Dynamic stock and end-of-life flow identification based on the internal cycle model and mean-age monitoring

• Dynamic stock (DS) and end-of-life flow (EoLF) are set by consumer uncertainty.
• DS and EoLF are affected by economic cycles, technology, eco and social factors.
• Reliable DS and EoLF prediction for durables and end-products is still a challenge.
• The method identifies key parameters of the EoLF exit distribution and early loss.
• It provides real time DS and EoLF identification/prediction by mean age monitoring.

Planning of end-of-life (EoL) product take-back systems and sizing of dismantling and recycling centers, entails the EoL flow (EoLF) that originates from the product dynamic stock (DS). Several uncertain factors (economic, technological, health, social and environmental) render both the EoLF and the remaining stock uncertain. Early losses of products during use due to biodegradation, wear and uncertain factors such as withdrawals and exports of used, may diminish the stock and the EoLF. Life expectancy prediction methods are static, ignoring early losses and inapt under dynamic conditions. Existing dynamic methods, either consider a single uncertain factor (e.g. GDP) approximately or heuristically modelled and ignore other factors that may become dominant, or assume cognizance of DS and of the center axis of the EoL exit distribution that are unknown for most products. As a result, reliable dynamic EoLF prediction for both durables and consumer end-products is still challenging. The present work develops an identification method for estimating the early loss and DS and predicting the dynamic EoLF, based on available input data (production + net imports) and on sampled measurements of the stock mean-age and the EoLF mean-age. The mean ages are scaled quantities, slowly varying, even under dynamic conditions and can be reliably determined, even from small size and/or frequent samples. The method identifies the early loss sequence, as well as the center axis and spread of the EoL exit distribution, which are subsequently used to determine the DS and EoLF profiles, enabling consistent and reliable predictions.