## 1 Introduction
When analyzing the associated error of element random positioning, it is generally assumed that the impacts of an element's position errors show on the impact of amplitude and phase excitation errors. Hence, excitation with both phase and amplitude errors have a normal distribution profile, and the relationship that exists between variances and single electrical variables, like sidelobe level, was derived by employing a statistical approach [16; 17; 18; 19; 20]. But the impacts of random position error as a type of structural error cannot be quantified easily by phase and amplitude tolerances. Reference [14] introduced a statistical approach for quantifying the uncertainties in structural parameters and material properties affecting the performance of mmWave antenna arrays. The study utilized probabilistic methods to assess the sensitivity of antenna gain, beamwidth, and sidelobe levels to variations in structural integrity, providing valuable insights for robust antenna design and optimization. Reference [21] worked on symmetrical and asymmetrical bends' influence on antenna array performance. The impacts of antenna array plane distortions, which include potato chip, sag, Bessel, and sinusoidal profile, are presented in [22] (see Figure 1). However, [21; 22] took systematic error into consideration without accounting for the random position errors which are inevitable in fabrication and operation processes. Furthermore, some works were also tailored towards influences of random error, such as [23], which evaluated how active phased array (hexagonal) performance is impacted by random error (s), and they made useful guides available. However, systematic distortion was not considered in this work. References [24; 25] show that the influence of random error is the same as the effect of excitation current error (s), and random current errors (s) on antenna performance were critically looked into, but no direct relationship was given between random error and performance of the antenna. Furthermore, reference [26] estimated position error (s) in subarrays and its effect on array behavior employing theoretical statistical probability. In this method, many repeated computations are needed to determine antenna statistical performance. Refs. [27,28] present a linear relationship between systematic distortion and random error to evaluate their influence of array behavioral patterns. Conversely, in a practical sense, the numbers of systematic errors and random errors show a large variation; therefore, linear relationships mitigate random error impacts whenever there is a large variation between the two errors. Also, random error is stochastic in nature while systematic error is deterministic; the combined errors lead to random performance of electromagnetics. Therefore, whenever random error exists, it is better to determine the performance of EM from a statistical approach. This paper, therefore, proposes a method that employs array random positioning for an effective statistical performance assessment of the antenna array. Therefore, based on electromechanical coupling, a coupled structural-EM statistical model is proposed, and the model is verified using Ansoft HFSS model-based results. By considering the coupled effects of structural dynamics and electromagnetic behavior, we can develop more resilient and dependable mmWave antenna arrays capable of operating effectively in diverse conditions. Ultimately, this research contributes to the advancement of mmWave technology, enabling the realization of high-speed, reliable, and efficient wireless communication systems for a wide range of applications.