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Reply to further comments on ‘Suggestions on the nomenclature of powder mixtures’
Powder
Technology,
35 (1983)
135
135 - 136
Letter to the Editor
Reply to Further Comments on ‘Suggestions on the Nomenclature of Powder Mixtures’
H. EGERMANN PharmaceuticaI Technology Division. Organic and Pharmaceutical Chemistry, Innsbruch, A-6020 Innsbmch. Innrain
Institute of University of 52 o (Austria)
(Received January 19,1983)
In his recent comments on powder mixing terminology, Thiel [l], essentially repeated the arguments previously given by Thiel, Lai and Hersey [Z]. He proposed the terms ‘random’ and ‘ordered’ to be used to differentiate between mixes of free-flowing, noninteractive constituents, and mixes of interactive powders, in which adhesion of a fine component to coarser carriers takes place. Accordingly, ‘ordered’ and ‘random’ may also be applied to incomplete mixes, where (T, the standard deviation of sample composition, is greater than ffn, the sample standard deviation of the fully randomized system [l, 21. Thiel [l] did not propose suitable suggestions as to how the manifold inconsistencies [3,4] which arise from this use of nomendature might be eliminated. Rather, he presented some ideas about quality control of powder mixtures, in particular about the problems he believes to exist in defining the boundary between pseudorandom (a = aa) and ordered (9 < aa): He mentions that s, the standard deviation found in spot samples, is only an estimate of 9, the standard deviation of the parent population; calculation of confidence limits for s implies normal distribution and is only possible on a certain Ievel of probability 1 - o, thus being associated with a probability cx of error. From this he concludes that it is impossible to prove that an ordered mix does exist in practice [l J. Following this argument, it is impossible to prove the quahty of any powder mix_ The existence of a limited probability LYof error is an overall feature of statistical quality
control. As a consequence, from the statistical view of Thiel [l], differentiation between (pseudo-)random and ordered is possible just on the same level of certainty, or uncertainty, as it is true for any quality control of powder mixes. In practice, confidence limits usually are calculated on a level 1 -(Y of 0.95, but any other level may also be chosen_ Another source of error, which Thiel assumes, is a non-normal, skewed distribution in pseudorandom mixes, which may arise from the presence of agglomerates of the fine component [l J_ This again is a surprising view, as agglomerates can exist in incomplete mixes ((5 > oa) only_ Pseudorandom mixes, by definition, show the standard deviation (TR which conforms to full monoparticular dispersicn of the constituents [3, 51. For incomplete mixes, however, where agglomerates actually may yield skewness of distribution [S, 71, Thiel, in striking contrast to his own view, suggests quantifying the homogeneity by the standard deviation s or some other statistical measure Ill_ The fact that so far no plain evidence of ordered mixes is available is not a consequence of the limitations inherent in statistical quality control. The major reason is that, in the present state of knowledge, ordered systems (a < oR) cannot be produced by means of actual mixing operations_ Recently, it has been shown [5] that for interactive powders the best possible mix is a pseudorandom mix, which has the same quality as the fully randomized system (a = oa)_ Experimentally, pseudorandom mixes have been produced under real mixing conditions (refs. in [3]). Thus, in contrast to Thiel [1 J, it is very important to have a terminology which allows clear differentiation from other types of mixes; on the one side, the best possible mix (0 = oa) must be defined against systems Of higher quality (o < oa), which, theoretically, may be realized by mechanical arrangement of the different particles into an ordered pattern. On the other side, distinction between (pseudo-)random (a = ua) and inCOmplete (0 > UR) may be very helpful in @
Ekevier
SequoiaJPrinied
in The
Netherlands
practical situations, e.g. in selecting adequate measures to improve mixing quality IS]. HoFever, one has to agree with Hersey and his co-workers [2] that additional terms are necessary which permit distinction between mixes of interacting constituents and mixes of free-flowing powders. Recently, ‘interactive mixture’ and ‘non-interactive mixture’ have heen proposed by Egermann and Orr [9 J_ These terms appear to. be superior to ‘ordered’ and to ‘random’. They meet more closely the actual situation, they do not refer to the degree of mixing, and they provide an unambiguous terminology of powder mixtures [9]_
References 1 W. J. Thiel, Powder Technol.. 33 (1982) 287: . 2 W. J. Thiel, F. Lai and J. A. Hersey, Powder Technoz-.28 (1981) 117. 3 H. Egermann, Powder TechnoZ.. 26 (1980) 235. 4 H. EgenGan. Powder TechnoZ.. 30 (1981) 289. 5 H. Egerrndnn,‘Powder TechnoL. 27 (1980) 203. 6 N. A. Orr and E. A. Sallam, J. Pharm. Phnrmac. 30 (1978) 741. 7 H. Egermann, ht. J. Pharm Tech. % Prod. Mfr. 3 (1982) 59. 8 H. Egermann, Volume of papers of the International Conference on Parmoceutical Powder Mixing, London, 17th Febrz&y 1982. 9 H. Egermann and N. A. Orr. (submitted to Powder Technology).
