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在一系列假设的基础上，给出了安全监测系统单位时间内校验次数的泛函，用变分法求泛函极值，得出了校验费和损失费最小的校验周期数学模型．在校验费和损失费一定的情况下，当故障（泄漏）率较高时，校验周期应短些，反之则长些．根据安全监测系统和易燃易爆重大危险源常见的无故障工作时间的分布类型，给出了与之相应的校验周期数学模型的具体形式．计算实例说明，本模型是合理的，它对校验周期的确定具有一定的理论和实际意义．
Based on a series of assumptions, the functional of safety monitoring system is given, and the extremum of function is obtained by variational method. The mathematical model of calibration cycle with the smallest verification fee and the lowest penalty is obtained . In the case of certain verification fee and loss, when the fault (leakage) rate is higher, the verification period should be shorter and vice versa. According to the distribution types of common non-fault working hours in safety monitoring system and major flammable and explosive dangerous sources, the corresponding mathematical model of calibration period is given. The calculation example shows that this model is reasonable and has certain theoretical and practical significance for the determination of the calibration cycle.