### Tolerance Allocation  
Reasonably allocating assembly tolerances is crucial in the complex precision product manufacturing process [28; 29; 30]. A rigorous tolerance can increase the assembly accuracy and enhance the product performance [31]. However, it requires more stringent processing and assembly requirements for products, thus resulting in significantly higher production costs and longer production cycles [32]. On the other hand, a loose tolerance can reduce the difficulty of the parts processing and product assembly, but it will decrease the assembly accuracy, reduce the assembly success rate, and adversely affect the final product performance [33]. Therefore, a proper tolerance allocation is needed to achieve the trade-off between the manufacturing cost and quality [34]. In general, tolerance is allocated on the basis of the experimental data, previous drawings, and expertise. In this context, manual approaches are common to check and assign the tolerance values on a trial-and-error basis [31]. To achieve a more efficient and sophisticated tolerance allocation considering both quality and cost issues, various methods of optimization steadily evolved [33; 34; 35]. To investigate the relation between manufacture cost and quality, [PERSON] et al. [36] proposed a concurrent tolerance allocation method, which established a nonlinear optimization model that simultaneously considered both the design and process tolerances. In concurrent tolerance context, [PERSON] et al. [37] proposed an efficient collaborative hybrid tool for computer-aided integration to an optimal tolerance allocation based on a combination of unique transfer and difficulty coefficient evaluation. [PERSON] et al. [38] integrated the process capability index into the product lifecycle cost and developed a flexible cost tolerance optimization model that simultaneously considers the part manufacturing costs, process capabilities, and quality loss factors and is designed to minimize the cost and to determine the reasonable tolerances. In the context of Industry 4.0, the requirement of products' sustainability services has been raised to a higher level. [PERSON] et al. [39] proposed a data-driven methodology to improve tolerance allocation using product usage data. Due to the nonlinear and multivariable quality of tolerance allocation models, optimizing and solving them can be challenging. According to literature research, two types of algorithms have been used to solve this problem. They are deterministic optimization algorithms and stochastic optimization algorithms [19; 31; 40; 41]. For the deterministic optimization algorithm, [PERSON] et al. [28] introduced the variable coefficient reciprocal squared model into the tolerance allocation model and solved the model using the Newton Iteration method. For the stochastic optimization algorithms, [PERSON] et al. [42] proposed a tolerance allocation model for interchangeable assemblies that employs the simulated annealing algorithm. [PERSON] et al. [43] employed a genetic algorithm to optimize the tolerances of the components in a gear system, aiming to achieve the desired assembly precision, minimum part rejection rate, and lowest manufacturing cost. Moreover, some scholars have employed intelligent algorithms, such as a Scatter Search [44], non-dominated genetic algorithm [45], and Monte Carlo simulation [46] to optimize the trade-off between the tolerance and cost. To ensure the final quality, a limit situation was considered in previous tolerance allocation methods, i.e., the final product quality should be guaranteed even if the assembly error of each process reaches the tolerance boundary. This causes each process' tolerance to be stringent, which is uneconomical. However, in actual assembly, each process' error does not usually reach the tolerance boundary but performs better than the boundary value in most case. Therefore, the as-built data measured during the assembly process have considerable value for reducing the assembly difficulty and cost.