Title: Stochastic theory of tool life - theoretical developments on the injury theory

Authors: Marcello Braglia; Davide Castellano; Marco Frosolini

Addresses: Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, via Bonanno Pisano 25/B, 56126 Pisa, Italy ' Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, via Bonanno Pisano 25/B, 56126 Pisa, Italy ' Dipartimento di Ingegneria Civile e Industriale, Università di Pisa, via Bonanno Pisano 25/B, 56126 Pisa, Italy

Abstract: This paper aims at presenting a revisited and extended version of the injury theory, originally developed by Ramalingam and Watson (1977) and Ramalingam (1977). This theory allows deriving tool-life distributions when either a single catastrophic event or a gradual and cumulative wear process terminates the tool useful life. Since these models cover great importance in tool-life modelling, this paper would contribute in this direction with further observations and results, giving special attention to the mathematical formulation. In particular, besides deriving known results following a different approach, we extend the theory to the case of multiple machines with both single- and multi-tool configurations. Moreover, as examples we derive different expressions of the tool-life distribution in the cases studied related to particular formulations of the injury rate.

Keywords: tool wear; tool life; stochastic modelling; injury theory; tool management.

DOI: 10.1504/IJMMNO.2014.065398

International Journal of Mathematical Modelling and Numerical Optimisation, 2014 Vol.5 No.4, pp.265 - 279

Received: 25 Feb 2014
Accepted: 11 May 2014

Published online: 23 Oct 2014 *

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