Reliability prediction of the series system with spares subject to Weibull failure
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This research effort has developed a mathematical model for predicting the system reliability of a series system with spares subject to Weibull failures. Many modern equipment systems are designed in a series configuration with spares available when necessary. The Weibull distribution is one of the most widely applied and flexible failure distributions used to describe and model present day single component systems. Due to the theoretical intractability of the Weibull distribution in spares models, it is extremely difficult to solve the multiple integration involved in this type of model analytically. Therefore, a numerical integration method using Simpson's Rule was selected as a tool to address the problem of multiple integration of the Weibull distribution. Then, a recursive algorithm was developed for the reliability prediction of a series system with spares subject to a general failure model (including the Weibull distribution). The developed model has been validated for accuracy using a two component series system with spares. A sensitivity analysis has also been performed on the two parameters of the Weibull distribution, and the effect of adding spares or stages on the system reliability has been assessed. This research also demonstrates the application of the developed reliability prediction model with a realistic example pertaining to a tool reliability problem common to manufacturing industries.