By Phillip Cutler, P.E.
Editor’s Note: This is the third article in a year-long series that focuses on the details and more technical aspects of one common thing precast concrete producers do on a daily basis.
When we mention statistical analysis of test results, most people likely cringe, but some brave souls might jump at the opportunity to dive into a data set to see what is happening in various processes of batching and fresh concrete testing. Either way, it’s an important topic worthy of discussion as it directly impacts the quality of our concrete.
For this example, we will investigate test results and batching data for a 5,000-psi self-consolidating concrete mix design over a 12-month period. There were 40 discrete data points in this population with a complete batch plant ingredient print out and a full set of plastic concrete test data for each. Data points were pulled from plant records as few as twice per month and as frequent as seven times per month over this population.
Before we dive in to the statistical analysis, let’s familiarize ourselves with terms and definitions.
Mean – There are several kinds of mean in various branches of mathematics (especially statistics). For a data set, the arithmetic mean, also called the mathematical expectation or average, is the sum of the values in the population is divided by the number of values in the population. The mean is represented as X-bar.
Standard deviation – In statistics, the SD, also represented by the lower-case Greek letter sigma σ, is a measure that is used to quantify the amount of variation or dispersion of a set of data values.
X-bar chart and R chart – An X-bar chart and R chart is a pair of control charts used with processes that have a subgroup size of two or more. The standard chart for variables data, X-bar and R charts help determine if a process is stable and predictable. The X-bar chart shows how the mean or average changes over time. The R chart shows how each data point in the subgroup changes over time and is also used to monitor the effects of process improvement theories.
Upper control limit – The UCL is a pre-established value, and in this case, it will be set by the mean plus 3 standard deviations of the population.
Lower control limit – The LCL is a pre-established value, and in this case, it will be set by the mean minus 3 standard deviations of the population.
Concrete density (unit weight)
Our first set of charts illustrates control chart plots of concrete density or unit weight (lb./ft.3) tests. A plot of these test values is of particular interest and importance to the plant as a direct measure of concrete yield. When a producer batches a load of concrete, they expect to fill a form or series of forms with that load. If the batched concrete density is lower or higher than expected, the batch will produce over or under the target relative yield value, respectively.
Looking first at the X-bar chart (Fig. 1), we see one concrete density data point below the LCL and at least three additional significant spikes in the values for density. The remainder of the data points fall fairly close to the mean value. We also note that the mean of this population is slightly above the target value set by the mix design. While we expect to see some variability in the actual test results from day-to-day, points outside of the calculated control limits are opportunities for further investigation by plant quality personnel. The first dip below the LCL should be investigated. Starting at point 15, there are 6 successive values above the mean, which should also trigger a closer look.
Fig. 1: X-bar chart showing the unit weight of each sample in comparison to the mean unit weight of the entire population.
Looking at the R chart in Fig. 2, we see the ranges of unit weight from point to point. Again, we recognize an opportunity to investigate the root cause of nearly a three-pound-per-cubic-foot difference in consecutive weeks. Looking beyond the major spikes in the range chart, it appears that the process is fairly predictable and slightly over target.
Fig. 2: R chart showing the change in unit weight values (lb./ft.3) compared to the mean change for the entire population.
Compressive strength
Next, let’s take a look at the compressive strength for overnight, 7-day and 28-day time durations (Fig. 3). At first glance, we see that with the exception of the last data point, the concrete reaches reasonable and generally adequate overnight stripping strengths. There are at least three points of interest on the plot of the overnight break values that would be considered for further investigation, which are Sample Number 11, 14 and 40, representing values of 4,050 psi, 4,250 psi and 1,792 psi, respectively.
Fig. 3: Compressive strength values at 1 day, 7 days and 28 days for each sample.
The 7-day and 28-day strength plots exhibit similar trends but there appears to be greater variation in the 28-day breaks beyond data point number 29. In addition, the 7-day break line indicates that the process is predicting less than the 5,000-psi design strength consistently from data point 19 through point 29. The 28-day plot is fairly consistent until data point 29 where the process indicates more unpredictable results.
Using the R chart (Fig. 4) and plotting the point-to-point change in 28-day compressive strength, we illustrate the variation of the 28-day strength values over the year. If we neglect points 30 and 31 initially, we see that the 28-day strength values are predictable and fairly consistent within a range of approximately 300 psi. Looking at the entire data set indicates that there is some type of process anomaly occurring at points 30 and 31 resulting in values above the upper control limit. This represents an opportunity to conduct further investigation on possible root causes.
Fig. 4: R chart showing the change in 28-day compressive strength values (psi) compared to the mean change for the entire population.
Aggregate moisture content
Our next set of data to investigate is aggregate moisture content. In Fig. 5 we see values for 3/8 inch stone, 3/4 inch stone and sand plotted from January through December. As expected, the moisture contribution from the fine aggregate is significantly higher than that of the coarse aggregate. In addition, we see the coarse aggregate moisture content has significantly less variation than the fine aggregate.
Fig. 5: Total aggregate moisture contribution by the 3/8 stone, 3/4 stone and sand, per batch.
Investigating further, we again look to the R chart (Fig. 6) to illustrate the variation. The variation in the fine aggregate moisture content is significant, making predictability difficult if not impossible in our example. There does not appear to be a correlation in the three parameters we have investigated thus far. However, there are many more possibilities and parameters that can be plotted together.
Fig. 6: R chart showing the change in aggregate moisture content (lbs.) from sample to sample.
Interaction of variables
In some analyses it is not readily apparent that there may be an assignable cause of the variation in the test data as shown on the either the X-bar or R chart. These cases encourage us to take a deeper look at the data for a possible correlation between multiple test parameters. For example, as shown in Fig. 7, two variables – unit weight and air content – are plotted together on the same graph. Our first observation is that the density and air content are tracking together. For some samples, both the unit weight and air content appear to rise and fall simultaneously, while other samples exhibit the opposite behavior. Is this a characteristic of this particular mix design or all mix designs used at the plant? Should we be seeing a different relationship? What is this correlation telling us? Can we determine an assignable cause or do we look elsewhere?
Fig. 7: Comparison of unit weight (lbs./ft.3) and air content (%) of each sample.
Benefits of statistical analysis of test data
The benefits of performing statistical analysis of test data are sometimes not obvious. Plants can identify reasons for changes in their batch and continuously refine processes to drive variation to zero. Refining your mix design over time can save money on raw material cost and make processes more predictable and reliable. Certified plants are required to perform concrete testing, so why not use the data you’re already collecting to your advantage? The odds of determining the root cause of a process problem by analyzing test data is significantly higher than by random sampling alone. The data – especially when presented visually, as in graphs where trends and outliers are more obvious – will point you toward the cause of the anomaly, help refine your decisions and make the appropriate changes.
Plants that use test data and perform statistical analysis to investigate process variation with the goal of driving their process variation closer to zero are performing a continuous improvement activity. NPCA Certified Plants participating in continuous improvement activities in Section 1.1.4 of the NPCA Quality Control Manual for Precast Concrete Plants would earn an additional point toward their audit score by performing this analysis on a regular and ongoing basis.
All of the plots in this example were generated using the standard functions in Microsoft Excel. There are many statistical analysis software programs on the market that can be used to perform data analysis. There are also add-ins available that can enhance the performance of Excel for this purpose.
A special thanks goes to Scituate Concrete Products for sharing a portion of their batch and test data in support of this article.
If you have questions, contact Phillip Cutler, P.E., director of quality assurance programs.
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