## 1 Introduction
Such static tests enable the verification of primary parameters such as generated thrust and pressure within the rocket motor casing. They also validate the system's safety and reliability, identifying potential failures or safety issues before flight tests are conducted [1]. A basic setup for conducting static firing tests on rocket motors includes a test stand, load cells, pressure transducers, other specific sensors (thermocouples, strain gauges, etc. ), and a data acquisition system. Figure 2 illustrates a typical configuration for measuring impulse on a test bench used for rocket motors' static tests (static firing). Figure 3 presents a typical performance curve of a solid propellant rocket motor, obtained through static tests and a data acquisition system. From the thrust graph exemplified in Figure 3, the total impulse is defined as the area under the thrust curve as follows:  
\[I_{t}=\int_{I_{0}}^{t_{1}}F\cdot dt \tag{1}\]  
Figure 2: An example of a rocket motor test firing stand. where \(I_{t}\) is the total impulse in N's, and \(F\) is the rocket motor thrust in N. Generally, numerical integration is performed to obtain the total impulse, and this computation might introduce errors. Indeed, it is well established that no measurement or test is perfect and that imperfections give rise to measurement errors in the result. Consequently, the result of a measurement is only an approximation of the value of the measurement. It is only complete when accompanied by a statement of the uncertainty of this approximation. According to ISOGUM [8], the uncertainty of the measurement result is a parameter associated with the measurement result that characterizes the dispersion of values that can reasonably be attributed to the measurand. Metrological reliability in the static testing of rocket motors is a little-explored field but is of great importance in aerospace engineering. Highlighting what was previously mentioned, static tests are fundamental for evaluating the performance of rocket motors before they are used in actual launches. The search for methodologies to increase the accuracy of thrust and total impulse measurements motivates studies focusing on sensor calibration and implementing advanced data analysis techniques to minimize errors and uncertainties. Recent research on the static testing of rocket motors highlights various advancements and methodologies. However, each measurement chain has intrinsic characteristics and requires specific analysis. The propulsion jet testing laboratory at the Brazilian Army Technological Center has a gap in determining uncertainties in the measurement system and using this information for compliance assessment. Studies focusing on developing and optimizing thrust measurement systems to evaluate rocket motor performance emphasize the need for accurate measurements using load cells and thrust stands [9; 10]. Another significant effort discussed the development of a static test bench that considered two thrust measurement axes arranged at 90\({}^{\circ}\)[11]. A study by [PERSON] et al. [12] also presented an approach to small-scale rocket motor thrust stand designs that emphasize the importance of accurate thrust measurements but address the topic without considering measurement uncertainty. [PERSON] et al. [13] presented an uncertainty analysis for thrust measurement of turbofan engines used in civil aviation, among other key insights. [PERSON] et al. [14] presented the uncertainty analysis of the thrust measurement system for axial force transmitted through an array of 10 load cells, five of which are under tension and five of which are under compression. Figure 3: An example of a typical rocket motor thrust curve. The total impulse is the area under the thrust curve and is generally calculated by numerical integration. [PERSON] and [PERSON] [15] analyzed hysteresis and uncertainty in Test Stand 500 at the NASA Marshall Space Flight Center East Test Area, a facility for testing hybrid rocket engines.