ORIGINAL CONTRIBUTION Structural reliability assessment of cracked pipes: The role of probability of detection data Rodolfo Mussini 1 | Héctor Cancela 2 | Thomas Clarke 3 1 Materials Testing Institute (IEM), Engineering Faculty, UdelaR, Uruguay 2 Computing Institute (INCO), Engineering Faculty, UdelaR, Uruguay 3 Laboratory of Physical Metallurgy, NDT Group, School of Engineering, UFRGS, Brazil Correspondence R. Mussini, Materials Testing Institute (IEM), Engineering Faculty, UdelaR, J. Herrera y Reissig 565, 11300, Montevideo, Uruguay. Email: rodolfo@fing.edu.uy Funding information CSIC‐UdelaR, Grant/Award Number: R&D 57/2016 57/2016 Abstract The structural reliability of industrial pipes, including those in the nuclear, oil, and gas industries, has a significant impact on the safety of people and the environment. This work aims to develop a computational structural reliability model method in conjunction with the failure assessment diagram method and the user‐defined probability of detection curves of non‐destructive testing are used. The concept of “reliability factor of a repair” is proposed. Then, the effects of the pipe inspection considering different user‐defined probability of detection curves and different values of the reliability factor of a repair on probability of failure are discussed. The main results include the identification of cases where performing repairs do not guarantee an improved reliability, as well as the consequences of considering the repair as a “perfect process” which result in non‐conservative assessments. KEYWORDS computational structural reliability, Monte Carlo simulation, NDT, pipes, POD 1 | INTRODUCTION The structural reliability of industrial pipes, including those in the nuclear, oil, and gas industries, has a signif- icant impact on the safety of people and the environment and on the finances of companies. One of the first studies on the structural reliability of pressurized components with cracks was conducted by Becher and Pedersen 1 in nuclear industry. Subsequently, Harris et al 2 and Harris and Lim 3 recognized the importance of service inspections using non‐destructive testing (NDT) methods in terms of the probability of failure with and Nomenclature: a , maximum depth of semi‐elliptical crack; a th , threshold for a given POD pt ;2c, crack length; CVN, Charpy V‐Notch energy; D 0 , outer diameter; FAD , failure assessment diagram; G 0 to G 4 , influence coefficients; K P I , stress intensity factor based on the primary stress; K SR I , stress intensity factor based on the secondary and residual stresses; K IC , plain strain fracture toughness; K mat , material fracture toughness used in the assessment; K r , fracture parameter; L P r , plastic collapse parameter based on the primary stress; M S , surface correction factor for surface cracks; M NS S , surface correction factor for surface cracks (net section collapse based on the lower bound limit load solution); M t , surface correction factor for through‐wall cracks; MCS, Monte Carlo simulation; N (DET) , number of successful detection attempts; N (NO - DET) , number of unsuccessful detection attempts; N (MCS) , number of simulations; NDT, non‐destructive testing; p, internal pressure; pdf, probability density function; P m , primary membrane stress; P b , primary bending stress; P f (DET) , component of the failure probability when the crack is detected; P f (NO - DET) , component of the failure probability when no crack is detected; P f (W) , failure probability; PSF a , partial safety factor for the crack size; PSF k , partial safety factor for the fracture toughness; PSF S , partial safety factor for the applied stress; POD(a), probability of detection; PND(a), probability of non‐detection; POD pt , plateau of the probability of detection for a given a th ; Q, shape factor for an elliptical crack; R i , inner radius; R 0 , outer radius; SRM, structural reliability model; t, wall thickness; UT, ultrasonic testing; α, reliability factor of a repair; λ a , shell parameter; μ a , mean of the maximum semi‐elliptical crack depth measurements; σ a , standard deviation of the semi‐elliptical crack depth measurements; σ ys , yield strength; σ P ref , reference stress based on the primary stress; Φ * , plasticity correction factor; Φ, cumulative distribution function for the standard normal distribution Received: 2 February 2018 Revised: 7 August 2018 Accepted: 2 October 2018 DOI: 10.1111/ffe.12941 Fatigue Fract Eng Mater Struct. 2018;1–10. © 2018 Wiley Publishing Ltd. wileyonlinelibrary.com/journal/ffe 1