Computer-implemented systems and methods for generating generalized fractional designs
View Patent ↗A method and system for creating a design plan to test a product characteristic are described. One or more factors, level corresponding to the factors, and partitions for testing the product characteristic are determined. For each partition, an active matrix is generated. The product characteristic can be tested at each partition using the levels for the factors specified by the corresponding active matrix.
1. A computer-implemented method for causing testing of a product characteristic in a processing facility, the method comprising:
determining, by a computing device, (i) a plurality of factors corresponding to different parameters for testing the product characteristic, (ii) a plurality of levels corresponding to different settings of each factor, and (iii) one or more partitions for testing the product characteristic;
decomposing, by the computing device, the plurality of factors to generate a plurality of level sets, wherein each level set comprises zero or more levels assignable to each factor at each partition;
generating, by the computing device, a plurality of orthogonal arrays by distributing elements of each matrix using at least one Latin square matrix, wherein (i) each orthogonal array corresponds to a partition and (ii) an element of each orthogonal array indexes a level set from the plurality of level sets produced from the decomposition;
performing, by the computing device, at each of the partitions, steps comprising:
mapping each row of the corresponding orthogonal array to the plurality level sets to form a combination of level sets, wherein each row of the orthogonal array determines the formation of the combination by specifying the level sets to combine; and
concatenating the plurality of combinations of level sets generated from the rows of the orthogonal array to form an active matrix, wherein each row of the active matrix specifies a level of each of the plurality of factors for testing the product characteristic at the corresponding partition; and
causing, by the computing device, testing of the product characteristic in the processing facility that adjusts, at each one of the one or more partitions, the different parameters using the levels specified by the corresponding active matrix.
2. The computer-implemented method of claim 1 , wherein the one or more partitions comprise a plurality of points in time for testing the product characteristic.
3. The computer-implemented method of claim 1 , wherein each factor is associated with a type comprising one of a quantitative, categorical, discrete or ordinal type.
4. The computer-implemented method of claim 1 , wherein each orthogonal array has a size of p n-1 by n, wherein p represents the number of the one or more partitions and n represents the number of the plurality of factors.
5. The computer-implemented method of claim 1 , further comprising reducing each orthogonal array if a level set is an empty set with no elements.
6. The computer-implemented method of claim 5 , wherein reducing the orthogonal array comprises removing each row in the orthogonal array that includes an element indexing to an empty set of the plurality of level sets.
7. The computer-implemented method of claim 1 , wherein the active matrices for the one or more partitions cover all combinations of the plurality of levels for the plurality of factors.
8. The computer-implemented method of claim 1 , wherein each active matrix achieves orthogonality and balance.
9. The computer-implemented method of claim 1 , wherein the Latin square matrix is random.
10. The computer-implemented method of claim 1 , wherein generating the orthogonal arrays at the one or more partitions comprises:
a. determining the number of the one or more partitions (p) and the number of the plurality of factors (n);
b. forming a plurality of matrices A i based on a set X of cardinality p, wherein i ε[1,p];
c. creating a Latin square matrix of size p by p;
d. augmenting each of the plurality of matrices A i based on the Latin square matrix; and
e. repeating steps c to d if the number of columns of each of the plurality of matrices A i is less than n, wherein each of the plurality of matrices A i represents an orthogonal array.
11. The computer-implemented method of claim 1 , wherein the product characteristic represents a metric related to a pharmaceutical formulation and the plurality of factors represent parameters for testing the pharmaceutical formulation with respect to the metric.
12. The computer-implemented method of claim 11 , wherein the metric comprises stability of the pharmaceutical formulation.
13. The computer-implemented method of claim 11 , where the plurality of factors comprise one or more of an active pharmaceutical ingredient (API) concentration, a pH level, a methionine concentration, or a temperature level.
