Evaluation of Implicit Reliability Level Associated with Fatigue Design Criteria of Nuclear Class-1 Piping

  • J. MishraEmail author
  • V. Balasubramaniyan
Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


Fatigue design of Class-1 piping of NPP is carried out as par Section-III of American Society of Mechanical Engineers (ASME) Boiler and Pressure Vessel code. The fatigue design criteria of ASME are based on the concept of safety factor, which does not provide means for management of uncertainties for consistently reliable designs. In this regard, a work is taken up to estimate the implicit reliability level associated with fatigue design criteria of Class-1 piping specified by ASME Section III, NB-3650. The methodology employed for reliability evaluation is FORM, HORSM and MCS, where limit state function is derived using mean fatigue curve developed by Argonne National Laboratory. A number of important aspects related to reliability of various piping product and joints are discussed, and implicit reliability level is evaluated.


ASME Fatigue Implicit reliability FORM HORSM Piping 



Constant term of polynomial

A, B, C

Constants of Langer equation

\( b_{ij} \)

Coefficients of univariate basis function


Coefficients of multivariate basis function

C1, C2

Secondary stress indices for the specific component under investigation


Expected accumulated damage ratio for the service life

\( D_{\text{o}} \)

Outside diameter of pipe

\( D_{f} \)

Cumulative damage ratio that leads to failure

\( f_{{X_{i,\ldots,n} }} (x_{i} , \ldots ,x_{n} ) \)

Joint probability density function of the random variables X i

\( F_{\text{en,nom}} \)

Nominal environmental fatigue correction factor

\( F_{\text{en}} \)

Factor on life due to environmental effects

\( F_{\text{se}} \)

Factor on life due to size effect


Factor on life due to surface finish


Factor on life due to conservatism in fatigue definition

\( g(X) \)

Limit state function


Moment of inertia

K1, K2

Peak stress indices

m, n

Material parameters


Resultant moment due to a combination of design mechanical loads

\( nb \)

Number of stress-range levels

\( n_{\text{eqv}} \)

Number of equivalent full temperature load cycles


Number of cycles

\( N_{\text{air,RT}} \)

Number cycle to failure in the air environment

\( N_{f} \)

Fatigue life or total number of cycles to failure

\( N_{fi} \)

Number of cycles to failure in ith stress-range level

\( N_{\text{water}} \)

Fatigue life in the water at service temperature

\( O^{\prime} \)

Transformed DO levels

\( P_{0} \)

Range of service pressure

\( P_{f} \)

Failure probability

\( R_{m} (x) \)

Regular polynomial

\( S_{a} \)

Alternating stress intensity

\( S_{m} \)

Allowable stress intensity value of the metal

\( S_{n} \)

Primary plus secondary stress intensity value

\( S_{p} \)

Peak stress intensity value

\( T^{\prime} \)

Transformed temperature


Nominal wall thickness of product

\( T_{m} (x) \)

Chebyshev polynomial

\( U_{i} \)

Usage factor at the ith stress-range level

\( X_{i} \)

Random variables


Section modulus

\( \varepsilon_{a} \)

Alternating strain amplitude

\( \dot{\varepsilon}^{\prime} \)

Transformed strain rate


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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Safety Research Institute, Atomic Energy Regulatory BoardKalpakkamIndia

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