For complex and durable products such as automobiles and construction machinery, the quality and reliability characteristics of these products become more and more complex. However, in many cases, the technical ability of users is not enough to perfect the daily maintenance of the product. Warranty policy plays an increasingly important role between manufacturers and users. Aiming at the problem that the availability of the two-dimensional (2D) warranty product is difficult to meet the actual needs of users during the warranty period, this paper makes use of the accelerated failure time (AFT) model to construct the failure rate function of the product based on imperfect preventive maintenance (PM), establishes the 2D warranty availability model and gives an effective solution. On this basis, this paper obtains the optimal PM interval with the numerical algorithm and particle swarm optimization (PSO) taking the maximal availability of the 2D warranty product as the optimization objective and compares the results and speed of the two algorithms. Finally, the validity and accuracy of the model are verified by a numerical example which provides a scientific basis for the manufacturer to formulate the 2D warranty strategy.

In practice, the assumption of failure independence between components is seldom valid, especially for those complex systems with complicated failure mechanism. Users can decide whether to purchase extended warranty (EW) at the end of basic warranty, and there are many factors that influence this decision, such as product reliability and EW price. In order to solve the problem of EW pricing for multi-component systems with failure interaction reasonably, considering the failure interaction characteristics between components of the multi-component systems, under the condition of type II failure interaction, this paper constructed a dependent failure rate model and developed a EW cost model of two-component systems. Thus, after optimizing the preventive maintenance (PM) strategy, this paper obtained the optimal PM interval when EW cost is the lowest, which is a win-win strategy to reduce the EW price for manufacturers and users under the premise of ensuring the manufacturer's profit demand. Finally, the validity of the model was verified by a numerical example and sensitivity analysis for important parameters was presented.

The implementation of a joint preventive maintenance (JPM) strategy for complex product systems can significantly enhance maintenance effectiveness during the warranty period, alleviate the manufacturer’s warranty burden, and empower users with greater autonomy in maintenance activities. However, inadequate task allocation may lead to reduced product availability and increased financial burden on the manufacturer. This study proposes a JPM strategy for two-dimensional warranted complex product systems, with preventive maintenance being regular imperfect maintenance. Furthermore, the research examines the dynamics of the two-dimensional failure rate function under JPM strategies, leading to the development of nuanced warranty cost and availability models, and further develops a cost-effectiveness model. In pursuit of optimizing cost-effectiveness, a decision optimization model is formulated. This model encompasses decision variables such as the two-dimensional preventive maintenance intervals along with the timing and frequency of manufacturer intervention in preventive maintenance. The approach employed combines pattern search algorithms and genetic algorithms for model solutions. Finally, a JPM strategy for large engineering vehicles was developed. Comparing the JPM strategy given in this paper with several other strategies, the results show that the proposed strategy can effectively reduce warranty costs, improve availability, and ultimately improve cost-effectiveness. Through sensitivity analysis, the research provides managerial recommendations to guide the implementation of the proposed JPM strategies.

In order to classify spare parts by machine learning method, it is necessary to reduce the dimension of spare parts because of the large number of characteristic indexes. An improved dimensionality reduction method for local preserving projection is presented in this paper. The model optimizes the parameters in local preserving projection dimensionality reduction by using kernel function parameter estimation method. The accuracy and efficiency of dimension reduction classification model are improved. Finally, through an example analysis, the simulation results show that the proposed dimension reduction method can solve the problem of spare parts classification better. It also improves the accuracy and efficiency of traditional classification methods.

In the field of modern industry, equipment is becoming larger and more complex. Some precision components, especially electronic components and mechanical components, will suffer from external vibration and shock and traumatic failures during operation. Therefore, the analysis of the failure process of multi-component system under the condition of common cause failure is of great significance to improve the guarantee efficiency of multi-component equipment system. When multi-component equipment system is running, the problem of traumatic failures of components under shock is not considered in the calculation of spare parts demand for the system. Based on the analysis of the correlation between equipment degradation failure and shock failure, a spare parts demand calculation model under random shock is established in this paper. Finally, the feasibility of the method is verified by an example. The simulation results show that the model can solve the problem of spare parts demand calculation of multi-component mechanical equipment under random shock.