## 4 The Implementation of Trends and Results
For the linear model, a significance of 0.0000 is observed; for the nonlinear model, the significance is noted at 0.0000; for Gompertz model, the significance is noted at 0.0000. Figure 5: Nonlinear sales trend for product A. After applying the Gompertz function to the sales data, the model parameters were estimated through an iterative process, ensuring that the best possible fit was achieved. The model fit metrics were determined (Table 1), leading to the following summary:  
The Akaike Information Criterion (AIC) and the Bayesian Schwarz Information Criterion (BIC) are indicators that can be used to select a suitable model for the data under study. The lower value of the criterion, the more suitable the model. To verify the sales trend of Product A, the Mann-Kendall test (Table 2) was applied. When performed on the current dataset, the test yielded a variance S = 226 and a standardized test statistic Zs = 3.8242. The corresponding \(p\)-value of the test was \(p\) = 0.0001, which indicates that the trend is statistically significant at all three significance levels of 10%, 5%, and 1%. Table 2 presents the trend values at the 10%, 5%, and 1% significance levels. It can be observed that, at the 10%, 5%, and 1% significance levels, the Zs value falls within the acceptable range, indicating that the sales records exhibit a statistically significant trend. Given that the value of S (variance) is 226, this further supports the presence of a positive sales trend for Product A. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Sum of Squared Error** & **Mean Squared Error** & **Significance** & **AIC/BIC** \\  & **(SSE)** & **(MSE)** & **Significance** & **AIC/BIC** \\ \hline Linear & 1342.8433 & 22.3807 & 0.0000 & 360.73/364.92 \\ Nonlinear & 660.0689 & 11.0022 & 0.0000 & 320.12/326.41 \\ Gompertz & 584.0173 & 9.7336 & 0.0000 & 312.78/319.06 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Model summary—product A. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Zs** & **Critical Value** & **Significance Level** \\ \hline
3.8242 & \(>\) & 1.6449 & at 10\% significance level \\
3.8242 & \(>\) & 1.9600 & at 10\% significance level \\
3.8242 & \(>\) & 2.5758 & at 10\% significance level \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Zs values at 10%, 05%, and 1% significance level. Figure 6: Gompertz curve for product A sales with predicted interval. Sales of product A--fuse boxes are presented in Figure 6, which confirms a more appropriate trajectory within its industry. The mean square error (MSE) is 9.7336, the lowest for the Gompertz trend, indicating the degree of deviation between the model's predicted values and the actual measured data. Figure 6 illustrates the sales trend of product A over time:  
* In the growth phase (January 2020) 1 \(<\) \(t\) \(<\) 22 (October 2021) an exponential increase in sales of product A is observed, which requires an expansion of production capacity to meet the growing demand. * At the saturation point \(t\) = 22 (October 2021) sales of product A stabilize, which indicates that the peak in sales of product A has been reached. * in the phase \(t\) \(>\) 23 (November 2021) there is a decrease in sales of product A, which signals a decrease in demand. * Although sales of product A are within the prediction interval, Figure 6 shows that sales of the product oscillate around the calculated exponential curve. The observed pattern highlights the need for product innovation, either through design improvements, enhanced features, or targeted marketing strategies, to sustain competitiveness and prevent a long-term decline in demand. Figure 7 shows the nonlinear sales trend of product B--power distribution cabinets. Based on the sales data for product B, the quadratic trend appears to be a more appropriate model to capture the sales dynamics. Statistical analysis of the trends shows that the quadratic trend explains 62.71% of the variability in the data, indicating a higher level of accuracy compared to the linear model (35.56%).