Monte Carlo simulation using Excel(R) spreadsheet for predicting reliability of a complex system

Abstract

A technique for performing Monte-Carlo simulation using an Excel spreadsheet has been developed. This technique utilizes the powerful mathematical and statistical capabilities of Excel. The functional reliability block diagram (RBD) of the system under investigation is first transformed into a table in an Excel spreadsheet. Each cell within the table corresponds to a specific block in the RBD. Formulae for failure times entered into these cells are in accordance with the failure time distribution of the corresponding block and can follow exponential, normal, lognormal or Weibull distribution. The Excel pseudo random number generator is used to simulate failure times of individual units or modules in the system. Logical expressions are then used to determine system success or failure. Excel's macro feature enables repetition of the scenario thousands of times while automatically recording the failure data. Excel's graphical capabilities are later used for plotting the failure probability density function (PDF) and cumulative distribution function (CDF) of the overall system. The paper discusses the results obtainable from this method such as reliability estimate, mean and variance of failures and confidence intervals. Simulation time is dependent on the complexity of the system, computer speed, and the accuracy desired, and may range from a few minutes to a few hours.