###### Abstract  
For the repair level and spare parts stocking problems, generally METRIC type methods and Level of repair analysis (LORA) are used separately. Since LORA does not consider the availability of capital goods, solving LORA and spare parts stocking problems sequentially may lead to suboptimal solutions. On these considerations, this study presents a joint optimization method to minimize the service logistics cost under the constraints of system availability. Maintenance capability factor and maintenance decisions are introduced into the joint optimization model to express the influence of multiple failure modes on repair level and spare parts stocking. Thus, we establish the bridge relationship between LORA and METRIC models. The joint optimization model is solved by an improved iterative algorithm, and a typical fleet system is taken as an example to verify the correctness and effectiveness of the model and the algorithm. Compared with the optimization of spare parts inventory and maintenance level independently, the joint optimization method could effectively reduce the service logistic system cost. f _applied_  
30 June 2021  
or many-to-one link [12; 13]. However, there are few hypotheses about component failure modes in the previous studies. Failure modes of fleet's components are complicated, because of high speed, heavy load, or strong impulse conditions [14; 15]. Maintenance resources and cost implications of different failure modes are different, such as when a fleet system is in the state of short circuit, the corresponding corrective repair time distribution may not be identical [16; 17]. Therefore, multiple failure modes should be considered simultaneously for analyzing the repair level of the fleet's components. Modeling the joint optimization of spare parts stocks and LORA, the structure of operating system and service logistics system needs to be defined separately. [PERSON] builds a nonlinear integer programming model based on the single-echelon repair network and two-indenture system structure [18]. The system unavailable time, spare parts waiting time, and fault repair time are taken into account in this model. [PERSON] applies the enumeration method to the maintenance decision flow model to solve the feasible solution of a single-indenture system [19], and then develops the system to a two-indenture structure and suggests an iterative algorithm for handling the joint problem of spare parts stocks and LORA [20]. For the multi-echelon multi-indenture system, some researchers started seeking the approximate solution of the joint optimization model. [PERSON] investigates the estimated domain spectrum of decision variables by simulating parameter value changes [21]. Based on the fuzzy method, [PERSON] proposes a multivariable fuzzy parameter convex optimization algorithm to solve the EBO (Expected Back Order) problem [22]. By comparing with the convex optimization algorithm and sequential methods, [PERSON] demonstrates the iterative algorithm superior [23]. In reference [19], the authors acknowledge two drawbacks in their work. The first is related to considering a symmetrical repair network (i.e., making the same decisions at all locations of a given echelon for each component and resource). The second is related to the simplifying assumption of infinite repair capacities. These are also the main shortcomings of current research. Maintenance capability is an important parameter of multi-echelon multi-indenture system optimization models; only one of them is usually considered in the modeling. [PERSON] et al. formulate maintenance capability uncertainty as a chance-constrained framework [24]. One important conclusion of this research is that a higher maintenance capability level ensures a higher availability of spare parts.