With the wide application of remote sensing image, users are increasingly demanding for position accuracy, so the stability of the line of sight (LOS) for remote sensor is more and more important. On the other hand, as camera system complexity increases, the iterative method of components' designing and modeling again and again is increasingly unable to meet the requirements of design. The stability of the LOS is a key indicator for the decomposition of overall into components in the remote camera. At present, many camera designs only have a uncontrolled positioning accuracy index or overall LOS stability index at the beginning, and there is no publicly available LOS index decomposition design method based on top-level design. To improve the efficiency of camera design and reduce design iterations, a Monte Carlo method is proposed to decompose the thermal stability index of the camera's line of sight.Using the linear optical theory and taking a certain camera as an example, CODEV is used to obtain the visual axis sensitivity matrix of the optical system (Tab.1). On this basis, in order to decompose the LOS thermal stability index into various mirrors, the six degree of freedom displacement values of each mirror are regarded as random quantities, and each random quantity is regarded as a uniform distribution within the allowable value, constructing a large displacement distribution of the mirror. Multiplying the displacement and axis of sight sensitivity matrix, countless LOS results are calculated. The allowable use of LOS system indicators is known, and the probability of meeting the requirements in the constructed data can be obtained through statistics. The more constructs, the more accurate the calculation. By continuously adjusting the allowable value of the six degrees of freedom displacement of the reflector, the allowable value of optical components that meet the indicators can be obtained, thus decomposing the overall stability index of the camera's visual axis into various components such as primary mirror, secondary mirror, and tertiary mirror.According to the LOS sensitivity matrix of a certain camera (Tab.1), it can be seen that the influence of displacement of different optical components on the optical axis is not equivalent. Overall, the six degree of freedom displacement of the primary mirror has the greatest impact on the change of the optical axis. The weight ratio of the unit angular displacement of the primary mirror, secondary mirror, and tertiary mirror on the optical axis is close to 10∶2∶1, and the weight ratio of the translation displacement on the optical axis is close to 3∶2∶1. It is more reasonable to decompose the opposite weight ratio into the thermal stability tolerance of each optical element. The rationality of weight allocation was also verified through Monte Carlo tracing. The probability of a random LOS change at [-0.45″ -0.45″] is 77.9% when the weight of the primary mirror, secondary mirror, and tertiary mirror is 1∶2∶20. When the weight is 1∶2∶10, the probability can be increased to 92%. However, by doubling the thermal displacement tolerance of the tertiary mirror to 0.5 seconds, the probability can only be increased to 95.5% when the weight of the primary and secondary mirrors is 1∶2∶5, greatly reducing the efficiency of improvement.In order to solve the problem of decomposing the accuracy index of complex camera uncontrolled positioning into optical components, a Monte Carlo decomposition method based on the sensitivity matrix of the line of sight was proposed using the theory of linear optical systems at small angles. By constructing the tolerance probability distribution of each optical element and calculating the probability of achieving CE90 for the axis of sight index, the displacement of the optical element is ultimately determined. A certain camera underwent indicator decomposition, and the results showed that as the sensitivity increased, the indicators of the primary, secondary, and tertiary mirrors were set in inverse proportion to the optimal result. The temperature control tolerance of the tertiary mirror designed based on the decomposition results is significantly larger than the other two mirrors. Finally, this article validated the accuracy of indicator decomposition using finite element simulation, and the results showed that indicator decomposition can effectively guide the design of component components and minimize ineffective thermal control margins to the greatest extent.