498 Part IV Structural Reliabiliiy where, Pf is the failure probability; C is the consequence of the failure. A more general expression of the risk for practical calculation is given by (28.2) Then, the risk-based inspection can be planned by minimizing the risk. min[R) (28.3) The development of a system-level, risk-based inspection process includes the prioritization of systems, subsystems, and elements using risk measures, and definition of an inspection strategy (i.e., the frequency, method, and scope/sample size) for performing the inspections. The process also includes the decision about the maintenance and repair following inspections. Finally, there is a strategy for updating the inspection strategy for a given system, subsystem, or component/element, using the results of the inspection that are performed. Figure 28.1 illustrates the overall risk-based inspection process which composed of the following four steps: Definition of the system that is being considered for inspection Use of a qualitative risk assessment that utilizes expert judgement and experience in identifying failure modes, causes, and consequences for initial ranking of systems and elements in inspection. Application of quantitative risk analysis methods, primarily using an enhanced failure modes, effects, and criticality analysis (FEMCA) and treating uncertainties, as necessary, to focus the inspection efforts on systems and components/elements associated with the highest calculated safety, economic, or environmental risk. Development of the inspection program for the components, using decision analysis to include economic considerations, beginning with an initial inspection strategy and ending with an update of that strategy, based on the findings and experience from the inspection that is performed. Several feedback loops are shown in Figure 28.1 to represent a living process for the definition of the system, the ranking of components/elements, and the inspection strategy for each component/element. A key objective is to develop a risk-based inspection process that is first established and then kept up to date by incorporating new information from each subsequent inspection. Chapter 28 ProbabiZity and Risk Based Inspection Planning 499 r- I I t System Definition * Defines System, System Boundary, * Collect Information and fitness for purpose criteria I * Define Failure Modes * Define Failure Criteria * Identify Consequence I I I I * Redefine Failure Modes (1) Failure Modes, Effects, and Critically Analysis I- * Redefine Failure Causes * Redefine Failure Consequence * Assess Failure Probabilities for the Fitness for Purpose I I I I Risk Analysi I I I I I I I * Assess Consequences * Risk Evaluation (2) Development of Risk Based Inspection Program * Choose Potential Inspection Strategies * Define Potential for Damage States * Define Potential Damage for Inspection Damage * Estimate Effect of Inspection on Failure Probabilities * Choose Inspection Strategy and Perform Inspection * Perform Sensitive Studies * Choose Appropriate Inspection, Maintenance, (Frequency, Methods, Sampling Procedures) Repair (IMR) System I Figure 28.1 Risk-based Inspection Process (Xu et al, 2001) 500 Part IV Structural Reliabilig 28.3 Reliability Updating Theory for Probability-Based Inspection Planning 28.3.1 General Baysian models have been applied to reliability updating for probability-based inspection planning. This Section shall present two major approaches that have been developed in the pat 30 years. Updating Through Inspection Events to update the probability of events such as fatigue failure directly, (Yang, 1976, Itagaki et al, 1983, Madsen, 1986, Moan, 1993 & 1997). A simplified Bayesian method that only considers crack initiation, propagation and detection as random variables and independent components in a series system was proposed by Yang (1976) and Itagaki et a1 (1983). Updating Through Variables to re-calculate failure probability using the updated probability distributions for defect size etc. (Shinozuka and Deodatis, 1989). The change in reliability index is caused by the changes in random variables. The distribution of a variable can be updated based on inspection events. When the variables are updated, the failure probability can be easily calculated using the updated variables. However, if several variables are updated based on the same inspection event, the increased correlation between the updated variables should be accounted for. The approach for updating through inspection events will be further explained in the next sub- section. 