Principal Definitions of Reliability

  • Sergei V. Petinov
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 251)


The principal definitions of the in-service reliability of structures are briefly described, such as operational life, intended life, residual life, etc. The causes of structural failures, encircling incomplete knowledge of the service loading, materials properties, approximations in analyses, effects of production and revelations of the so-called “human factor” are indicated. An emphasis is made on the probabilistic considerations in evaluation of intended life of structures in design and of residual life at inspections and when the indication of the damage process are observed. The current concepts of reliable design are briefly discussed.

1.1 General

The in-service reliability (reliability) means the ability of a structure to perform and maintain its intended functions under stated conditions within a given operating time, life cycle. Reliability is provided, as said briefly in above, by durability (sustainability), safe operation, integrity, accessibility for inspection, and reparability.

The durability indicator is operational life of a structure, total time since it is placed in service or since recommencing service until the onset of a limit state. Alternatively, termination of service may be the result of economical considerations.

The operational life may be estimated in terms of time, by the number of hours (e.g., engine life cycle), years (ships and marine structures) or by the number of load cycles, fluctuations (structures of bridges, cranes, ships, etc.). And even in this case, time may be a preferred measure of operational life because in many applications the intensive variable loading periods are followed by moderate and insignificant loading phases or by the “off-trade” periods necessary for maintenance (e.g., painting) and for repair.

A key component of structural reliability is the intended life of structure. Intended life is established in design based on technical and economic considerations. It may be formulated in terms of probability, characterized by probability to exceed a certain time, or stated as a deterministic, non-random value (e.g., 25 years, 500 h). Evaluation of intended life in design is based also on considerations of strength, dynamic properties of a structure, application of design loads, and material resistance according to current standard procedures, reflecting the past experience.

Manufacturing of structure, even when the rules would be strictly followed, as said in above, unavoidably introduces deviations from the design, especially of local configuration of welded details. At this stage of life cycle, the properties of technological realization of structure would develop, and the structure acquires individual properties. Respectively, it allows the first refining assessment of intended life based on results of the postproduction inspection and evaluation of fitness for purpose. However, in entering service phase the reliability of structure remains a statistical characteristic mostly because of uncertainties in service loading.

Further on, in service the condition of structure is periodically assessed through inspections and information from monitoring systems aimed at detection of possible damages and making decision on continuation of service or on repair. Either of these decisions must be supported by assessment of residual life of structure commencing from inspection or repair until conditions for termination of service of structure would be attained.

Since the assessment of residual life is based on information on the current condition of the structure (in particular, of “critical location,” prone to development of damages) and on refining the loading history, the residual life becomes the individual property of structure.

The limit state is a set of conditions which form the moment when the life cycle of a structure would be exhausted. Termination of the life cycle may result in the obsolescence, decreasing of efficiency and safety, increasing intensity of local failures.

The onset of a limit state may be the result of accident overloads of structure, which could not be considered in design (e.g., recent combination of earthquake and tsunami in Japan, which caused serious failures at the nuclear power station “Fukushima”). A more regular scheme is realized when the limit state is attained by accumulation of damages (caused by fatigue, corrosive wear, progressive deformation of shells and panels, etc.).

Onset of a limit state is considered failure, although development of local damages and failures may occur early in service, well before exhaustion of life cycle, so-called “infant failure.” These are typically caused by errors in design, by violation of established procedures in manufacturing (e.g., by incomplete penetration welds, misalignments of the prime load-carrying members).

It may be impractical technically and economically to put efforts toward providing fail-proof service of certain systems, structures. It is important that in-service damages and failures were localized, not menacing integrity and safety of a structure, and economical consequences of damages were reasonable (cost of repairs, of interruption of service).

