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This paper proposes a modeling approach for characterizing the probability of wildfire ignition caused by faults on power distribution systems. The proposed model serves as a starting point in research literature to illustrate, from an analytical perspective, the many factors that influence wildfire ignitions in power distribution systems. This paper presents the series of events that leads to power-system-related wildfire ignitions, and characterizes the wildfire ignition probability as a combination of the probability that a fault occurs along a power distribution line segment, and the probability that the fault results in the sustained ignition of a vegetation fuel bed surrounding the line. The proposed model integrates a variety of data including environmental conditions, power system protection settings, and power system line flows. A case study is performed on a test 33-bus distribution system using observed historical weather data from a high-threat fire district in California. The California case study is utilized to investigate the effects of three primary factors (wind speed, line congestion, and protection settings) on wildfire ignition probability. [ABSTRACT FROM AUTHOR]