## 1 Introduction
Controlling the phase composition is an important factor, as well, since the presence of different phases (tetragonal, monoclinic, cubic) affects the mechanical properties and stability of the material. Optimization can be performed by minimizing or maximizing some objective functions, such as stiffness, mass, etc. [19]. Similarly, it is crucial to keep repeatable processing conditions to fabricate sintered ceramics with reproducible properties [20]. However, on the microscopic scale, random variation in strength may occur due to the randomly distributed microdefects that are common in quasi-brittle materials in terms of spatial arrangement, orientation, size, and shape [21]. Thus, it is convenient to estimate the likelihood of the crack propagation as a measure of the material's fracture resistance. Weibull analysis (WA) is a statistical analysis widely used in reliability applications to identify failure modes [22; 23]. It is an effective technique for obtaining material reliability results at a moderately low rate, with the reliability of the material or component being assured [24]. The Weibull modulus of aggregate tensile strength distribution is correlated to the heterogeneity of particle binding force distribution within the aggregate. The sensitivity of the Weibull modulus to detect small differences in the internal structure of aggregates depends on the standardization of aggregate shape and sphericity. The Weibull modulus is highly sensitive to the heterogeneity of particle binding force distribution within the aggregate. An increase in the heterogeneity of the particle binding force distribution results in a linear decrease in the Weibull modulus of the aggregate tensile strength [25]. The two-parameter (2P) Weibull distribution function, based on scale and shape parameters, is the most commonly used statistical model for characterizing the strength of modern ceramics [26]. The primary benefit of Weibull analysis is that it facilitates the analysis of failures, even with limited data samples. It also provides a graphical representation of the individual failure modes that can be readily interpreted, as well as an indication of the failure physics (based on the slope of the distribution). The probabilistic strength description parameters obtained from the Weibull distribution should match the observed material microstructure. Indeed, the Weibull distribution has been successfully used to describe the fracture strength of microscale materials such as silicon and composite-reinforcing fibers and has been used to a lesser extent for thin films, nanotubes/wires, and 2D materials [27]. The Weibull distribution has been extensively utilized in the fields of reliability analysis and durability testing of a wide range of industrial products. This distribution has been found to provide an effective representation of the degradation trajectory or the form of material failure. Additionally, it has been demonstrated to assist in addressing the challenges posed by uncertainty and randomness in damage caused by internal defects in brittle materials [28]. Despite significant success reported on the zirconia ceramics research, the mechanisms of its performance are not yet fully established. For instance, it is necessary to ascertain the details of the microstructural transformation and stability-dependent factors of \(t\):\(m\) phase proportions, surface chemistry, and porosity, as well as properties dependent on the applied load. The research described in this paper contributes to fill some of these gaps. The reproducibility of the properties of ceramics sintered out of ZrO\({}_{2}\) nanopowders obtained by electrospray deposition is a key factor for the successful improvement of the electroconsolidation device prototype, designed for further investigations. The objective of this paper was to analyze the distribution of properties, both for synthesis and processing parameters, using the Weibull model.