Aircraft maintenance methods are shifting from conservative maintenance approaches such as a periodic maintenance approach towards predictive maintenance approaches, leading to a reduction of costs, less unexpected aircraft-on-ground events and less wasted useful life of components. In this paper, we propose a new remaining useful life prognostics approach for aircraft engines and integrate this into a maintenance planning framework. First, an explicit health indicator is constructed from an implicit multi-sensor aircraft engine degradation data set using principal component analysis. Then, the remaining useful life prognostic model is developed using a polynomial chaos expansion approach, which allows for uncertainty quantification in the form of a probability density function which is faster than Monte Carlo simulation. A Markov decision process is used to determine the optimal time of maintenance for aircraft engines. During a case study, these optimal times for individual engines being part of a pool of operational engines are integrated using a linear programming model and a rolling horizon approach to obtain an optimised maintenance schedule. The prognostic model performs in the mid-range compared to other papers using the same data sets. Furthermore, with the current cost parameters the integrated remaining useful life maintenance planning strategy reduces costs by a factor of 3 and 2.5 compared to a periodic maintenance strategy or a run-to-failure maintenance strategy, respectively. The waste is reduced by a factor of 2.5 compared to periodic maintenance, while no failures occur. This research has demonstrated that the polynomial chaos expansion remaining useful life prognostic approach can be used for optimal maintenance planning for aircraft engines using a Markov decision process, showing benefits in terms of costs, waste and unexpected failures.