# Production Improvement Rate with Time Series Data on Standard Time at Manufacturing Sites
## 3 Production Improvement Rate with Time Series Data
### Production Improvement Procedures  
Initially, to prioritize improvements for products that contribute significantly to production and ensure the information's universality, we opted to categorize them based on the production volume. In this study, we determined the production volume criteria using monthly or yearly figures, creating three categories: small, medium, and large. These size judgments were based on Table 2 below, as shown in Figure 6.  
Figure 4: Procedure for calculating production lead time improvement rate. Through the analysis of the production volume, it was discovered that similar production volumes exhibit similar production patterns. This finding aligns with the objective of our study, which aims to apply production improvement rates to future production products with similar production plans. Second, rather than calculating the L/T improvement individually for each process, we aggregated the L/T for each product, resulting in what we term the total L/T. To clarify, if a product involves five processes, we sum the L/T values from these five processes. It is important to emphasize that the total L/T should only be calculated when the same product is produced and aggregated, as shown in Figure 3. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Distinguish**} & **Monthly** & **Yearly** & \\  & **Production** & **Production** & **Note** \\  & **(Units)** & **(Units)** & \\ \hline
**Low** & 0 to 500 & Under 5000 & \\ \hline
**Medium** & Over 500 & Over 5000 & \\  & to Under 10,000 & to Under 100,000 & \\ \hline
**High** & Over 10,000 & Over 100,000 & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Defining bins for production planning patterns. Figure 5: L/T improvement rate and utilization based on production volume. Figure 6: Defining bins for production planning patterns. (Example of monthly production variation for low volume products in green, Medium volume products in red, and high volume products in blue). In the third step, we used a straightforward average to compute the monthly L/T. For the total L/T, which is the summation of the L/T values from the second step's processes, an initial aggregation was performed. In this first aggregation, we calculated the average value of the total monthly L/T ratio. In the fourth step, the procedure calculated the monthly improvement rate for the total L/T derived in the third step. This rate was determined using the following equation: (Monthly Improvement Rate (%) = [(Total L/T of the Previous Month \(-\) Total L/T of the Current Month)/Total L/T of the Previous Month] \(\times\) 100). Fifth, we compiled the total L/T improvement rates by product on a monthly basis, based on the production volume bins established in the first step. Subsequently, we computed the monthly averages of these aggregated improvement rates corresponding to the same ranges (M+1, M+2, etc.). As part of our related research, we explored various types of averages and their applications. The geometric mean, a statistical method used to calculate the average change rate of a variable over a period of time, particularly for continuous change rate data like population growth, inflation, and economic growth, was examined. However, in this study, we did not utilize the geometric mean as our aim was to calculate the average monthly productivity improvement rate for multiple products within the same production band, over the same production interval. Therefore, we employed the harmonic mean to calculate the average monthly improvement rate for all the products within the same production volume category. Our study differs from previous research in three ways. Previous studies either calculated the production improvement rate of similar products or calculated the improvement rate of individual products. This study calculated the production improvement rates for products with similar production volumes. Previous studies used the following formula for the monthly production improvement rate based on the yearly target value for production improvement.