Linear Congruential Generator Design

 

The linear congruential method is a pseudo random number generator calculated with a linear equation as shown below:

                                                                     

                                                                                                                               

  (2)

 

 

 

where a and c are the multiplier and increment parameters respectively,  m is the module and Zi is the remnant integer from the ration in the right-hand side of equation (2).

 

To generate an experimental design, each variable in the design was  initialized setting Z0 as a random integer number in a range from 1 to 3, where each value has a probability of 1/3. Multiplier parameter a and modulus m were set to values of 1 and 3 respectively. The increment parameter c was defined as a function of the random number generated (rng) as follows: c = (0 if rng < 1/3, 1 if 1/3 and rng <2/3, or 2 if rng 2/3) +1. A series of numbers were then generated to match the number of necessary regression coefficients to fit a full quadratic model plus one.  A balanced design -with as many columns as design variables and as many rows as regression coefficients plus one- is generated with this method.