Injection molding is a widely utilized process for manufacturing polymers, and integrating sustainability into its practices is crucial. As the demand for material testing grows, efficient solutions for producing multiple samples become increasingly important. Family molds offer a practical solution by allowing multiple samples to be injected into a single cycle. However, designing family molds presents challenges, particularly in achieving a balanced flow between the different samples within the mold. This imbalance often leads to sink marks which can affect the accuracy of the sample tests. To address the issue of sink marks, this study proposes an analysis method focusing on sink mark depth and its variance. This paper presents a gray-based Taguchi method to systematically study the effect of processing parameters: Injection speed, melt temperature, injection pressure, holding pressure, holding time, and cooling time on both responses. Analysis of variance (ANOVA) shows that changes in melting temperature, holding time, and holding pressure have the largest impact on reducing sink marks compared to the other process parameters considered.