## 1 Introduction
[PERSON] [39] conducted a process capability analysis of tooling components manufactured in a laser power bed fusion (PBF) machine. This work considered the possible correlation between the position of the part in the chamber and the measured profile deviations. Although local differences were observed, they followed different patterns for consecutive trays, and capability analysis was conducted considering all manufactured parts from three different trays as a single batch. Despite the experimental effort, machine performance or process capability studies still have to address some relevant circumstances. First, depending on the size of the part, the batch size and the available workspace, several parts could be manufactured within the same tray. This leads to the dilemma of considering AM processes as single-state [40; 41] or multi-state processes [40]. Nevertheless, this possibility has not been previously considered in the available literature, where parts have been manufactured under a \"single state\" assumption [32; 38] or under a one part-per-tray strategy [35]. Second, machine performance studies should be based on uninterrupted runs under normal operating conditions, which is a demanding condition in AM, where processes have frequently very slow cycle times, raw materials are provided in small volumes, and unavoidable critical operations (like warm-up or tray levelling) could violate repeatability conditions. Third, once the optimal process configuration has been employed in a performance analysis, there are limited possibilities of improving the results by means of a modification of such configuration. Taking these circumstances into account, the present work proposes the application of a multi-state machine performance perspective to reduce the achievable tolerance intervals of features of linear size in material extrusion (MEX) processes. The main steps of the proposed quality improvement methodology (Figure 1) are:  
* Statistical methods are used to analyse the dispersion and the location of the distribution of measured values between different states, to determine whether the production of a given geometrical feature should be treated as single-state or multi-state. * The results are used to determine the type of compensation that should be applied by means of a design for additive manufacturing strategy. * The 3D design files are modified to reduce deviations between manufactured values and theoretical values. * The variation in the achievable tolerance range, before and after the optimization of design, is evaluated by establishing a target machine performance index. The method proposed in this work is encompassed in the \"design optimization\" stage of the optimization framework described in [42]. More specifically, it could be applied as a previous step to a process capability analysis and serve as a guide for adjusting production to minimize the effect of machine-related inaccuracies. The objective of the proposed method is to reduce the achievable tolerance intervals in AM processes to make them a viable alternative to conventional processes. A feature of linear size (FoLS) [43] consisting of the external surface of a hollow right circular cylinder, manufactured in a MEX machine was selected as a case study. The paper is organized as follows: Section 2 describes the proposed method and the experimental plan. The results of the case study are provided in Section 3 and are discussed in Section 4. Finally, the conclusions of this work are summarized in Section 5.