This article describes the historical background, uncertainties in structural parameters, classifications, and application areas of probabilistic analysis. It provides a discussion on the basic definition of random variables, some common distribution functions used in engineering, selection of a probability distribution, the failure model definition, and a definition of the probability of failure. The article also explains the solution techniques for special cases and general solution techniques, such as first-second-order reliability methods, the advanced mean value method, the response surface method, and Monte Carlo sampling. A brief introduction to importance sampling, time-variant reliability, system reliability, and risk analysis and target reliabilities is also provided. The article examines the various application problems for which probabilistic analysis is an essential element. Examples of the use of probabilistic analysis are presented. The article concludes with an overview of some of the commercially available software programs for performing probabilistic analysis.

This article describes the methodology for performing a failure modes and effects analysis (FMEA). It explains the methodology with the help of a hot water heater and provides a discussion on the role of FMEA in the design process. The article presents the analysis procedures and shows how proper planning, along with functional, interface, and detailed fault analyses, makes FMEA a process that facilitates the design throughout the product development cycle. It also discusses the use of fault equivalence to reduce the amount of labor required by the analysis. The article shows how fault trees are used to unify the analysis of failure modes caused by design errors, manufacturing and maintenance processes, materials, and so on, and to assess the probability of failure mode occurrence. It concludes with information on some of the approaches to automating the FMEA.

A 10-in. diam, spiral-welded AISI 1020 carbon steel pipe carrying water under pressure developed numerous leaks over a four mile section. The section was fabricated using submerged-arc welding from the outside surface. Each welded length of pipe had been subjected to a proof pressure approximately twice the specified design pressure and two-thirds the approximate yield point of the parent metal. No failures or leakage were observed during proof testing. Metallurgical examination corroborated visual checks, indicating a distinct lack of root penetration in the split areas. Splitting occurred as a result of inadequate root penetration. The most likely source of difficulty in the welding process was the linear speed. Probably, the failures would not have occurred in absence of the welding problem. Also, the pipe was inadequate for the specified design pressure, as well as the reported maximum system pressure.

Two AISI type 316 stainless steel dished ends failed through the formation of intergranular stress-corrosion cracks (IGSCC) within a few months of service. The dished ends failed in the straight portions near the circumferential welds that joined the ends to the cylindrical portions of the vessel. Both dished ends were manufactured from the same batch and were supplied by the same manufacturer One of the dished ends had been exposed to sodium at 550 deg C (1020 deg F) for 500 h before failure due to sodium leakage was detected. The other dished end was used to fabricate a second vessel that was kept in storage for 1 year Clear evidence of sensitization was found in areas where IGSCC occurred. Sensitization was extensive in the dished end that had been exposed to sodium at high temperature, and it occurred in a narrow band similar to that typical of weld decay in the dished end that had been kept in storage. Solution annealing was recommended to relieve residual stress, thereby reducing the probability of failure. It was also recommended that the carbon content of the steel be lowered, i.e., that a 316L grade be used.

A DC-10 in transit from Denver to Chicago experienced failure of the center engine. The titanium compressor disk burst and severed the hydraulics of the plane. Investigation supports the conclusion that the cause of the disk rupture was the presence of a large fatigue crack near the bore emanating from a hard alpha (HA) defect. Such defects can result from occasional upsets during the vacuum melting of titanium. These nitrogen-rich alpha titanium anomalies are brittle and often have associated microcracks and microvoids. A probabilistic damage tolerance approach was recommended to address the anomalies, with the objective of enhancing rotor life management practices. The ongoing work involves the use of fracture mechanics and software (called DARWIN.) optimized for damage tolerant design and analysis of metallic structural components.

This article provides an outline of the issues to consider in performing a probabilistic life assessment. It begins with an historical background and introduces the most common methods. The article then describes those methods covering subjects such as the required random variable definitions, how uncertainty is quantified, and input for the associated random variables, as well as the characterization of the response uncertainty. Next, it focuses on specific and generic uncertainty propagation techniques: first- and second-order reliability methods, the response surface method, and the most frequently used simulation methods, standard Monte Carlo sampling, Latin hypercube sampling, and discrete probability distribution sampling. Further, the article discusses methods developed to analyze the results of probabilistic methods and covers the use of epistemic and aleatory sampling as well as several statistical techniques. Finally, it illustrates some of the techniques with application problems for which probabilistic analysis is an essential element.

