Steve Beeler

You have a goal…I have a way to get you there.

Statistical Sampling

Lake Michigan Water Levels

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Lake Michigan shore line

Record high Lake Michigan water levels and dune erosion have been big concerns along the “north coast” in recent years.  As beaches disappeared under the rising water, homes near the shoreline were threatened.

Barge with crane on Lake Michigan

Property owners resorted to armoring the coastline with huge boulders to dissipate wave energy.  In many cases, cranes on barges were required to place the boulders.

I finally got around to doing a statistical analysis on Lake Michigan water levels using data from the United States Army Corps of Engineers.  For years, control charts have been in my operations engineering toolkit.  Why not apply statistical process control to a natural phenomenon?

An X-bar & R chart is commonly used to measure the magnitude of common cause (random) variation and to assess statistical stability (constant probabilities).  For a sample plan, I used one data point per year in subgroups of five.  That is, each data point on the X-bar chart is an average of five years and each data point on the range chart is the difference between the highest and lowest value in that five-year period.  With 103 years of data (1918 to 1921), this sample plan provided twenty data points, the minimum required to calculate control limits.

Control chart of Lake Michigan water levels

The range chart (bottom) is in control.  All points are within the control limits and there are no trends.  This means the magnitude of year-to-year water level variation has been constant over the last 100+ years.

On the other hand, the X-bar chart (top) does not exhibit statistical control.  While it is mean centered with no trends, there are multiple points (4 above and 6 below) outside the control limits.  This suggests that the five-year sample plan has underestimated the range.  In other words, the within subgroup variation did not entirely capture the common cause (that is, random) variation in Lake Michigan water levels.

In retrospect, this is not surprising.  While 103 years seems like such a long time, it is not even an instant from a geologist’s perspective.  A sample plan with a longer duration appears to be called for but then there would not be enough subgroups to calculate control limits.

Given that the range chart is stable, I suspect that the X-bar chart (i.e., average water levels) would be too if we had data sampled over a sufficiently long period of time.

Others are interested in the Great Lakes.  Enough, apparently, to warrant a scientific publication, the Journal of Great Lakes Research.  In it, I found an abstract that supports my hypothesis of stable Lake Michigan water levels: “Historical Variation of Water Levels in Lakes Erie and Michigan-Huron” by Craig T. Bishop.

From this abstract I learned that the earliest “reliable” Great Lakes water level data were recorded in 1819.  From historical and archeological evidence, Bishop concludes that “… over at least the last 1,800 years, climate-related variations in maximum mean annual water levels have probably not exceeded those measured on Lakes Erie and Michigan-Huron since A.D. 1819.”

That sounds like Lake Michigan water levels have been stable for a long time.  In 2022 and again in 2023, the water is down from record levels and beaches are reappearing.  The spectacular sunsets never left.

Lake Michigan sunset

If you would like to perform your own statistical analysis on Great Lakes water levels, click HERE for a link to the United States Army Corps of Engineers data set.

Source Inspection for Zero Defects

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As the highest form of error proofing, source inspection for zero defects is such a powerful concept that it merits a close look.

Source inspection is 100% inspection, not statistical sampling, for causal factors that lead to defects. Defects are prevented through immediate action to remove causal factors. While this may sound complicated, it is not. In fact, examples of source inspection are everywhere around us.

source inspection for zero defects

The logic behind source inspection is pretty simple. Before completing an action of some kind, check for causal factors of defects. If causal factors are present, then the action is stopped before completion, and before the defect occurs.  With the causal factor(s) removed, the action can be restarted and completed without creating a defect.

Source Inspection

Everyday examples are all around us:

Automobiles. A little fender bender in the parking lot is a annoying defect. All vehicles with automatic transmissions have a safety interlock that requires the driver to have their foot on the brake pedal before shifting out of park.

On-line forms. In this case, the defect is missing information on an airline reservation, a catalog purchase, or whatever. Possible causal factors: error of omission or typographical error. Source inspection: if a required data entry field is empty, incomplete, or in the wrong format, the reservation or ordering process will not advance to the next screen until the field is filled correctly.

Thermocouples. A residential natural gas explosion would be a very bad defect. Possible causal factor: no pilot light. Gas water heaters, furnaces, fireplaces, and so on have thermocouples. If the pilot light is on, the thermocouple is hot and gas is allowed to flow. If the pilot light goes out, the thermocouple cools down and shuts off the gas flow.

With the explosion of sensors and connectivity in Manufacturing 4.o, there will be more and more opportunities to apply source inspection for zero defects.

Will source inspection make statistical sampling and control charts obsolete?  Absolutely not.  Use statistical process control to reduce causal factor variability to minimize interruptions and increase productivity.

Quality improvement is a big part of my day job as a Professional Engineer.  Visit my Operations Engineering page for methods and case studies.

 

Zero Defects

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In high-volume manufacturing, are zero defects achievable? For every dimension on every part in a complex assembly, probably not. But for key customer characteristics, a qualified yes.

A qualified yes because zero defects require 100% inspection but not all types of inspection can reduce and ultimately eliminate defects. Just working harder will not achieve zero defects…you also have to be very clever about it.

zero defects

For a statistically stable process with a high capability, the chance for a defect caused by common cause variation has been practically eliminated to less than one chance in the millions. This is a fine achievement. However, no amount of hard work can repeal the second law of thermodynamics. Entropy, or disorder, is always increasing…this is why leaves blow into your garage, not into lawn and garden bags. Defects can and will be produced by even the best processes.

Statistical sampling and control charts cannot guarantee that all defects will be detected. The second law ensures all stable processes will eventually be visited by a special cause and will produce defects. If the special cause is continuous, defective products produced since the last good sample will have to be found and repaired. If a special cause is intermittent, defects may or may not be found in the sampling plan.

Judgment inspection discovers defects and separates the good from the bad. Defects are contained but neither reduced or prevented. A quality system relying on judgment inspection tolerates in-system defects and their effects on downstream processes. Forever. Judgment inspection deserves its bad reputation as a low value added activity.

Informative inspection investigates the cause of defects and feeds the information back to the source. Defects are reduced but the quality system is still tolerant, to a lesser degree, of in-system defects. The effectiveness of informative inspection is proportional to the immediacy of corrective actions: the shorter the feedback loop the better.

Source inspection checks for factors that cause defects. Immediate action corrects problems before a defect can occur. Defects are prevented by controlling their causal factors Because special causes can never be eliminated, only through 100% source inspection and immediate corrective action can zero defects be achieved.

Terminology

Process Capability = the ability of a process that is in statistical control to consistently meet customer requirements