An arc discharge lamp starts usually through two steps, one is breakdown of gap and the other is glow-to-arc transition following the breakthrough.
If impurity gases exist, lamp starting voltage, namely, breakdown voltage and glow-to-arc transition voltage, increase. The impurity effect is represented as (E²-E₀²)/E₀², that means an increasing ratio of electron energy loss by impurity gas to that by dominant gas, is proportional to relative impurity gas density, where E and E₀ are the axial electric field strength of the discharge space containing and not containing impurity, respectively.
Using values of lamp starting voltage, it is able to determine relative density of impurity gas and also decreasing constant of impurity gas density in the discharge lamp operating with impurity getter action. For example, density of the impurity gas, N₂ in a 400 watt metal halide lamp decreases as n=n₀ exp (-t/3), where t is time (hours).

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By using the cumulative occurrence rate curve of the horizontal plane illuminance E₀ from an unobstructed hemisphere of sky, the rate of switch-off time duration can be estimated for a designated illuminance E, where switch on and offs occur too frequently. In practical integrated lighting design, however, the number of switch on and offs will have to be reduced. This is done by taking the designated illuminance width in stead of designated illuminance.
Taking this into consideration, E₀-cumulative occurrence rate and the number of switch on and offs are calculated once again from the original recorded data for each 10%, 20%and 30% illuminance width of designated E.
Based on these results, a utilization technique for integrated lighting design is presented. For a typical office room, the lighting engineer can easily estimate the rate of switch-off time duration. This estimation is made using a chart which is a combination of E₀-cumulative occurrence rate curves and daylight factor distribution curves in an office room.

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