Reliability-centered maintenance (RCM) is a systematic methodology for preventing failures. This article begins by discussing the history of RCM and uses Society of Automotive Engineers (SAE) all-industry standard JA1011 as its model to describe the key characteristics of an RCM process. It then expands on questions involved in RCM process, offering definitions when necessary. Next, the article describes the approach of RCM to failure modes and effects analysis (FMEA), the failure management policies available under RCM, and the criteria of RCM for deciding when a specific failure management policy is technically feasible. Then, after discussing the ways that RCM classifies failure effects in terms of consequences, it describes how RCM uses failure consequences to identify the best failure management policy for each failure mode. Next, the building blocks of RCM are put together to create a failure management program. The article ends with a discussion on some practical issues pertaining to RCM that lie outside the scope of SAE JA1011.

Reliability-centered maintenance (RCM) is a systematic methodology for preventing failures. This article discusses the history of RCM and describes the key characteristics of an RCM process, which involves asking seven questions. The first four questions comprise a form of failure modes and effects analysis (FMEA), and therefore, the article explains the approach of RCM to FMEA and the failure management policies available under RCM. It reviews the ways that RCM classifies failure effects in terms of consequences and details how RCM uses failure consequences to identify the best failure management policy for each failure mode. The article concludes with a discussion on some practical issues pertaining to RCM that lie outside the scope of SAE JA1011.

A 140 ft. (42.7 m) long boom on a dragline crane used in coal strip-mining operations failed. One of the principal load-bearing longitudinal beams or chords of the trussed boom had fractured adjacent to a bolt hole at a location about halfway along the length of the boom. Over the lifetime of the crane, several repairs had been made to the boom. At least a year before the failure, a reinforcing gusset plate had been bolted and welded to this chord at this location. Stereomicroscopy revealed microcracks in the weld metal. A fatigue crack 45 mm (1.8 in.) long was observed to emanate from this microcrack. Scanning electron microscopy showed an overload crack extended across the remaining cross section of the chord. It was concluded that the presence of the bolt hole used to attach the gusset plate to the chord created a stress riser adjacent to the hole. Repeated high tensile stresses on the chord during the lifting of enormous loads initiated a fatigue crack in the weld region adjacent to the bolt hole.

This article provides information on life assessment strategies and conceptually illustrates the interplay of nondestructive evaluation (NDE) and fracture mechanics in the damage tolerant approach. It presents information on probability of detection (POD) and probability of false alarm (PFA). The article describes the damage tolerance approach to life management of cyclic-limited engine components and lists the commonly used nondestructive evaluation methods. It concludes with an illustration on the role of NDE, as quantified by POD, in fully probabilistic life management.

Initially, two vertical double-acting two-stage compressors delivering chlorine gas at a pressure of 100 psi appeared to be running satisfactorily. About six months later the LP piston-rod of the No. 2 compressor failed due to burning, the compressor being worked double-acting at the time. About five months later, the HP piston rod of the No. 1 compressor failed in a similar manner. Specimens for microscopic examination were cut from the rod in the region of the failure and from the extreme end that had been situated above the piston and hence not subjected to an appreciable rise in temperature. The material was a steel in the normalized condition with a 0.35% C content. It appears probable that deficient lubrication of the gland resulted in overheating of the rod due to friction. The presence of a sprayed-metal coating was probably an additional factor in promoting failure, as it would present to the gas a surface area considerably greater than that of a homogeneous material.

An E-Brite /Ferralium explosively bonded tube sheet in a nitric acid condenser was removed from service because of corrosion. Visual and metallographic examination of tube sheet samples revealed severe cracking in the heat-affected zone between the outer tubes and the weld joining the tube sheet to the floating skirt. Cracks penetrated deep into the tube sheet, and occasionally into the tube walls. The microstructures of both alloys and of the weld appeared normal. Intergranular corrosion characteristic of end-grain attack was apparent. A low dead spot at the skirt / tube sheet joint allowed the Nox to condense and subsequently reboil. This, coupled with repeated repair welding in the area, reduced resistance to acid attack. Intergranular corrosion continued until failure. Recommendations included changing operating parameter inlet to prevent HNO3 condensation outside the inlet and replacement of the floating skirt with virgin material (i.e., material unaffected by weld repairs).

Initial investigation showed that a landing gear failure was the result of a hard landing with no evidence of contributory factors. The objective of reexamination was to determine whether there was any evidence of metallurgical failure. The landing gear was primarily an AISI type 6150 Cr-V steel flat spring attached at the top end to the fuselage and at the bottom end to the axle. Failure occurred at the clamping point near the top end of this spring. The failure showed evidence of severe brinelling at one corner in the clamping area. The fracture surfaces were clean, fresh, and indicative of a shock type of failure pattern. Closer examination, however, showed a fatigue crack at one corner. At this point, there was definite evidence of progression and oxidation. It was concluded that the corner in question was subjected to repeated brinelling resulting from normal landing loads, probably accentuated by looseness in the clamping device. The resulting residual tensile stress lowered the effective fatigue strength at that point against drag and side loads.