28.3.2 Inspection Planning for Fatigue Damage Fatigue failure is defined as the fatigue crack growth reaches the critical size, e.g. wall thickness of the pipe. Based on fracture mechanics, the criterion is written in terms of the crack size at time t. By integrating Pans law, the limit state function can be written as, (See Part IV Chapter 27 of this book, Madsen et al, 1986) (28.4) where, Y(a,X) is the finite geometrical correction factor, ES is the stress modeling error, EY is randomized modification factor of geometry function, vo is the average zero-crossing rate of stress cycles over the lifetime, r(.) is the Gamma function. Basically, two most common inspection results are considered here, namely: no crack detected, and crack detected and measured (and repaired), see Madsen et a1 (1986). No Crack Detection This means that no crack exists or the existing crack is too small to be detected. This inspection event margin for the ith detail can be expressed as, (28.5) in which, a(ti) is the crack size predicted at inspection time ti, aD is the detectable crack size. Chapter 28 Probability and Risk Based Inspection Planning 501 The detectable crack size aD is related to a specified inspection method and modeled as a stochastic variable reflecting the actual probability of detection (POD) curve. Among several formulations of POD available, the commonly used exponential distribution is selected in this case: P,(a,) = 1 - exp( -?) (28.6) where h is the mean detectable crack size. Crack Detected and Measured If a crack is detected and measured for a weld detail i, this inspection event can be written as 1p.i (tr)= am -ai ('1) = Y(a,)-Y(ao)-Civot,E;A"T(l+~) =O (28.7) where, a,,, is the measured crack size at time tI and regarded as a random variable due to uncertainties involved in sizing. "(a) is a function reflecting the damage accumulation from zero to crack size a and is defined as (Paris and Erdogn, 1963, Newman and Raju, 1981), Repair Events The inspection itself does not increase the reliability of the structures, but it makes possible to take the necessary corrective actions like repair if a crack is detected. After repair, it is assumed that the material parameters and initial crack size follow the previous models but are statistical independent. This repair event based on crack detected and measured is the same as given by Equation (28.7), i.e. IR=I,,. After repair the failure event also needs to be modified as discussed below. Reliability Updating Through Repair If a crack is detected, measured and repaired, statistical properties of the material are expected to be the same magnitude but statistically independent. Weld defects, aR, after (underwater) repair depends upon the repair and post-repair treatment methods (grind, aRg or weld, aRw). Here it is assumed to follow the same model as a. The new safety margb after repair, MR(t), becomes (28.8) where, fR is the repair time. Parameters aR, CR, mR are assumed to follow the previous models but are statistically independent. Updated failure probability for repaired structural details is written as 502 Pari IV Structural Reliability PF,, = P[M,(t) 5 4 IR(tR) = 01 t > t, (28.9) It should be mentioned that an alternative way to consider repair effect is to update the random variables in equation (28.8) based on inspection events first. Then, the reliability can be estimated through repair safety margin by introducing initial crack size aR depending upon repair methods applied. 28.4 Risk Based Inspection Examples The methodology presented in Part IV Section 25.5 could be extended to risk-based inspection planning (Sun and Bai, 2001). As an example, the risk is defined as: Risk=(Consequence of failure)x(Likelihood of failure) where consequence of failure can be measured by: C1: Loss of hull, cargo and life, which is the most serious consequence; C2: Minor oil spill, serviceability loss and salvage; C3: Unscheduled repair and serviceability reduction. and likelihood of failure may be divided into three categories: L1: Rapid corrosion rate; L2: Nominal corrosion rate; L3: Slow corrosion rate. In the present analysis, it is assumed that all components with corrosion wastage larger than the critical size with certain probability of detection (POD) will be replaced and after that, their state will be recovered to the original. The inspection are made in each year (Annual Survey), 2.5 years (Intermediate Survey) and 5 years (Special Survey) based on the survey strategy by classification societies. The four levels of POD for thickness measurement are considered, i.e. 60%, SO%, 90% and 95% under the inspection condition that POD is 99.9% when the thickness of corroded component reaches 75% of the original one. The tentative reliability indices against hull girder collapse (one of most serious consequence of