Errors are common to the system. In safety-critical systems, quantitative analysis of errors is necessary. However, the previous reasoning and verification methods rarely consider errors. The errors are usually described with the interval numbers, so that the linear assertion was spread and the concept of linear error assertion was given. Furthermore, combined with the properties of convex set, a method to solve the vertices of linear error assertion was proposed, and the correctness of this method was proved. By analyzing the related concepts and theorems, the problem to judge whether there was implication relationship between linear error assertions was converted to the problem to judge whether the vertices of the precursor assertion were contained in the zero set of the successor assertion, so as to give the easy-to-program steps of judging the implication relationship between linear error assertions. Finally, the application of this method to train acceleration was given, and the correctness of the method was tested with the large-scale random examples. Compared with the reasoning methods without error semantics, this method has advantages in the field of reasoning and verification of systems with error parameters.

Aiming at the uncertain issue of the production plan in manufacturing industry, an optimal scheduling method which combined the prediction of maintenance point with the adaptive algorithm of genetic and simulated annealing was proposed. First of all, the Auto Regressive Integrated Moving Average model (ARIMA) was used to predict equipment failure rate; then the Weibull distributed model was used to reverse the equipment maintenance point in the future by equipment failure rate; finally, regarding the maintenance point as a constraint condition, the traditional production scheduling problem was solved by the adaptive hybrid algorithm of genetic and simulated annealing. The random scheduling situation of equipment for maintenance was analyzed in combination with the practical situation of the factory, and to determine the optimal scheduling scheme, the minimum makespan was regarded as a goal to obtain the scheduling plan of each task and maintenance point of each equipment. Experimental results show that the adaptive genetic and simulated annealing algorithm has good performance. In the production workshop of a certain factory in Hebei, the average failure rate of the equipment which used optimization scheduling method was relatively reduced by 3.46 percent than that before optimization.

In order to apply the Internet of Things (IoT) gateway to various scenarios, a light-weight rules engine was proposed, through which users can define personalized rules on demand. However, the limited resource for computing and storage prevents the traditional rules engine, such as JRules, being applied on the IoT gateway directly. By the "related facts" attribute added to each rule and the mechanism of "Agent-Inference", both the running time and the response time of the rules engine were reduced. Adding the "related facts" attribute to each rule can reduce the number of the rules involved in matching operations, and the mechanism of "Agent-Inference" can reduce the waiting time for available rules. Based on these methods, a Faster Light-weight Rules Engine (FLRE) was implemented and applied to IoT gateways. The experiments on different-size data sets showed that the running efficiency was increased by 8%-30% with adding "related facts" attribute, and the response time was decreased by 7%-35% with using mechanism of "Agent-Inference". The evaluation shows the two methods are effective to apply the light-weight rules engine to the IoT gateway.