Trend-resistant and cost-efficient cross-over designs for mixed models

Abstract

A mixed model approach is used to construct optimal cross-over designs. In a cross-over experiment the same subject is tested at different points in time. Consider as an example an experiment to investigate the influence of physical attributes of the work environment such as luminance, ambient temperature and relative humidity on human performance of acceptance inspection in quality assurance. In a mixed model context, the subject effects are assumed to be independent and normally distributed. Besides the induction of correlated observations within the same inspector, the mixed model approach also enables one to specify the covariance structure of the inspection data. Here, several covariance structures are considered either depending on the time variable or not. Unfortunately, a serious drawback of the inspection experiment is that the results may be influenced by an unknown time trend because of inspector fatigue due to monotony of the inspection task. In other circumstances, time trend effects can be caused by learning effects of the test subjects in behavioural and life sciences, heating or ageing of material in prototype experiments, etc. In addition, the costs for using the subjects and for altering the factor levels between consecutive observations are also taken into account. An algorithm is presented to construct cost-efficient cross-over designs that are optimally balanced for time trend effects. The robustness of the computed run orders against misspecification of the covariance pattern is also investigated and a number of examples illustrate utility of the outlined design methodology.