On the Sampling Distribution of the Mode and Its Use with Standard Times

The mode - the most likely value—of the distribution of task times is proposed as the definition of the standard time in certain nonmanufacturing applications. Three objectives of the use of time standards are discussed: personnel motivation and control, short-term work scheduling, and medium-range manpower planning. While the mean is the appropriate measure for the second and third, the mode may be preferable for the first. The sampling distributions of two estimators of the mode of the gamma distribution are investigated. A definition based on the maximum likelihood estimators of the distributional parameters is relatively easy to implement and has a much smaller sampling variance than the Pearson mode.