A Spreadsheet Simulation Model for Estimating Reliability of Two Load-Sharing Weibullian Units Subjected to Varying Load

A Monte Carlo Simulation Method is presented for estimating the reliability of a system comprising of two load-sharing Weibullian units sharing a load that can depend on the mission being performed or can vary during a given mission. The load at the beginning of a mission is randomly selected from an appropriate distribution representing the load. The Weibull parameters Δ (shape) & η (scale) of these load bearing units are then calculated using an acceleration model. When a unit fails, the Weibull parameters of the other working unit are updated to reflect that it bears the full load. Simulation is performed in an Excel® Spreadsheet using the built-in random number generator function [= Rand ()]. Failure times based on any distribution can be generated and used by this methodology. Excel’s® logical functions are then used to determine system success or failure. Multiple runs are performed by a Macro developed to collect and tabulate the simulation data. Excel’s® Data Analysis and graphical capabilities are exploited to analyze and present the results in a suitable manner. The simulation model presented mimics the real scenario closely and is particularly applicable to mechanical and electro-mechanical systems whose failure times follow a Weibull distribution. Setting the value of shape parameter Δ = 1 yields an exponentially distributed failure time thus making the model also applicable to evaluation of load-sharing systems composed of electrical units.