Introduction
The previous blog,
The Stonemont Quality KPI, focused on
explaining the
Stonemont KPI and the potential use of this value as a
measurement of risk associated with aggregate products, asphalt mixes, and
concrete mixes. In this blog, we will show
an example of using the KPI and the associated statistical measurements for an asphalt
mix design. While the discussions here
will focus on asphalt mixes, the same principals can be applied to aggregate
products and concrete mixes.
Stonemont software uses the KPI and the associated
statistics in several reports and analysis tools available in the program. One of these tools is “Mix Risk”, which uses
the Stonemont KPI to provide an evaluation of potential future performance of a
mix design prior to or during production of the mix. The Mix Risk tool is
available when performing any
blending of aggregates including asphalt and
concrete mixes.
What is Mix Risk?
When designing an
asphalt mix, you include multiple aggregate
components that presumably have been sampled and therefore have a measured
average gradation and variation or standard deviation. Sometimes the gradations for components used
in constructing asphalt mixes are developed from a limited number of samples
obtained within a short time frame. For example, a small set of samples are
obtained from a source stockpile, and the average of those samples is used for
the component when constructing a design. Since this is a small sample set, it
may not accurately represent the average or variation of the gradation. If the variation is too small it may result
in an artificial confidence in the mix. If
the variation is too large, it may serve as a safety factor to the mix design but
that can result in a less than ideal mix if it is changed to account for this
increase in variation. When possible, it
is best to use a set of samples over a longer time period that will better
reflect the true average and variation of the material.
Mix Risk uses a Monte-Carlo simulation to evaluate the mix
design considering the uncertainty with each of the component gradations as
defined by their means and standard deviations. A Monte-Carlo simulation is a mathematical
technique that relies on repeated random sampling to obtain numerical results
that allow the process (producing the mix) to be simulated many times
over. In
Stonemont software, Mix Risk will
create a set of randomly generated gradations using the mean and standard deviations
for each component and combine them using the percent each is contributing to the
design. The randomly generated gradations,
each of which represents a plausible combination of aggregates in the mix
design, are then analyzed using the Stonemont KPI.
Both the average and standard deviation values associated
with the component gradations are important. The average values are used to
construct a mix in an effort to reach some desired target value. However, the average value by itself doesn’t
reflect the variation associated with each component gradation. Therefore the
combined gradation of the mix will vary during production. Understanding how that mix may vary during
production from the average design is the key benefit of a Mix Risk analysis. The results of the Mix Risk analysis will
allow you to make informed decisions regarding the viability or risk of
producing the mix.
Asphalt Mix Example
An example might lend insight into the value of using the mix
risk tool. Figure 1 shows the
proportions for an asphalt mix. This mix
could be a new mix or it could be a mix already in production. For the purposes of this example, the
aggregate components are being produced and tested at a co-located quarry that
uses Stonemont Software so the data can be easily queried and updated. We are evaluating the mix to determine how
the component gradations are having an effect on the mix design. The percentage of each component has been
entered and is displayed in the “TMA” (Total Mass of Aggregates) column.
|
Figure 1. |
Figure 2 is another view of the same mix showing more
details of the blended result using the average grading of each component and
the percent contribution of each component. Each aggregate component gradation
was queried for the last 3 months in order to update the mean and standard
deviation values. Notice that the updated
blended result for each sieve meets the specifications and is generally close
to the target values. We could stop
here and go on with the belief that our mix will be or is being produced within
specification. However, we have not yet
accounted for the variability of each component.
|
Figure 2. |
Now it is time to run the Mix Risk tool to assess the
variability of each component for the purpose of evaluating the risk of the mix
being produced as non-conforming to specifications. As previously mentioned Mix Risk will create
a set of randomly generated gradations using the mean and standard deviations
for each component and combine them using the percent each is contributing to
the design. It is typical to have Mix
Risk generate several hundred or a thousand plausible blends. The results of a Mix Risk analysis are shown
in Figure 3. It is a good idea to scan
the KPI column for low KPI values, generally values below 90 or 95.
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Figure 3. |
In this case, the ½” sieve shows a KPI of 79 and therefore
warrants a closer look. Note that the ½”
sieve Ppk column shows a value of 0.46, which is below the 0.67 threshold
indicating the generated mean value of 69.1 is less than 2 standard deviations
away from the closest specification boundary (67.5). The Ppk/Pp value indicates that the mean is
significantly off-center in regards to the specification limits. As we discussed in the previous blog that
explained the Stonemont KPI, being less than 2 standard deviations away from
the closest specification boundary can increase the risk of producing non-conforming
material and therefore lower the percent within specification (PWS) value that
is routinely used as a basis for pay factors. The conformance to specification (CTS) and PWS
values are quite similar and this should be expected from the Mix Risk tool as
these gradations are mathematically generated and it is a large sample
size. A comparison between CTS and PWS
is most useful on production sampling results.
One of the most useful parts of the Mix Risk Analysis is the
ability to easily navigate between histograms to review the randomly generated
distribution for each sieve size in the mix.
The histogram for the ½” sieve is shown in Figure 4. You will notice that the left-tail of the
distribution is outside of the lower specification, which is a visual
representation of non-conforming results.
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Figure 4. |
Based on these results, we now understand that we have an
increased risk of producing non-conforming material due to the ½” sieve
size. If we look closely at the ½”
sieve, we will notice that the simulated standard deviation is a very
reasonable 1.17, which indicates that the mean value of the material is too
close to the specification boundary. If
this is a new mix the aggregate blend should be modified to try and shift the
final result on the ½” sieve to be greater than say 2.5% from the lower
specification boundary of 67.5 to reduce the risk of non-conformance. If this is an existing mix one may want to
investigate the cause of the mean shift away from the mix JMF. Although Mix Risk identified a potential or
possibility for increased risk of producing non-conforming material, it doesn’t
indicate that this mix won’t perform well or that non-conforming material will
even be produced. It does however give
you some potential insight to the possible costs of accepting this increases
risk because you may be able to use the simulated PWS and perform a
hypothetical pay factor calculation.
This may help better understand the risk in terms of cost.
James Beal
Adrian Field