How many combinations of tests would be there for example, if a can take values from 1 to m b can take values from 1 to n c can take values from 1 to p a, b and c can take m, n and p distinct values respectively. What are the total number of pairwise combinations possible?With a pairwise testing tool that I am testing, I am getting 40 results for m = n = p = 6. I am trying to mathematically understand how I get 40 values.

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How many combinations of tests would be there for example, if  a can take values from   1 to   m  b can take values from   1 to   n  c can take values from   1 to   p  a,   b and   c can take m, n and p distinct values respectively. What are the total number of pairwise combinations possible?With a pairwise testing tool that I am testing, I am getting   40 results for   m  =  n  =  p  =  6. I am trying to mathematically understand how I get   40 values.

Dominique Holmes · Accepted Answer

You are looking for strength 2 covering arrays. In each pair of columns every pair of symbols occur -- this ensures all 2-way interactions are observed in some way. Here&#039;s a very simple example of a covering array of strength 2 with 2 columns:                    11                            12                            21                            22                            12                                123456                            612345                            561234                            456123                            345612                            234561            If you look at each entry and write the list (r,c,s), where r is the row index, c is the column index, and s is the symbol, you will construct an orthogonal array (as depicted below) -- a covering array of strength 2 with the minimum number of rows (36).                    111                            122                            133                            .        .        .                            661            In fact, Latin squares exist for all orders n. So if you have three columns (e.g. three variables) and n symbols for each variable, then you can always find a strength 2 covering array with n2 rows.Many combinatorial designs give rise to particularly efficient covering arrays. Strength 2 covering arrays with more than three columns and n2 rows are equivalent to sets of mutually orthogonal Latin squares (the reference shows the construction).In your case, if you have 40 results, then you are not using the most efficient covering array.

Alessandra Clarke · Accepted Answer

If each parameter had   10 choices you&#039;d be testing   300 vs   1000 combinations, namely hold   a constant and vary   b  ,  c through   10  ⋅  10  =  100 values. Similarly hold,   b constant; then   c. As the number of variables   k increases you get better savings, roughly   (  k  N      )    2   vs.       N    k  , where   N  = max domain size. For QA purposes usually such rough upper bounds suffice. Do you have an intended application where you need something more precise? If so perhaps you should reveal some further details, e.g. the distribution of the sizes of the domains, etc.

How many combinations of tests would be there for example, if a can take values from 1

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