A generalized probabilistic formula relating occupant behavior to environmental conditions

• The formula is derived from memoryless hypothesis and psychophysical function.
• It better represents the characteristics of environment-related occupant behavior.
• The coefficients u, l, and k in the formula can be assigned physical meanings.
• The formula was preliminarily validated using a real case of turn-on-light action.
• How to extend the basic formula to more complicated situations are described.

The occupant behavior (use of heating, use of air conditioning, use of light, opening of windows, adjustment of curtains and blinds, etc.) in a building is usually closely related to the environmental conditions. This paper presents a novel general mathematical formula for describing the relationships between such behavior and the environmental conditions based on a memoryless hypothesis and psychophysical function (Stevens' power law). Compared to existing formulas, the proposed formula is simple and harmonizes both the threshold and stochastic characteristics of an occupant's response to environmental stimuli. Preliminary test showed that the formula has good applicability and reliability. The proposed formula can serve as a basic reference for detailed modeling of an occupant's heating, air conditioning, lighting, window opening, and shading adjustment behavior in the future.