## 1 Introduction  
All aspects of manufacturing such as machine investment cost, manufacturing cost, the functionality of the product, quality of manufacturing, and the reliability of the product directly connect with tolerance allocation. Hence, most of the researchers are still focusing on this research topic to improve manufacturing efficiency. It involves the allocation of critical dimensions of an assembly, known from the product's functional requirements. As per the literature, more equations are available based on the combinations of the component's tolerance values; however, few equations provide better results. Tolerance allocation requires discovering the best possible combination of the component's tolerances by considering the manufacturing objective(s) and the associated constraints. The researchers proposed different tolerance allocation strategies in different periods. The summary of those strategies is explained here. Further, the detailed comparison of the strategies is given in the Supplementary File as Table S1. Meta-Heuristic Method (MHM): In this method, the tolerance accumulation model, namely the root sum square (RSS) method [1; 2; 3; 4; 5; 6], was used to calculate the assembly tolerance value by summing the randomly picked discrete tolerance values. Initially, the discrete tolerance values were identified by splitting the process tolerance limits. Most of the researchers had applied the MHM such as simulated annealing algorithm [7] and genetic algorithm [8; 9; 10; 11; 12; 13; 14; 15; 16; 17] for this purpose. Heuristic Method (HM): The application of this method is seldom found in literature, since the usage of thumb rules, previous experiences, and standards [18; 19] in solving the tolerance allocation problems. Nevertheless, the alternative methods, namely the branch and bound algorithm [20] and design of experiments [21], were used to identify the effective tolerance allocation models. Further, a new method was developed by integrating HM with Tabu search for optimal tolerance allocation and subsequent manufacturing cost reduction [22]. [PERSON] (2020) [23] minimized the manufacturing cost of the mechanical assemblies by properly allocating the tolerances and choosing the right dimensional properties. [PERSON] et al. (2021) [24] proposed a computer-aided design model for analyzing the tolerance in manufacturing the mechanical assemblies. Discrete Cost Function (DCF) and Continuous Cost Function (CCF) Models: The researchers have used different cost function models [25; 26; 27; 28; 29; 30] in the various periods to evaluate the manufacturing cost. These models were classified as DCF and CCF based on their nature. However, the researchers mainly used the CCF model, since it yields closed-form solutions to the tolerance allocation problems. On the other hand, the DCF models [4; 26; 31] were not preferred due to the model fitting errors during the manual formulation. Further, several studies have been carried out by considering the objective function as the sum of quality loss (as per Taguchi quality loss concept) and manufacturing cost [1; 8; 32; 33; 34; 35; 36; 37; 38; 39; 40; 41]. Simple, Complex, and Non-Linear Assembly: The researchers used different tolerance allocation methods to obtain a solution concerning product type. For instance, the LMM was only used for simple products [1; 8; 42; 43], which have only two mating components. Several works have been reported on finding the optimum allocated tolerance values for the components of complex assembly [44; 45; 46; 47; 48; 49; 50; 51]. A limited number of authors have concentrated on non-linear assembly products that consist of more than two components [20; 26; 38]. Alternative Process Selection (APS): In practice, it is possible to produce components using more than one alternative process. It is necessary to select the proper process for the correct component to reduce the manufacturing cost.