Efficiency effects of variation in controlled experimental variables

When a designed experiment is conducted, the exact levels of controlled experimental variables specified by the design may not be attainable. Two different types of situations can occur in which the actual settings of the design variables deviate from the target design settings. In one case, the actual settings obtained are unknown. In the other case, the actual settings are known; however desirable design properties such as orthogonality may have been lost. This paper examines the impact of known and unknown errors in experimental variables for designed experiments in which the response is assumed to be approximately linear in the region of interest. For comparison, the well known situation where the target values of the experimental variables can actually be obtained will also be considered.