A large number of specifications for concrete quality which are based on statistical data, limit the number of poor results in strength tests. The usual specification prescribes no more than V erroneous results out of n number of tests. The concept behind this specification is that the proportion of defective concrete in a structure must not exceed v/n. An attempt is made to show that if the number of tests n is small (as is often the case) there is a high probability that the proportion of defective concrete accepted according to the above rule, is greater than v/n. For example, if it is specified that no more than one test result out of ten can be erroneous and if 10, 20 or 30 tests are carried out, the probability of accepting a low-quality concrete (e.g. Concrete which is more than 10% defective) is 0.505, 0.375 and 0.302 respectively. On the other hand, the probability of eliminating a high-quality concrete, if more than one test result out of ten is found erroneous, is very low. For the cases cited above, the probability is 0.110, 0.106, 0.104 respectively. It is proposed that, in the case where a proportion of low-strength concrete equivalent, at the most to v/n is acceptable in a structure, the standard prescribed be modified so as to specify that no more than V-1 out of n test results be erroneous. Therefore the probability of an error of acceptance is reduced and becomes approximately equal to the probability of an error of refusal. With reference to the cases cited above, if the objective is to obtain no more than 10% defective concrete, the specification for ten tests must be that no result can be erroneous, for 20 tests no more than one result, for 30 tests no more than two results. Therefore the probability of an error of acceptance is 0.313, 0.236 and 0.200 respectively, while the corresponding probability for an error of refusal is 0.375, 0.274 and 0.226 respectively.

  • Corporate Authors:


    12 Rue Brancion
    75737 Paris Cedex,   France 
  • Authors:
    • Koufopoulos, T
  • Publication Date: 1972-9-10

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  • Accession Number: 00099603
  • Record Type: Publication
  • Source Agency: Laboratoire Central des Ponts et Chausees (LCPC)
  • Files: ITRD, TRIS
  • Created Date: Nov 18 1975 12:00AM