failure) are set at 3.7 for the “new-built” state and 3.0 for the lower limit of corroded hulls. Figure 28.2 shows the time-variant reliability with the risk of C1 and L1 combination. It can be seen that thickness measurement and renewal for the components with POD of less than 80% should be carried out in each Annual Survey after the loth service year in order to meet the annual reliability index over the lowest limit of safety level. Figure 28.3 demonstrates the time-variant reliability with the risk of C1 and L2 combination. Chapter 28 Probability and Risk Based Inspection Planning 1.5 - 1 .o 503 - POD=80Y0 +POD=90% - POD=95% I, I I I I 4.0 I I 1 .o 0 5 10 15 20 25 30 35 1, years (1) Annual Survey 4.0 I 1 3.5 3.0 ~i 2.5 2.0 c k t, years (2) Intermediate Survey 4.0 , 1 3.5 3.0 d 2.5 2.0 c - + POD=95% 1 .o 0 5 10 15 20 25 30 35 t, years (3) Special Survey Figure 28.2 Time-Variant Reliability with Risk of C1 and L1 Combination 504 Part IV Structural Reliability 4.0 I I - POD=%% w 1 .O 0 5 10 15 20 25 30 35 t, years (1) Annual Survey 4.0 I I 3.5 3.0 2 2.5 c - POD=95% 1 .O 0 10 20 30 t, years (2) Intermediate Survey -++- POD=95% 0 5 10 15 20 25 30 35 t, years (3) Special Survey Figure 28.3 Time-Variant Reliability with Risk of C1 and L2 Combination Chapter 28 Probability and Risk Based Inspection Planning 4.0 , ~ 3.5 3.0 2.5 c L c3 2.0 1.5 1 .o 4.0 3.5 3.0 4 2.5 d 2.0 1.5 1 .o 4.0 3.5 3.0 4 2.5 d 2.0 1.5 1 .o f -POD=90% POD=95% - POD=80% -A- POD=90% 0 5 10 15 20 25 30 35 t, years (2) Intermediate Survey 4- POD=80% -A- POD=90% - POD=95% 0 5 10 15 20 25 30 35 t, years (3) Special Survey Figure 28.4 Time-Variant Reliability with Risk of C1 and L3 Combination 505 506 Part IVShuctural Reliability It can be seen fiom the above figure that thickness measurements and renewal for the components with POD of less than 80% should be carried out in order to guarantee the annual reliability index over the lowest limit of safety level during the first 20 service years. They may be done in Special Survey No.3 during the first 20 service years, but should be implemented in Annual Survey if the FPSO is required to keep in service over 20 service years. Figure 28.4 shows the time-variant reliability with the risk of C1 and L3 combination. From this figure, it is found that the annual reliability index is always greater than the lower limit of safety level and thickness measurement may not be necessary during the first 20 service years, but the thickness measurement and then renewal for the components with POD of less than 80% in Intermediate Survey should be carried out if the FPSO is required to keep in service over 20 service years. From the above example, we conclude that the inspection pIanning is dependent on the consequence of failure (lower limit of safety level), corrosion rate, ship age and probability of detection (POD). The requirements of inspection gradually more demanding with the increase of the consequence of failure (lower limit of safety level), corrosion rate and ship age and with the decrease of POD. The latter usually makes thickness gauging and judgement more difficult. 28.5 Risk Based ‘Optimum’ Inspection This Sub-section is based on Xu et a1 (2001). Experience with in-service inspections of ship and offshore structures have adequately demonstrated that there are two categories of damages: those could have been or were anticipated (natural, predictable) 0 those could not have been anticipated (human caused, unpredictable) A substantial amount (if not a majority) of damages falls in the second category - unpredictable and due to the ‘erroneous’ actions and inaction’s of people. Quantitative inspection analyses (e.g. probability or risk based inspection methods and programs) can help address the first category of defects by providing insights of when, where, and how to inspect and repair. However, such an analysis cannot be relied upon to provide information that addresses the second category of defects. Expert observation and deduction (diagnostic) techniques must be used to address the second category of defects. Such recognition techniques lead to the development of the ‘optimum’ inspection method (Xu et al, 2001). The overall objective of the ‘optimum’ inspection method is to develop an effective and efficient safety and quality control system in the life-cycle management of the structural systems. Inspection Performance Inspection performance is influenced by the vessel, the inspector, and the environment. The vessel factors can be divided into two categories: design factors and condition/ maintenance factors. Design factors, including structural layout, size, and coating, are fixed at the initial design or through the redesign