FAULT TREE ANALYSIS FOR BRINELL HARDNESS MEASUREMENT

Abstract

Purpose: The purpose of the paper is to determine the probability of the top event (top outcome) for Brinell hardness measurement. Top event in this case is defined as the failure of the measurement process. If the top eventoccurs, the measurement cannot be realized, or if the indentation (measurement) is realized, it cannot be calculated because of the gross error. The probability of the top eventwas evaluated by the quantitative Fault tree Analysis (FTA) with the direct numerical calculation and Monte Carlo simulation. While applying the Brinell method, the surface of the material is subjected to a standard pressure for a standard defined length of time by means of a carbide ball with a defined diameter. The diameter of the resulting indentation is inversely proportional with the hardness. Methodology: Used methodology is documented in the standard STN IEC 61 025:2007 Fault tree analysis (FTA). The Ishikawa income – outcome diagram was used to build Fault Tree Analysis. Statistical data of elementary failures (representing incomes) were collected during one year, and we also used data from a longer period (if available), especially for rarely occurring elementary failures. The elementary failures produce top event(representing outcome). With the knowledge of the probability of elementary failure or its intensity, we can estimate the probability of the top event. After creating the fault tree analysis, the excel program was developed in order to use the fault tree analysis to calculate the probability of the top event.Program allows accelerate basic calculation, as well as comfortable substitution the values of probability of occurrence individual basic events in order to study their influence on the top event. A Monte Carlo simulation was used as the verifying calculation. It is a numerical calculation method, which is based on the use of random variables and the theory of probability. The verification was carried out using Quantum XL software.