Summing up, the following causes of structural failures may be mentioned in different applications, e.g., in bridge, crane building, in transportation technologies:
  • Errors in design caused by application of erroneous or improper schematization of structures (models) and methods of analysis;

  • Limited knowledge, incomplete considering of functional and environmental loads, of material resistance in structural components;

  • Defects, imperfections developed in fabrication of structure (shape defects, flaws in welded joints, misaligning of the load-carrying structural details, etc.);

  • Errors in assessment of structural condition (missed fatigue cracks, details affected by excessive corrosive wear);

  • Improper repair of damaged structures, e.g., rewelding of fatigue cracks, causing development of residual welding stress, shape, and material inhomogeneities, resulting in rapid recommencing of fatigue process, etc.;

  • Improper actions, decisions of operators; recent examples—erroneous, immoral actions of navigators, causing sinking of passenger m/s “Bulgari,” of cruise liner “Costa Concordia” and loss of many passengers, etc.

In any case, the structural failure may be considered a random event.

1.2 Prediction of Intended Life of a Structure in Design

The intended life of structure in design may be assumed deterministic, non-random quantity; however, prediction of service life should be based on probabilistic considerations. This is because of
  • Feasible variation of the properties of a structure (dimensions and shape of structural components, of welded joints, in particular, resulting in manufacturing may differ from the designed characteristics, etc.);

  • The design loads presently are established based on statistical analysis and characterized in subsequent format; same is applied in the service data acquisition and analysis;

  • Statistical nature of fatigue resistance of structural components estimated by applying results of fatigue testing of specimens, characteristic by substantial scatter.

It should be noted, once again, that assumed design loading includes uncertain factors since the design codes reflect the past experience; conditions of future service cannot be strictly specified.

Extrapolation of accumulated information on service loads cannot consider effects of long periodic variations of weather conditions exceeding duration of observations, instrumentation assisted, in particular. An example is failure of a supermarket roof in St. Petersburg caused by excessive snow weight by far exceeding the design magnitude in winter of 2010–2011 (also, as reported lately, facilitated by defects in welded joints), Fig. 1.1.
Fig. 1.1

Snow load caused roof failure

By these reasons, the intended life of structure may be regarded a conditional indication of reliability, pertaining to particular branch of industry.

However, extension of service life of a designed structure, even conditional though, is an important factor, technically and economically. Prediction of intended life in design is based on a specific concept of reliability depending upon purposes and properties of a structure, quality of assessment of feasible damage processes, organization of condition control, and maintenance through the service life.

The concepts of reliable design discussed briefly in below were first developed in aviation technology based on understanding requirements of safety:
  • The safe-life concept, historically the first approach which reflected considering the role of fatigue in design, means that a structure has to be designed for a finite life on the principle that no damages (mostly, fatigue cracks) must be allowed during the design life. However, the models of fatigue and methods of assessment of fatigue of structures which might be used in design did not guarantee fulfillment of the principle. Therefore, the implementation of the concept required large factors of safety on design loads and material properties to ensure the above requirement.

  • Fail-safe concept allows for development of localized damage, and the safety factors should be established with respect to onset of catastrophic failure. The concept requires lower factors of safety but its realization needs in multiple load paths (i.e., structural redundancy), crack arrestors, and accessibility for inspection so that damage might be detected before the failure of one or more individual components would lead to total failure. The approach was developed initially in aircraft industry for airframes to provide minimum weight of structure.

  • Damage tolerant design is the approach presenting a refinement of the fail-safe concept. Damage is assumed to be initially present in critical structural components, and rigorous analyses must be carried out to predict the damage development and to assess residual strength. The results of the analyses are used to develop an inspection program for critical structural details that will ensure detection of damage well before the failure. If necessary, the structure would be redesigned to provide practical inspection intervals and to improve the durability of the structure. The damage to the service life must be limited and can be economically repaired.

Along with improvement of “philosophies” of the design and maintenance of structures, these concepts are being implemented in industrial segments. Recently, in design of welded structures was applied the safe-life concept. However, the methods of design based on application of the allowable stress concept and use of typified structural details, reliability of which was proved in past experience, did not meet the requirements of the concept. Therefore in service, as a completion, were applied components of the fail-safe concept, such as organizing of periodical inspections and assessments of current condition of structures aimed at detection of damages (corrosive wear, fatigue cracks) and prevention of their development into the stage menacing efficiency and integrity of structures.

