Multigrade,

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Multigrade,
Multivariable,.
Cusum Quality Control

• Ken W Day

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Multigrade, Multivariable, Cusum QC

• In October last year I gave a paper Concrete in
  the 22nd Century to the Concrete Institute of
  Australia Biennial, trying to look as far as
  possible into the future.
• Now however I have chosen to look into the past
  because my largest contribution to concrete
  technology is evidently still not universally
  understood.

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Multigrade, Multivariable, Cusum QC

• It took 25 years from the early 1950s to the late
  1970s to perfect my technique for analysing
  concrete compression test data.
• In the 25 years since then, the technique has
  spread widely as part of the ConAd QC program
• but still not fully incorporated in any national
  or international code of practice.
• So I want to take this opportunity to present its
  exact basic concepts.

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Multigrade, Multivariable, Cusum QC

• I need to present each of the three major
  components
• Multigrade,
• Multivariable
• Cusum
• and to add to them one further item
• Prediction from early age tests.
• I will take the three major components in reverse
  order

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Cusum cumulative sum analysis

• I did not invent cusum,
• It was developed in the UK chemical industry
  (Woodward and Goldsmith, 1964)
• first used for concrete QC in the UK in the 1970s
  (Testing Services, 1970).
• I started to apply it some six months later
  (independently of the Testing Services
  development).

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Cusum cumulative sum analysis

• Cusum involves subtracting a target value from
  each result and maintaining a cumulative sum of
  the remainders.
• Its main value is that it detects a change in a
  string of results about three times as quickly as
  a normal Shewhart Chart.
• Detection can be by mathematical analysis of the
  string of cumulative sums, or by graphing the
  cumulative sums.
• The graphical method is preferable because it is
  easier to detect and eliminate false changes due
  to testing error or abnormal circumstances.

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Cusum (cumulative sum analysis)

• My major contribution is to use the continuously
  updated current average of a variable as the
  target.
• This focuses the cusum on detection of change
  rather than adherence to a selected target.
• It also has huge significance for the ease of
  combining very large numbers of grades of
  concrete in a single cusum analysis.

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Cusum chart
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Use of V mask to detect change
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Cusum graph exhibiting false change
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Multivariable

• Multivariable relates to including graphs of
  other variables such as
• density,
• workability,
• temperature,
• tests on constituent materials such as cement
  strength and sand grading,
• also average pair difference of 28day results
  (to detect any deterioration in testing quality)
  all on the same sheet as concrete
  strength.

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Multivariable

• I started to do this in my first year in the
  concrete business (1952)
• but the idea still does not seem to have been
  fully accepted by the UK QSRMC (Quality Scheme
  for Ready Mix Concrete), even though I have
  presented papers there on two occasions.
• The concept is that changes in concrete strength
  will be mirrored in, and so confirmed and
  explained by, changes in one or more of the other
  variables.

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Multigrade

• Multigrade relates to combining the results of
  several (or many) grades of concrete in a single
  analysis.
• If done effectively, this gives an equivalent
  effect to increasing the frequency of testing
  many times over.

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Multigrade

• EN206, the European quality scheme, does this to
  a limited extent but makes hard work of it and
  has to limit it to a few similar grades of
  concrete.
• EN206 combines grades by adjusting or converting
  the results of other grades so that they can be
  analysed as though from a selected control grade.
  
• This requires initial and continued effort to set
  up and continually adjust the conversion process
  to be fully effective.

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Multigrade

• I have been happily applying my version to
  combining the results from hundreds of grades of
  widely different character with no human effort
  required (the computer does it all) for more than
  20 years.
• My technique is to cusum departures from the
  various current average values as though these
  were all from the same average value.
• While I was initially dubious of this, I have
  found that it works beautifully for strengths of
  20MPa or less to strengths of 100MPa or more, and
  including normal dense and structural lightweight
  concrete in the same analysis.

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Multigrade, Multivarible Cusum
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Early Age Prediction

• Normally early age means something of the order
  of 3 to 7days
• My contribution for normal results has been to
  recognize that a more useful prediction is
  obtained by adding the average gain to the early
  result than by assuming a percentage increase.
• This is because the early age result tends to be
  of a single specimen and to be subject to more
  than usual error. Applying a percentage increase
  multiplies the effect of any error.

