We present a methodology of performing a preliminary analysis when introducing multi-parametric diagnostics and examples of its application. We clarify the sources of error in determining the current value of a diagnostic parameter.An important task of diagnostic systems (DS) integrated with automated process equipment is continuous monitoring of the state of cutting tools [1][2][3][4][5]. The basis of all DS is the dependence of the parameters of the controlled signals on the state of the cutting edges. Data for DS comes from functional parameters (power, vibration, temperature, etc.) of the cutting process, which depend not only on the condition of the cutting edges, but also on other changing conditions [4, 6-10]. In the initial preparation, the values of the controlled parameters in all phases of processing are stored in the DS (this is a preliminary training of the DS), but it does not fully solve the problem, because some of the factors are random [10][11][12]. Such factors include random variation in acceptance and hardness of the workpiece surface, and also the shape of the wear pad of the cutting tool, which cannot be taken into account in the data characterizing the amount of wear, for example, on the back side. Variable hardness occurs even within a single workpiece and is determined by the prior technology of manufacture.Therefore, in addition to the desired factor (tool status), during the cutting process there may occur a number of perturbing random factors, which affect the value of the controlled parameters that can trigger a false alarm or acceptance of defectives by the DS. Since there can be many controlled parameters, the problem is resolved by forming a system of equations that is adequate for the number of variable factors, i.e., transitioning from one-parameter to multi-parameter diagnostics [13][14][15][16]. However, such a transition does not improve the situation for assessment of tool wear. For simplicity, consider the example of two variables.Suppose there are two linearly independent functions of two unknown arguments. Theoretically, when functions (diagnostic parameters) take specific values, the unknown arguments (perturbing factors, state parameters) can be found. Likewise a higher order system of equations can be formed with multiple arguments. The difficulty is that in most cases of implementing diagnostic procedures, the connection between diagnostic parameters and perturbing factors is not functional, but random. In this case, changes in the perturbing factors (wear, hardness, etc.) which lead to changes in indirect (diagnostic) parameters are not deterministic, as in functional connections, but random, reflected, for example, by their mathematical expectations. The knowledge only of the mathematical expectations contradicts the metrological requirements to indicate the uncertainty of the estimates obtained in the form of confidence intervals, which contain the true value with a desired probability, for example 95%.