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The computational assessment of system reliability of structures has remained a challenge in the field of reliability engineering. Calculation of the failure probability for a system is generally difficult even if the potential failure modes are known or can be identified, because available analytical methods require determination of the sensitivity of performance functions, information on mutual correlations among potential failure modes, and determination of design points. In the present paper, a method based on moment approximations is proposed for structural system reliability assessment that is applicable to both series and nonseries systems. The point estimate method is applied to evaluate the first few moments of the system performance function of a structure from which the momentbased reliability index and failure probability can be evaluated without Monte Carlo simulations. The procedure does not require the computation of derivatives, nor determination of the design point and computation of mutual correlations among failure modes; thus, it should be computationally effective for structural assessment of system reliability.

In structural reliability analysis, the uncertainties related to resistance and load are generally expressed as random variables that have known cumulative distribution functions. However, in practical applications, the cumulative distribution functions of some random variables may be unknown, and the probabilistic characteristics of these variables may be expressed using only statistical moments. In the present paper, in order to conduct structural reliability analysis without the exclusion of random variables having unknown distributions, the third-order polynomial normal transformation technique using the first four central moments is investigated, and an explicit fourth-moment standardization function is proposed. Using the proposed method, the normal transformation for independent random variables with unknown cumulative distribution functions can be realized without using the Rosenblatt transformation or Nataf transformation. Through the numerical examples presented, the proposed method is found to be sufficiently accurate in its inclusion of the independent random variables which have unknown cumulative distribution functions, in structural reliability analyses with minimal additional computational effort.

Percutaneous endoscopic gastrostomy (PEG) is a method widely used for patients with amyotrophic lateral sclerosis (ALS); nevertheless, its effect on survival remains unclear. The purpose of this meta-analysis study was to determine the effects of PEG on survival in ALS patients. Relevant studies were retrieved from PubMed, EmBase, and the Cochrane Library databases, from inception to June 2017. Studies comparing PEG with other procedures in ALS patients were included. Odds ratios (ORs) in a random-effects model were used to assess the survival at different follow-up periods. Briefly, ten studies involving a total of 996 ALS patients were included. Summary ORs indicated that PEG administration was not associated with 30-day (OR = 1.59; 95%CI 0.93–2.71; P = 0.092), 10-month (OR = 1.25; 95%CI 0.72–2.17; P = 0.436), and 30-month (OR = 1.28; 95% CI 0.77–2.11; P = 0.338) survival rates, while they showed a beneficial effect in 20-month survival rate (OR = 1.97; 95%CI 1.21–3.21; P = 0.007). The survival rate was significantly prominent in reports published before 2005, and in studies with a retrospective design, sample size <100, mean age <60.0 years, and percentage male ≥50.0%. To sum up, these findings suggested that ALS patients administered with PEG had an increased 20-month survival rates, while there was no significant effect in 30-day, 10-month, and 30-month survival rates.

In the second-order reliability method the principal curvatures, which are defined as the eigenvalues of rotational transformed Hessian matrix, are used to construct a paraboloid approximation of the limit state surface and compute a second-order estimate of the failure probability. In this paper, the accuracy of the previous formulas of SORM are examined for a large range of not only curvatures but also number of random variables and first-order reliability indices. For easy practical application of SORM in engineering, a simple approximation of SORM is suggested and an empirical second-order reliability index is proposed. By the new approximations, SORM can be easily applied without rotational transformation and eigenvalue analysis of Hessian matrixes. The empirical reliability index proposed in this paper is shown to be simple and accurate among the existing SORM formulas with closed forms. The proposed empirical reliability index gives good approximations of exact results for a large range of curvature radii, the number of random variables, and the first-order reliability indices.

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