Technology,
35 (1983)
135
135 - 136
Letter to the Editor
Reply to Further Comments on ‘Suggestions on the Nomenclature of Powder Mixtures’
H. EGERMANN PharmaceuticaI Technology Division. Organic and Pharmaceutical Chemistry, Innsbruch, A-6020 Innsbmch. Innrain
Institute of University of 52 o (Austria)
(Received January 19,1983)
In his recent comments on powder mixing terminology, Thiel [l], essentially repeated the arguments previously given by Thiel, Lai and Hersey [Z]. He proposed the terms ‘random’ and ‘ordered’ to be used to differentiate between mixes of free-flowing, noninteractive constituents, and mixes of interactive powders, in which adhesion of a fine component to coarser carriers takes place. Accordingly, ‘ordered’ and ‘random’ may also be applied to incomplete mixes, where (T, the standard deviation of sample composition, is greater than ffn, the sample standard deviation of the fully randomized system [l, 21. Thiel [l] did not propose suitable suggestions as to how the manifold inconsistencies [3,4] which arise from this use of nomendature might be eliminated. Rather, he presented some ideas about quality control of powder mixtures, in particular about the problems he believes to exist in defining the boundary between pseudorandom (a = aa) and ordered (9 < aa): He mentions that s, the standard deviation found in spot samples, is only an estimate of 9, the standard deviation of the parent population; calculation of confidence limits for s implies normal distribution and is only possible on a certain Ievel of probability 1 - o, thus being associated with a probability cx of error. From this he concludes that it is impossible to prove that an ordered mix does exist in practice [l J. Following this argument, it is impossible to prove the quahty of any powder mix_ The existence of a limited probability LYof error is an overall feature of statistical quality
control. As a consequence, from the statistical view of Thiel [l], differentiation between (pseudo-)random and ordered is possible just on the same level of certainty, or uncertainty, as it is true for any quality control of powder mixes. In practice, confidence limits usually are calculated on a level 1 -(Y of 0.95, but any other level may also be chosen_ Another source of error, which Thiel assumes, is a non-normal, skewed distribution in pseudorandom mixes, which may arise from the presence of agglomerates of the fine component [l J_ This again is a surprising view, as agglomerates can exist in incomplete mixes ((5 > oa) only_ Pseudorandom mixes, by definition, show the standard deviation (TR which conforms to full monoparticular dispersicn of the constituents [3, 51. For incomplete mixes, however, where agglomerates actually may yield skewness of distribution [S, 71, Thiel, in striking contrast to his own view, suggests quantifying the homogeneity by the standard deviation s or some other statistical measure Ill_ The fact that so far no plain evidence of ordered mixes is available is not a consequence of the limitations inherent in statistical quality control. The major reason is that, in the present state of knowledge, ordered systems (a < oR) cannot be produced by means of actual mixing operations_ Recently, it has been shown [5] that for interactive powders the best possible mix is a pseudorandom mix, which has the same quality as the fully randomized system (a = oa)_ Experimentally, pseudorandom mixes have been produced under real mixing conditions (refs. in [3]). Thus, in contrast to Thiel [1 J, it is very important to have a terminology which allows clear differentiation from other types of mixes; on the one side, the best possible mix (0 = oa) must be defined against systems Of higher quality (o < oa), which, theoretically, may be realized by mechanical arrangement of the different particles into an ordered pattern. On the other side, distinction between (pseudo-)random (a = ua) and inCOmplete (0 > UR) may be very helpful in @
Ekevier
SequoiaJPrinied
in The
Netherlands
practical situations, e.g. in selecting adequate measures to improve mixing quality IS]. HoFever, one has to agree with Hersey and his co-workers [2] that additional terms are necessary which permit distinction between mixes of interacting constituents and mixes of free-flowing powders. Recently, ‘interactive mixture’ and ‘non-interactive mixture’ have heen proposed by Egermann and Orr [9 J_ These terms appear to. be superior to ‘ordered’ and to ‘random’. They meet more closely the actual situation, they do not refer to the degree of mixing, and they provide an unambiguous terminology of powder mixtures [9]_
References 1 W. J. Thiel, Powder Technol.. 33 (1982) 287: . 2 W. J. Thiel, F. Lai and J. A. Hersey, Powder Technoz-.28 (1981) 117. 3 H. Egermann, Powder TechnoZ.. 26 (1980) 235. 4 H. EgenGan. Powder TechnoZ.. 30 (1981) 289. 5 H. Egerrndnn,‘Powder TechnoL. 27 (1980) 203. 6 N. A. Orr and E. A. Sallam, J. Pharm. Phnrmac. 30 (1978) 741. 7 H. Egermann, ht. J. Pharm Tech. % Prod. Mfr. 3 (1982) 59. 8 H. Egermann, Volume of papers of the International Conference on Parmoceutical Powder Mixing, London, 17th Febrz&y 1982. 9 H. Egermann and N. A. Orr. (submitted to Powder Technology).