Fault prognosis for batch production based on percentile measure and gamma process: Application to semiconductor manufacturing

Batch manufacturing processes (BMP) play an important role in many production industries, such as in semiconductor, electronic and pharmaceutical industries. They generally exhibit some batch-to-batch or unit-to-unit variations due to many reasons such as variations in impurities and deviations of the process variables from their trajectories. The process monitoring for these systems has been considered as rather fault diagnosis than as fault prognosis, this latter has received scarce attention in the literature. This paper presents a data-driven prognostic method for BMP organized in three steps. The first step allows to reduce the data size and to extract a raw health index which represents the operating state of the system. In the second step, variations in the health index are processed by the percentile measure which is use in a way that gives rise to monotonic profiles. In the third step, these profiles are modelled by gamma process as it is the most appropriate for the stochastic modelling of monotonic and gradual deterioration. The remaining useful life (RUL) is then estimated using an aggregate probability density function (pdf) with a confidence interval (CI) that ensures the safety margins in industry. Finally, the proposed method is applied on semiconductor manufacturing equipment with two industrial datasets provided by STMicroelectronics.