14. The computer-implemented method of claim 13 , further comprising selecting the plurality of levels for (i) the API concentration from within a range of 15 to 20 mg/ml, (ii) the pH level from within a range of 5.5 to 6.5, (iii) the methionine concentration from within a range of 5 to 15 mM, and (iv) the temperature level from within a range of 5 to 25 C.
15. The computer-implemented method of claim 11 , wherein the one or more partitions comprise a plurality of points in time selected from within a range of 0 to 36 months.
16. The computer-implemented method of claim 1 , wherein the product characteristic comprises a product feature, a process or a procedure.
17. The computer-implemented method of claim 1 , wherein each active matrix comprises one of an orthogonal or nearly orthogonal matrix.
18. A computer-implemented system for causing testing of a product characteristic in a processing facility, the system comprising:
a setup module for determining (i) a plurality of factors corresponding to different parameters for testing the product characteristic, (ii) a plurality of levels corresponding to different settings of each factor, and (iii) one or more partitions for testing the product characteristic;
a decomposition module for decomposing the plurality of factors to generate a plurality of level sets, wherein each level set comprises zero or more levels assignable to each factor at each partition;
an orthogonal arrays generation module for generating a plurality of orthogonal arrays by distributing elements of each matrix using at least one Latin square matrix, wherein (i) each orthogonal array corresponds to a partition and (ii) an element of each orthogonal array indexes a level set from the plurality of level sets produced by the decomposition module;
an active matrix generation module for generating an active matrix at each of the one or more partitions by:
mapping each row of the corresponding orthogonal array to the plurality level sets to form a combination of level sets, wherein each row of the orthogonal array determines the formation of the combination by specifying the level sets to combine; and
concatenating the plurality of combinations of level sets generated from the rows of the orthogonal array to form the active matrix, wherein each row of the active matrix specifies a level of each of the plurality of factors for testing the product characteristic at the corresponding partition; and
an implementation module for causing testing of the product characteristic in the processing facility that adjusts, at each of the one or more partitions, the different parameters using the levels specified by the corresponding active matrix.
19. The computer-implemented system of claim 18 , wherein each orthogonal array has a size of p n-1 by n, wherein p represents the number of the one or more partitions and n represents the number of the plurality of factors.
20. The computer-implemented system of claim 18 , wherein the orthogonal arrays generation module is further configured to reduce each orthogonal array if a level set is an empty set.
21. The computer-implemented system of claim 18 , wherein the product characteristic represents a metric related to a pharmaceutical formulation and the plurality of factors represent variables for testing the pharmaceutical formulation with respect to the metric.
22. The computer-implemented system of claim 21 , wherein the metric comprises stability of the pharmaceutical formulation.
23. The computer-implemented system of claim 18 , wherein the orthogonal arrays generation module produces the plurality of orthogonal arrays by:
a. determining the number of the one or more partitions (p) and the number of the plurality of factors (n);
b. forming a plurality of matrices A i based on a set X of cardinality p, wherein i ε[1,p];
c. creating a Latin square matrix of size p by p;
d. augmenting each of the plurality of matrices A i based on the Latin square matrix; and
e. repeating steps c to d if the number of columns of each of the plurality of matrices A i is less than n, wherein each of the plurality of matrices A i represents an orthogonal array.
24. The computer-implemented method of claim 1 , wherein the product characteristic comprises stability of a pharmaceutical formulation, and wherein causing testing of the product characteristic in the processing facility comprises causing adjustment, at each one of the one or more partitions, the different parameters comprising at least one of an active pharmaceutical ingredient (API) concentration, a pH level, a methionine concentration, or a temperature level.
25. The computer-implemented system of claim 1 , wherein the product characteristic comprises stability of a pharmaceutical formulation, and wherein the implementation module is configured to cause testing of the product characteristic in the processing facility that adjusts, at each one of the one or more partitions, the different parameters comprising at least one of an active pharmaceutical ingredient (API) concentration, a pH level, a methionine concentration, or a temperature level.