Probabilistic Analysis of a Robot System with Redundant Safety Units and Common-Cause Failures

B S Dhillon

doi:10.4236/iim.2009.13022

Abstract

This paper presents reliability and availability analyses of a model representing a system having one robot and n-redundant safety units with common-cause failures. At least k safety units must function successfully for the robot system success. The robot and other failure rates and the partially failed system repair rates are assumed constant and the failed robot-safety system repair time is assumed arbitrarily distributed. Markov and supplementary variable methods were used to perform mathematical analysis of this model. Generalized expressions for state probabilities, system availabilities, reliability, mean time to failure, and variance of time to failure are developed. Plots of some resulting expressions are shown.

Highlights

This paper presents reliability and availability analyses of a model representing a system having one robot and n-redundant safety units with common-cause failures
Pj(x,t) x: The probability that at time t, the failed robot-safety system is in state j and the elapsed repair time lies in the interval [x, x+ x]; for j = n+1, n+2, n+3
This paper presented reliability analyses of a system having one robot and n-redundant safety units with common-cause failures

Summary

Introduction

Over the years, a number of serious accidents and other safety-related problems involving robots have occurred [1,2,3,4,5,6,7,8,9,10]. This paper presents reliability and availability analyses of a robot system having one robot and n-redundant safety units subject to common-cause failures. At least k safety units must function normally for the successful operation of the robot system. A common-cause failure can occur only if at least k safety units and the robot are functioning successfully. The robot-safety system has a total of (n-k+4) distinct states. It means the array of numerals representing system states may be discontinuous.

Notation

Analysis

Time Dependant Availability Analysis

Steady State Availability Analysis

Conclusions