Failures of various types of hydraulic couplings used to connect pipes in a naval vessel are described and used to illustrate some of the general procedures for failure analysis. Cracking of couplings, which were manufactured from nickel-aluminum- bronze extruded bar, occurred in both seawater and air environments. Cracks initiated at an unusually wide variety of sites and propagated in either longitudinal or circumferential directions with respect to the axis of the couplings. Fracture surfaces were intergranular and exhibited little or no sign of corrosion (for couplings cracked in air), and there was very limited plasticity. Macroscopic progression markings were observed on fracture surfaces of several couplings but were not generally evident. At very high magnifications, numerous slip lines, progression markings, and striations were observed. In a few cases, where complete separation had occurred in service, small areas of dimpled overload fracture were observed. It was concluded from these observations, and from comparisons of cracks produced in service with cracks produced by laboratory testing under various conditions, that cracking had occurred by fatigue. The primary cause of failure was probably the unanticipated presence of high-frequency stress cycles with very low amplitudes, possibly due to vibration, resonance, or acoustic waves transmitted through the hydraulic fluid. Secondary causes of failure included the presence of high tensile residual stresses in one type of coupling, undue stress concentrations at some of the crack-initiation sites, and overtorquing of some couplings during installation. Recommendations on ways to prevent further failures based on these causes are discussed.

An intergranular stress-corrosion cracking failure of 304 stainless steel pipe in 2000 ppm B as H3BO3 + H2O at 100 deg C was investigated. Constant extension rate testing produced an intergranular type failure in material in air. Chemical analysis was performed on both the base metal and weld material, in addition to fractography, EPR testing and optical microscopy in discerning the mode of failure. Various effects of Cl-, O2 and MnS are discussed. Results indicated that the cause of failure was the severe sensitization coupled with probable contamination by S and possibly by Cl ions.

Crane collapse due to bolt fatigue and fatigue failure of a crane support column, crane tower, overhead yard crane, hoist rope, and overhead crane drive shaft are described. The first four examples relate to the structural integrity of cranes. However, equipment such as drive and hoist-train components are often subject to severe fatigue loading and are perhaps even more prone to fatigue failure. In all instances, the presence of fatigue cracks at least contributed to the failure. In most instances, fatigue was the sole cause. Further, in each case, with regular inspection, fatigue cracks probably would have been detected well before final failure.

The propeller from a small private airplane came off in flight. The head ends of all six attachment bolts remained in the propeller hub when it was found. Two threaded shanks with nuts remained with the engine, while the remaining four shank ends with their nuts were missing. Parts available for examination, in addition to the hub and attachment bolts, were the two propeller blades and the engine crankshaft. The purpose of this examination was to determine the nature and probable cause of failure in the six attachment bolts. Indications of fatigue failure and wear were the major findings in visual and low power microscopic examination. Fracture surfaces indicated failure was initiated in the threads in four bolts and in the shanks in two. The group of four bolts failed primarily due to tensile loads, while the other two bolts failed primarily due to bending loads. It was concluded that failure was due to improper installation torqueing of the bolts.

Several cases of failures in gray cast iron paper machine dryer rolls were evaluated. The rolls were found have ground outer cylindrical surfaces on which the paper web is dried. They were found to rotate about their longitudinal axes at speeds from 50 to 250 rpm while containing saturated steam from 35 to 380 kPa. Failures were found to occur in the shell body, in a head near a hand hole or a manhole opening, or in a head near the journal-to-head interface. A cleavage fracture was revealed by scanning electron microscopy regardless of the driving stress for failure. Fracture surface were found to exhibit chevron marks typical of fatigue or raised points or tears pointing in the direction of the probable origin of failure. The characteristics of the thinwall cast iron structures like the variation in composition due to pouring from multiple ladles, variation in solidification rates, and variation in tensile strength to be noted during inspection were described.

The repeated failure of a welded ASTM A283 grade D pipe that was part of a 6 km (4 mi) line drawing and conducting river water to a water treatment plant was investigated. Failure analysis was conducted on sections of pipe from the third failure. Visual, macrofractographic, SEM fractographic, metallographic, chemical, and mechanical property (tension and impact toughness) analyses were conducted. On the basis of the tests and observations, it was concluded that the failure was the combined result of poor notch toughness (impact) properties of the steel, high stresses in the joint area, a possible stress raiser at the intersection of the spiral weld and girth weld, and sudden impact loading, probably due to water hammer. Use of a semi- or fully killed steel with a minimum Charpy V-notch impact value of 20 J (15 ft·lbf) at 0 deg C (32 deg F) was recommended for future water lines. Certified test results from the steel mill, procedure qualification tests of the welding, and design changes to reduce water hammer were also recommended.