The damage tolerant design concept, as said in above, is based on allowance of development of “historical” damages within the specified life of a structure on condition that transition of damages into the critical phase can be reliably predicted and prevented in service.

However, the current methodology and material properties database cannot provide the requirements of the concept and intensive research is carried out presently to “fill the gap.”

1.3 Assessment of Residual Life of Structure in Service

Assessment of residual life of a structure in service allows reducing the range of uncertainties, which affect evaluation of service life. It provides the sound base for development of schedule of inspections and allows putting corrections into the order and scale of repairs, to specify loading regimes. Respectively, evaluation of residual life in service provides individualization of service properties of structure and may be regarded a principal component of service and maintenance control system [1]. Figure 1.2 illustrates a feasible sequence of actions necessary to maintain reliability of a structure through the whole life cycle, starting from design and until repair and follow-up extension of service.
Fig. 1.2

Flowchart of actions aimed at providing reliability of structures in design and in service

The life estimations in design and in service based on the current condition assessment are carried out keeping with the common principles. The procedure consists of the following components: evaluation of the loading history characteristics, structural analysis, calculation of characteristic stresses (strains, when appropriate), evaluation of the strength and reliability indicators, where the empirical data on the material resistance at “critical location” are needed.

The loading history in certain applications is composed of random sequence of events of randomly varied intensity separated by the random time intervals. Such scheme is applied for the description of the snow load on the roof of buildings. The collection of the observation data and subsequent statistical analysis allows establishing the average regularity of the snow load formation, revealing the tendency (the trend) and probable deviations from the averages.

The important group of loading histories includes the continuous random variable in time successions regarded as continuous random processes. These are traffic and wind loading of bridges, specifically of large span-suspended bridges, wave loading of marine structures and ships, etc. Wind velocity consists of the two components, of slowly varying and of rapidly changing parts, gusts, both randomly varied. Sea waves at every sea state are characterized by average height and period with random deviations at every moment. Consequently, the description of regularity and intensity of such processes needs in probabilistic analysis and establishing the necessary statistical characteristics.

Similarly, results of experimental evaluation of mechanical properties of materials reveal notable scatter which makes necessary application of statistical analysis for description of design characteristics. The most pronounced scatter is observed in fatigue testing of material specimens, especially in testing under the load limits control. Statistical analysis of fatigue test results was initiated many years ago and became a regular procedure, extended over the assessment of other characteristics of mechanical properties of materials.

Application of probabilistic analysis allows considering physical properties of external excitation and of other components in assessment the in-service strength and reliability of structures. Meanwhile, it should be noted that statistical analysis is applied to the past experience, to accumulated data by the moment of analysis. Evaluation of averages provides prediction of feasible trends in variation of statistical characteristics; however, the trends may be monotonous over relatively short periods of time compared to intended service life of a structure. It would cause unavoidable uncertainties in estimation of statistical characteristics of strength and reliability parameters, and respectively, the condition monitoring measures and maintenance are necessary to reduce the probability of structural damages.

The above brief overview of principal factors affecting reliability of structures makes reasonable discussion of elements of the probability theory, of spectral analysis of random processes, and of statistical dynamics, given in Chaps.  2 and  3.


  1. 1.
    Bolotin VV (1984) Prognosirovanie resursa mashin i konstrukziy (Life prediction of structures and machine components) Mashinostroenie Pubs, Moscow, p 312 (in Russian)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Sergei V. Petinov
    • 1
    • 2
  1. 1.Department of Hydraulics and StrengthInstitute of Civil Engineering, Peter the Great St. Petersburg Polytechnic UniversitySt. PetersburgRussia
  2. 2.Institute for Problems in Mechanical Engineering, Russian Academy of Sciences (IPME RAS)St. PetersburgRussia

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