1 Introduction Objectives Understand uncertainty and variability and

1. Introduction Objectives • Understand uncertainty and variability and their significance in design • Understand concept, benefits of reliability-based design • Learn definition of reliability • Understand definitions and difference between reliability analysis and reliability design • Understand importance of human errors • Learn how to perform failure mode analysis 1

Uncertainty and variability • All engineering problems involve uncertainty and variability. – Uncertainty: lack of knowledge. – Variability: natural variability due to inherent random nature of phenomena and processes • Practically all quantities that enter in engineering calculations are uncertain (we do not know their values). – – – Wave loads on an ship Turbulence loads on an aircraft Yield stress of steel Error in finite element analysis Probability distribution of yield stress Variability Uncertainty 2

Motivation Any system can fail no matter how well it is designed and built Probability density L Ld Rd R R, L Interference area 3

Traditional deterministic design uses safety factor to assess safety • Safety factor=Rd/Ld • Two designs can have same safety factors but significantly different failure probabilities • A large safety factor does not guarantee that a design is safe • In most cases, deterministic design leads to over design but occasionally can produce unsafe designs. 4

Underdesign Overdesign Can we afford this? 5

Challenge: Design reliable highly complex systems Number of identical components in series Reliability 1 0. 999 100 0. 90 1, 000 0. 37 10, 000 0 6

Reliability-based design explicitly accounts for uncertainties, produces safer and more economical designs than deterministic design 7

Why reliability-based design • Reduce warranty and goodwill costs • Reduce waste due to overdesign • Be able to design reliability into highly complex systems 8

Reliability: Definition (Kececioglu, 2002) • Reliability: Probability that equipment will perform its intended function satisfactorily at a given age for a specified mission time when used in the manner and for purpose intended while operating under the specified application and operating environments. 9

Analysis versus design • Reliability analysis: Find reliability of a given system • Reliability-based design: Design a system that has acceptable reliability • Analysis is easier than design because in analysis we know the system. 10

Human errors • Decrease reliability • Examples – – Design errors Manufacturing errors Operation errors Maintenance errors • Example of operation error: Pilot tries to land under dangerous conditions, defective tire is installed in a car, captain of a ship fails to undertake appropriate bad weather countermeasures 11

Accounting for human error in reliability assessment Human error? Yes No Failure Survival 12

Accounting for human error in reliability assessment Probability of failure given occurrence of human error> Probability of failure given that there is no error 13

Failure mode analysis Intact system … Level 1 Level 2 Failure 1 … Failure n … System failure level 14

System failure probability = Probability of failure 1×Probability of failure 2 given failure 1×…×Probability of failure at system level+… 15

Types of reliability analysis Requires lots of data • Traditional approach: estimate reliability measures directly using data about failures • Bottoms-up approach: estimate reliability measures from primitive variables describing sources of variability More intelligent 16

Suggested reading • E. Nikolaidis, “Types of Uncertainty in Design Decision Making, ” Engineering Design Reliability Handbook, CRC press, 2004, p. 8 -1. • Rajagopal, R. , “An Industry Perspective on the Role of Nondeterministic Technologies, ” Mechanical Design, Engineering Design Reliability Handbook, CRC press, 2004, p. 4 -1. • Cafeo et al. , “The Need for Nondeterministic Approaches in Automotive Design: A Business Perspective, ” Engineering Design Reliability Handbook, CRC press, 2004, p. 5 -1. 17