Abstract: Coal spontaneous combustion in goaf is one of the main disasters affecting mine safety.Index gases and coal temperature are the key parameters for the early warning of coal spontaneous combustion.The mathematical model between them and their statistical characteristics are the bases of constructing coal spontaneous combustion early warning system.Through temperature programmed control experiment,the gases concentrations curve of 88 groups of coal samples with coal temperature are obtained.The gas concentration is fitted by exponential function,polynomial function and Logistic regression function.R2 and SSE and MES are used as evaluation indexes to select Logistic regression function as the best fitting function.Logistic model is used to fit the curve of index gases to obtain the four parameters A1,A2,p and x0 of the CO and C2H4.Based on the statistical characteristics,the values of the above four parameters are determined and their validity is tested,and the constitutive equation of “gas-temperature” is obtained.Finally,based on the statistical characteristics,the first occurrence and inflection temperatures of gases with different indexes are summarized and the early warning indexes of coal spontaneous combustion are constructed.from the experimental results,it can be concluded that ① within the range of 30-350 ℃ experimental temperature,the variation of index gas concentration is divided into fluctuation section,stable section and attenuation section,and the gas concentration and coal temperature conform to Logistic regression model:the fitted parameters for CO and C2H4 were A1(CO)=23,A2(CO)=14 990,p(CO)=11,x0(CO)=294; A1(C2H4)=0.3,A2(C2H4)=27,p(C2H4)=17,x0(C2H4)=283.② CO initial temperature,first inflection point temperature,C2H4 initial temperature,first inflection point temperature,and C2H2 initial temperature can be used as the early warning indexes of coal spontaneous combustion with values are 30,158,120,204 and 285 ℃,respectively.③ Based on the initial temperature and inflection point temperature,coal spontaneous combustion is divided into 6 hazard levels:safety,low risk,average risk,greater risk,significant risk and mega risk.The corresponding response measures can be taken according to the different levels.