Designing Experiments in Cycles

Experimental observations are frequently collected sequentially, allowing for lurking variables to affect the response and cause a trend in the results. Often the order in which the observations are collected is randomised to minimise the impact. However, when information about the behaviour of the trends has been found in previous experiments, it is possible to use this knowledge to obtain better designs that ensure that the studied relationship and the effect of the trend are estimated accurately. We consider cases where the cyclic nature of the experiments allows for obtaining such information prior to the main study. We propose a general methodology for designing such experiments, based on the framework of generalised linear models. The proposed methodology considers a larger class of problems than previously researched, allowing for the effect of a time trend on both the mean and variance of the response.