Contributions to design of experiments

When using a fractional factorial design, some runs may be more difficult to implement than others. There may then be a need to use a fractional factorial design that does not contain any undesirable runs. As this should not go at the expense of the information that such a design can provide for the factorial effects of interest, it is important to develop techniques that provide alternative designs with the same information matrix for the effects of interest as a given design. This problem will be addressed for 2-level fractional factorial designs;One of the methods that will be considered is based on a relationship between this problem and the problem of trade-off in block designs. By exploring this relationship, the extensive results on t-trades can be used for construction of the desired factorial designs. This provides also additional incentive for the continued development of the theory of trade-off. We will also present two programs to generate fractional factorial designs that are information-equivalent to a given design;Based on a relationship between fractional factorial designs and balanced incomplete block designs, the ideas in the aforementioned programs will be used for a program to generate balanced incomplete block designs with various supports and support sizes, avoiding possible undesirable blocks. Finally, these ideas will also be used for two programs to generate [pi]PS sampling designs that satisfy requirements on the second-order inclusion probabilities, if any, and that avoid any undesirable samples in their support