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This article deals with a repairable k-out-of-n: G system with retrial feature and two maintenance policies. All components in the system have two failure modes, mode a failure and mode b failure. When a component fails, the failed component will be repaired instantly if the repair equipment is idle. Otherwise, it enters into a retrial orbit and tries again after some time until it is repaired. The single repair equipment may be subject to breakdown in a busy period, and in order to improve system reliability, the idle repair equipment will be performed preventive maintenance. The Markov process theory and Laplace transform method are adopted to compute the reliability indexes of the system. Also, four optimization design models are constructed to determine the optimal repair rates of the components with two failure modes, and the minimization problems of the total expected cost function per unit time and the cost-effectiveness ratio are solved. To verify the correctness of the model, numerical analysis is executed to demonstrate the impact of each parameter on system reliability indexes, the optimal solutions of different optimization design models are obtained by using differential evolution algorithm and genetic algorithm. [ABSTRACT FROM AUTHOR]

Background and Aims The long-term impact of maternal smoking during pregnancy [MSDP] on the risk of Crohn's disease [CD] and ulcerative colitis [UC] in adult offspring remains uncertain. The present study aimed to investigate the individual and combined effects of early life exposure [MSDP], offspring personal behaviour [smoking], and genetic risk on the development of CD and UC in adult offspring. Methods We conducted a prospective cohort study using UK Biobank data, including 334 083 participants recruited between 2006 and 2010, with follow-up until December 31, 2021. Multivariable Cox regression models were used to evaluate the associations of genetic factors, maternal and personal smoking, and their combination with CD and UC. Results Participants exposed to MSDP had an 18% increased risk of CD compared to those without MSDP (hazard ratio [HR] = 1.18, 95% confidence interval [CI] = 1.01–1.39). However, no significant association was found between MSDP and UC risk [HR = 1.03, 95% CI = 0.92–1.16]. Personal smoking increased the risk of CD and UC, and had a numerically amplified effect with MSDP. Participants with high genetic risk and MSDP had a 2.01-fold [95% CI = 1.53–2.65] and a 2.45-fold [95% CI = 2.00–2.99] increased risk of CD and UC, respectively, compared to participants without MSDP and with low genetic risk. Conclusions Our prospective cohort study provides evidence that MSDP increases the risk of CD in adult offspring, whereas no evidence supports their causal association. Additionally, smoking and genetic susceptibility had a numerically amplified effect with MSDP on CD and UC, but the interaction lacked statistical significance. [ABSTRACT FROM AUTHOR]

This paper investigates the reliability and sensitivity analysis for a repairable k-out-of-n:G system with retrial of failed components. Such a model has important practical applications in fully automatic systems, and the most typical one is fully automatic manufacturing system. Markov models for availability and reliability of the system whose components are all subject to two failure modes are presented. There is no waiting space for failed components in the system. If a failed component finds the repairman busy and it can not be repaired at once, it will enter into the retrial orbit and try again for repair after some random period of time. Some reliability indexes, including steady-state availability, reliability function and mean time to system first failure, are derived by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided as well. Finally, some numerical experiments are conducted to show the effects of system parameters on the system reliability indexes. [ABSTRACT FROM AUTHOR]

This paper studies a K − o u t − o f − N retrial system with mixed standby components and a single repairman under Bernoulli vacation schedule. Such a model is motivated by some machine repair systems in practice. The repairman may either go for a vacation of random length with probability p or stay idle in system with probability 1 − p after the completion of a repair. If a component fails, it is repaired at once when the repairman is idle, whereas whether the repairman is busy or vacation, the failed components enter into an orbit. The expressions of steady-state availability, reliability function and the mean time to system first failure are obtained by using vector Markov process and Laplace transform theory. Sensitivity analysis and relative sensitivity analysis are provided. An application example of the intelligent automatic system is demonstrated. Finally, some numerical experiments are conducted to show the impacts of system parameters on reliability indexes. The results presented in the paper may be useful for machine repair system engineers. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a discrete time Geo/Geo/1 queue system with non-preemptive priority and multiple working vacations. We assume that there are two types of customers in this queue system named "Customers of type-Ⅰ" and "Customers of type-Ⅱ". Customer of type-Ⅱ has a higher priority with non-preemption than Customer of type-Ⅰ. By building a discrete time four-dimensional Markov Chain which includes the numbers of customers with different priorities in the system, the state of the server and the service state, we obtain the state transition probability matrix. Using a birth-and-death chain and matrix-geometric method, we deduce the average queue length, the average waiting time of the two types of customers, and the average busy period of the system. Then, we provide some numerical results to evaluate the effect of the parameters on the system performance. Finally, we develop some benefit functions to analyse both the personal and social benefit, and obtain some optimization results within a certain range. [ABSTRACT FROM AUTHOR]

This paper investigates the steady-state availability of a repairable series-parallel system with redundant dependency. The different types of components and repairmen are taken into account, the failure rate of the operating component varies as the number of other failed components and the repair rate of the failed component is constant in each parallel redundant subsystem. To quantify the redundant dependency, a modified failure dependence function is introduced to determine the failure rate of the components in each subsystem. Markov theory and matrix analysis method are used to get the steady-state probability vector of each subsystem and the steady-state availability of the entire system. A numerical example is presented to illustrate the obtained results and to analyze the effect of redundant dependency class on the system availability. [ABSTRACT FROM AUTHOR]