Abstract

Citation

Researchers should cite this work as follows:

• Winkel, B. (2022). 7-008-MachineReplacement-ModelingScenario. SIMIODE, QUBES Educational Resources. doi:10.25334/N3RA-R937

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Article Context

Description

Students build an integro-differential equation model using a convolution for machine replacement strategies for two different machine failure models: (1) exponentially distributed failure (student exercise) and (2) fixed time replacement. We discuss all the necessary probability notions which support the building of the convolution model and solve it for (2) while asking students to solve a general situation and then apply their findings to address (1).

We apply the notion of convolution and Laplace transform to a machine maintenance problem in a large facility. We seek the replacement function R(t) for the number of machines to be replaced in the time interval [0, t] to meet a set demand function, and N(t), for the number of machines in operation at time t. We are given probability information on F(t), the fraction of the machines that were new at time t₀ which are still in operation at time t₀ + dt, for the two different scenarios (1) and (2) above.

We offer a separate Appendix with some introductory probability notions.