeks 2–11 tells you straightaway that one person per week is unable to satisfy your customers’ needs and expectations.

Next, you plot the data in time order on a control chart for individual values—also known as a process behavior chart—to gain yet more insight; more insight = better decisions. (See Figure 2.) You do this to examine:
1. Process behavior: Do the data indicate predictability, or consistency, in the weekly requests?
2. Range of variation: How many requests can be expected under “routine” conditions?

Having demonstrated that there is a difference when using an inhaler, we can estimate how big this is. The average increase in peak flow of 29 L/min is easily calculated and can also be shown visually in a histogram (Figure 7):

In Figure 8, we see a kind of “wavy” pattern—also indicative of autocorrelation for those familiar with the term, and for these data the lag one autocorrelation value is 0.76—because there are many cases of successive values being equal. We illustrate this in Figure 9 using a subset of the data; the highlighted points are those that have the same value as the previous point (25 of the 75 points are highlighted).

Figure 6 leaves no doubt: When using an inhaler, the result is higher peak flow values. This means that the airways in the lungs are open to a greater, and better, extent. Note that the “inhaler” data—right side of Figure 6—display predictable behavior (chart not shown), meaning that the upward shift was consistently sustained over weeks 28 to 36.

• There is one, and only one, signal in these 50 data, which is the count of 15 requests from week 51, the final working week of the year.
• The data themselves place an upper limit on “routine requests” at 14 (see the value of 14.12 for the upper limit, labeled UCL, which stands for upper control limit).
• This limit of 14 comes exclusively from the data and is an estimate of the highest number of requests to expect, or plan for, in a single week when things are “normal.”
• If, in any single week, 15 or more requests come in, the data give you a signal of something different having happened.
• The week 51 signal means that a cause, or reason, to explain this point above the limit should be identifiable: You learn that the last week of the year is said to be different because, for the customers who make the requests, it represents the final opportunity to close out all requests in the calendar year to meet deadlines and objectives.

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Aside from Week 51, the year can be characterized as predictable due to the consistency displayed by the data (i.e., there are no outliers, runs, trends, or shifts that characterize inconsistent behavior).

Having listened to the voice of the process, Scott and the team opted to go close to the average, with 60 packages per day as the “nominal target.” Depending on the stock level at the start of a new day, more or less units would be made to hit this nominal target.

Returning to the request we got to try to detect signals in the data, we indeed detected them and have again shown that control chart signals tell you about events, or changes, in your process that are worth knowing about. We’ve also highlighted an important “watch out”—chunky data. And, we’ve demonstrated that effective control charting can’t be automated because of the data-specific issues discussed above.

Figure 3: Control chart of the daily sales data