Single-step tightening is simple and fast compared to multi-step tightening, and it is therefore frequently used during the tightening of bolts in flange structures. However, single-step tightening to maintain uniformity is more difficult to achieve. To address this problem, existing methods such as the Elastic Interaction Coefficient Method (EICM) and Tetraparametric Assembly Method (TAM) have been investigated for load uniformity in single-step tightening. In order to improve the computational efficiency and accuracy of the traditional methods, a new single-step tightening method is proposed in this paper. This method can realize the design of the initial preload force simply by measuring the change in bolt load in a specific sequence. It is verified by numerical simulation that this method can realize the uniform distribution of bolt load. In addition, this paper will provide suggestions for the optimal tightening sequence for the single-step tightening method.

Consider a k / n ( G ) system, in which the system components are composed of multiple dependent failure mechanisms, and the dependence between the mechanisms is connected by the Gumbel-Hougarrd (GH) Copula. This paper presents a progressively hybrid censored test based on the k / n ( G ) system. Based on the censored test, the IFM(Marginal inference) method is used to estimate the model parameters and system reliability. Meanwhile, the MH (Metropolis-Hastings) sampling mixed with the Gibbs sampling method is proposed to realize the Bayes estimation of the model parameters and system reliability. Also, under the non-informative prior conditions, the conditional posterior density of the shape parameters of the marginal Weibull distribution is proved to be log-concave. The Monte Carlo simulation results showed that the proposed Bayes method is better than the traditional IFM method. Finally, the model and method proposed in this paper are applied to real data.

The reliability of a weighted degradation $(n_{1}, n_{2}, \ldots, n_{m})$-out-of-$n$ system consisting of multiple types of components is investigated in this article. The system comprises $m$ types of components, with the $i$th type ($i=1,2,\ldots,m$) containing $n_{i}$ components, and the total number of components is given by $n=\sum _{i=1}^{m}n_{i}$. Each component contributes differently to the system through an assigned weight, and the system is considered operational if the total weight of all functioning components meets or exceeds a predefined threshold $k$. Component performance is assumed to degrade over time, and failure occurs when the degradation level surpasses a specified failure threshold. Dependence among components of the same type is modeled using Copula functions. A system reliability function is developed based on the survival signature method, incorporating both the structural characteristics of the system and the survival probabilities of different types of components. A two-stage Bayesian approach is employed for parameter and reliability estimation, implemented via the Hamiltonian Monte Carlo algorithm. Numerical simulations are conducted to demonstrate the accuracy and robustness of the proposed method, and its applicability and effectiveness are further illustrated using real data.