that may accompany repair. Conditiodmaintenance factors reflect the change in a vessel as it ages, including the operation history and characteristics of individual damagesldefects (crack, corrosion, bucking), its size, and its location. Chapter 28 Probability and Risk Based Inspection Planning 507 The person (inspector) who carries out an inspection can greatly influence the inspection performance. Performance varies not only from inspector to inspector, but also from inspection to inspection with the same inspector based on his mental and physical condition. Factors associated with the inspector include experience, training, fatigue, and motivation. The environment, in which the inspection is carried out, has a major influence on performance. The environmental factors can be divided into two categories: external factors which cannot be modified by inspection procedures and procedure factors that can be modified. External factors include weather and location of the vessel, that is, whether the inspection is performed while underway, while in port, or while in dry-dock. Procedural factors reflect the condition during the inspection (lighting, cleanliness, temperature, ventilation), the way in which the inspection is conducted (access method, inspection method, crew support, time available), and the overall specification for inspection (inspection type). Inspection Strategies Inspections, data recording, data archiving (storage), and data analysis should all be a part of a comprehensive and optimum inspection system. Records and thorough understanding of the information contained in these records are an essential aspect of inspection programs. Inspection is one part of the ‘system’ that is intended to help disclose the presence of ‘anticipated’ and ‘unanticipated’ defects and damage. Development of inspection programs should address: Timing and scheduling (when?) Objectives (why?) Where and How Many? The consequence evaluation essentially focuses on defining those elements, and components that have a major influence on the quality and safety of a FPSO. Evaluation of the potential consequences should be based on historical data (experience) and analysis to define the elements that are critical to maintaining the integrity of a FPSO. The likelihood evaluation focuses on defining those elements that have high likelihood’s of being damaged. Experience and analyses are complementary means of identifying these elements. Elements to be inspected (where and how many?) Defects, degradation, and damages to be detected (what?) Methods to be used to inspect, record, archive, and report results (how?) Organization, selection, training, verification, conflict resolution, and responsibilities (who?) The definition of the elements to be inspected is based on two principal aspects: Consequences of defects and damage Likelihood of defects and damage [...]... California at Berkeley 13 Xu, T., Bai, Y., Wang, M & Bea, R.G (2001), “Risk based Optimum Inspection of FPSO Hulls”, OTC12949, May 2001 14 Yang, J.N., (1976), “Inspection Optimization for Aircraft Structures Based on Reliability Analysis”, Journal of Aircraft, AAIA Journal, Vol 14, No 9, pp 1225-1234 15 Yazdan, N and Albrecht, P (1990), “Probabilistic Fracture Mechanics Application to Highway Bridges”, Engng... Assessment for Nuclear Power Plants”, NUREG/CR-2300, Nuclear Regulatory Commission, Jan 1983 13 NTS (1998), “Risk and Emergency Preparedness Analysis” NORSOK 2-013, Norwegian Technology Standards, March 1998 14 Toeliner, J (2001), “Safety Partnerships with Contractors: A HooverDiana Project Success Story”, OTC 13080 15 Trbojevic, V.M (2002), “ALARP Principle in Design”, Proceedings of O Conference 16 UK HSE... stern), high puncture loads may be generated The collision response and consequence for the platform may be predicated using non-linear finite element analysis @ai and Pedersen, 1993), see Part I1 Chapter 14 of this book 30.2.4 Collision Risk Reduction When considering risk reduction measures, the type of vessel representing the greatest risk to the platform needs to be analyzed For the passing vessel collision, . categories: design factors and condition/ maintenance factors. Design factors, including structural layout, size, and coating, are fixed at the initial design or through the redesign that. Symp. On the Role of Design, Inspection and Redundancy in Marine Structural Reliability, National Academic Press, Nov. 2. Madsen, H.O. et a1 (1986), “Methods of Structural Sufefy’l, Prentice-Hall,. became an important subject for the design and construction of marine structures. The objective of design projects is to engineer safe, robust and operable structural systems at minimum life