A case study on modelling and analysing machine breakdowns

Abstract

Most manufacturing models to date have assumed independence of all random variables in the system. In practice, autocorrelation effects are present in production lines time series. In this thesis, we extend this literature by studying autocorrelation in machine times to failure in detail. Our work focuses on the practical aspects of detecting and modelling autocorrelated uptimes, as well as including them in simulations.

We apply a practical procedure to detect autocorrelation in uptimes. The procedure has very mild assumptions and compensates for the number of machines it is applied to, ensuring that the probability of a Type I error is kept low.

We then provide two ways to model autocorrelated times to failures. The first is to use ARMA models including GARCH terms. We also provide a method based on the Markov-Modulated Poisson Process, a special case of the Markov Arrival Process.

For both methods discussed above, we provide diagnostic plots and a quantitative way to select the most appropriate model for a given series of uptimes. This allows us to automatically select an appropriate model.

Finally, to enable Ford to use our methods in simulation, we provide a way to generate simulated uptimes from each of our models.

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Identifiers

ORCID for Athanasios Avramidis: orcid.org/0000-0001-9310-8894

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