Time-to-Failure Approach for Estimating the Shelf Life of Freeze-Dried Carotenoid-Enriched Apples: Forecasting the Deterioration of Quality Properties for Different Packaging Types and Storage Conditions

This study focused on incorporating total carotenoids (TC) into Pink Lady apples using vacuum-impregnation with carrot juice at 20, 30, 40, and 50°Brix and then assessing the shelf life of the impregnated apples after freeze-drying. The highest TC (12.30 ± 0.48 mg β-carotene/100 g) and minimal shrinkage were achieved using 20°Brix juice (20CJ). The freeze-drying of vacuum-impregnated apples with 20CJ reduced the time to reach equilibrium conditions compared with fresh apples. The shelf life of the freeze-dried impregnated samples was determined using time-to-fail models (TTF) at different conditions of package permeability (P = 2.17 × 10^–15 and 1.04 × 10^–6 g/s × Pa × m), temperature (T = 15, 25, and 35 °C), and relative humidity (RH = 0, 35, and 75%). TTF predictions indicate a T-independent shelf life, exceeding 105 days for P evaluated at RH < 35%. Sensory evaluation indicates that consumers preferred impregnated freeze-dried apples with intermediate hardness textures (above 18.14 N) and TC > 0.81 mg β-carotene/100 g in dried apples stored at RH = 35% and T = 15 °C.