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(No Transcript)
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The free QC program
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Free Programs

• I should warn you that the free programs are not
  likely to remain free permanently (other than on
  a demonstration basis) owing to a recent
  partnership between Contek, Shilstone and myself

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Early Age Prediction

• For very early results it is necessary to have a
  temperature history record and to express the age
  as an Arrhenius Equivalent Age (EA) rather than a
  physical age.
• The concept (and a competing but less accurate
  concept of temperature x time maturity) is well
  known but the usual technique is to construct a
  strength v maturity (or EA) graph, measure the
  maturity (or EA), and read off the strength.

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Early Age Prediction

• Construction of the calibration graph requires
  substantial effort
• A more serious fault is that this technique
  assumes that the concrete is the same as that
  used to construct the graph and so cannot react
  to changes in concrete quality and cannot be used
  for QC.

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Early Age Prediction

• I have devised a simple program that continuously
  and automatically feeds back and corrects the
  Arrhenius constants so that predictions of 28day
  strength (and any other desired age) based on the
  actual concrete in question can be obtained
  within a few hours.
• Such results can be used for QC where the
  additional expense of temperature monitoring is
  considered justified

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Combined Effect

• The real power of my overall system lies in the
  way that these separate elements combine
  together.
• It is the way I do cusum that enables such
  widespread multigrading,
• the use of cusum that links multivariables, and
• the use of multivariables to confirm and explain
  the detection of change.
• these features enable the detection and cause of
  change to be established several weeks earlier
  than most (all?) other control systems.

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Combined Effect

• The earlier detection and trend rectification
  itself reduces the overall variability of the
  concrete being produced
• and I have demonstrated that the number of
  results required to detect a given change is
  directly proportional to their basic variability.

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Availability of the Technique

• The technique was made substantially available as
  a Lotus spreadsheet in a series of 10 articles
  appearing bi-monthly in Concrete International in
  1988-89.
• Apart from this it has only been available as
  part of the ConAd computer program, marketed by
  the authors company, Concrete Advice Pty. Ltd.
  in the 1990s, and now, since the sale of that
  company, by Command Alkon Inc.

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Availability of the Technique

• To enable the basic technique to become a
  standard item, available to all, there is now a
  free program available on my website
  www.kenday.id.au.
• This program falls far short of ConAd in many
  respects but it does enable all the features
  presented here to be employed,
• with the exception that the multivariables
  available are limited to strength, density,
  slump, and temperature and only eight cusum
  graphs can be drawn.

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Specification of Concrete

• While not the subject of the current address, a
  few words on this subject may be helpful.
  Although it has taken 50 years in some cases, it
  seems that the whole world is coming to accept a
  view I have been presenting since the early
  1950s. In 1958 I wrote
• The only rational objective for any but 100
  testing is not to discover and reject faulty
  products but to ascertain the minimum quality
  level of the production.

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Specification of Concrete

• The article went on to assert that the only
  really fair and effective basis for quality
  regulation is the imposition of a cash penalty
  for marginally defective concrete based on a
  statistical analysis of test data.
• I am still of that opinion, even though (so far!)
  it does not appear to be shared by anyone else in
  the world.
• maybe another 50 years?

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Specification of Concrete

• An effective control system must have two quite
  separate and to some extent opposing features.
• One is to form a very accurate view of the mean
  strength and variability of the concrete supplied
  to date (no hurry).
• The other is to detect as quickly as possible
  when the quality of the concrete being supplied
  changes (no requirement for accuracy or
  infallibility).
• Any attempt to combine the two is likely to fail
  to accomplish either.

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Summary and Conclusion

• 1) Test data (including specimen density) should
  be entered in the system on the day it is
  obtained and visually assessed daily using
  automatically generated multigrade,
  multivariable, cusum graphs.

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Summary and Conclusion

• 2) Cusum analyses should use the constantly
  updated average values of all variables as a
  target rather than a specified target.

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Summary and Conclusion

• 3) Data should multigraded by cusuming these
  differences as though from the same mean rather
  than transforming results to a control grade.

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Summary and Conclusion

• 4) Data should include strength at 7days or
  earlier transformed into a 28day strength
  prediction by adding the current average gain.
  Prediction should NOT involve any assumption that
  a low early age result is likely to also show a
  lower subsequent gain.

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Summary and Conclusion

• 5) The daily assessment should include at least
  the first few rows of a table ranking all grades
  in order of departure of current and predicted
  mean strengths from their target values.
• 6) Cusums should include average pair difference
  of 28day results as an indication of testing
  quality.