Trend robust two-level factorial designs

Limiting the possible influence of time order effects may be an important consideration in designing a sequential experiment. We consider the problem of finding trend robust run orders of two-level factorials when the time effects are modelled via a first order autoregressive error model or via a time series model. In both cases, run orders are trend robust if the factors change level many times. Other run orders can be quite inefficient, even if they are free of low-degree polynomial trends. We present a simple algorithm for constructing run orders of two-level factorial designs with many level changes.