Stochastic Approach to Planning of Spares for Complex Deteriorating Industrial System

Abstract

An easily implementable stochastic model for planning the inventory of spare components needed for corrective replacements of system components is presented. The probability of spare shortage in a given time interval is chosen as the decision criterion. The model is based on the assumption that the system contains a great number of identical independent components subject to wear-out. It can be used to determine the minimal number of spare components needed at the beginning of the planning interval to fulfil the requirement for an acceptable shortage probability during this interval. Besides, the model enables calculation of the probability of spare shortage during a given time interval considering the existing inventory level at the beginning of this interval. The model contains a few constant parameters that can be estimated from the component field data. It also includes two time dependent parameters which are calculated using the renewal function from the renewal theory. A discrete approximation which enables relatively simple calculation of the renewal function for any peak-shaped probability density function is derived. Assuming that the probability density function of component failure times is described by the normal density function, the renewal process characteristics are presented in terms of component mean time to failure and corresponding standard deviation. The error of our approximation for the renewal function is estimated. The model is applied to two components of electric locomotives in Slovenian Railways. The results obtained show that even small changes of the level of spares in the existing inventory can result in considerable changes of the spare shortage probability.

Key Words:

• Deteriorating system
• inventory
• maintenance
• spare parts
• stochastic process
• wear-out.

Additional information

Notes on contributors

Alenka Brezavšček

Alenka Brezavscek is an Assistant Professor at the Faculty of Organizational Sciences, University of Maribor, Slovenia. Her research interests are stochastic processes, system reliability and availability, and information system security.