Inference for cumulative risk model under step-stress experiments and its application in nanocrystalline data

With the popularity of step-stress accelerated life testing, researchers are exploring more possibilities for models that relate the life distributions under different stress levels. Cumulative risk model assumes that the effects of stress changes have a lag period before they are fully observed, which guarantees the continuity of the hazard rate function. This paper studies the cumulative risk model for Lomax distribution with step-stress experiments. For maximum likelihood estimation, Newton-Rapson method is adopted to get point estimates. Meanwhile, the asymptotic normality of the maximum likelihood estimator is used to obtain asymptotic confidence intervals. For Bayesian estimation, point estimates and highest posterior density credible intervals under squared error loss function with informative prior and non-informative prior are derived using Metropolis-Hastings method and Metropolis-Hastings within Gibbs algorithm. To evaluate the effects of stress change time and the length of lag period, as well as the performance of different methods, numerical simulations are conducted. Then a real nanocrystalline data set is analyzed.

Automatic simulation-based testing of autonomous ships using Gaussian processes and temporal logic

A methodology for automatic simulation-based testing of control systems for autonomous vessels is proposed. The work is motivated by the need for increased test coverage and formalism in the verification efforts. It aims to achieve this by formulating requirements in the formal logic Signal Temporal Logic (STL). This enables automatic evaluation of simulations against requirements using the STL robustness metric, resulting in a robustness score for requirements satisfaction. Furthermore, the proposed method uses a Gaussian Process (GP) model for estimating robustness scores including levels of uncertainty for untested cases. The GP model is updated by running simulations and observing the resulting robustness, and its estimates are used to automatically guide the test case selection toward cases with low robustness or high uncertainty. The main scientific contribution is the development of an automatic testing method which incrementally runs new simulations until the entire parameter space of the case is covered to the desired confidence level, or until a case which falsifies the requirement is identified. The methodology is demonstrated through a case study, where the test object is a Collision Avoidance (CA) system for a small high-speed vessel. STL requirements for safety distance, mission compliance, and COLREG compliance are developed. The proposed method shows promise, by both achieving verification in feasible time and identifying falsifying behaviors which would be difficult to detect manually or using brute-force methods. An additional contribution of this work is a formalization of COLREG using temporal logic, which appears to be an interesting direction for future work.

Reliability modeling of three-state systems with multiple types of components

In this paper, a system consisting of three states: perfect functioning, partial functioning, and down is considered. The system is assumed to be composed of several non-identical groups of binary components. The reliability of the system states under various assumptions on the component lifetimes is investigated. For this purpose, first, a new concept of bivariate survival signature (BSS) is introduced. Then, under the assumption that the component lifetimes of each type are exchangeable dependent, representations for the joint reliability function of the state lifetimes are obtained based on the notion of BSS. In the particular case, three-state systems composed of two types of different modules such as general-series (parallel) systems and systems with component-wise redundancy are investigated. Several examples are presented to illustrate the theoretical results.

Reliability assessment of autonomous vehicles based on the safety control structure

The recent social trends and accelerated technological progress culminated in the development of autonomous vehicles (AVs). Reliability assessment for AV systems is in high demand before its market launch. In safety-critical systems (SCSs) such as AV systems, the reliability concept should be broadened to consider more safety-related issues. In this paper, reliability is defined as the probability that the system performs satisfactorily for a given period of time under stated conditions. This paper proposes a reliability assessment framework of AV, consisting of three main stages: (i) modeling the safety control structure through the Systems-Theoretic Accident Model and Processes (STAMP); (ii) mapping the control structure and functional relationships to a directed acyclic graph (DAG); and (iii) construct a Bayesian network (BN) on DAG to assess the system reliability. The fully automated (level 5) vehicle system is shown as a numeric example to illustrate how this suggested framework works. A brief discussion on involving human factors in systems to analyze lower levels of automated vehicles is also included, demonstrating the need for further research on real case studies.

Performance reliability analysis of multi-state degraded system with improved Lz transform

Universal Generating Functions and Lz transformations have been widely used in the reliability modeling of multi-state systems. In order to solve the problem of complex calculations due to the dense random combination of multi-state performance parameters in the Lz transformation, a screening function is defined before the Lz transformation, and the screening function is combined with the performance threshold to screening the state performance parameters in advance, and the process is simplified through the screen matrix and the screen block diagram, effectively reduce the combined dimensions and quantity, improve the efficiency of reliability analysis, and combine with specific examples for application verification.

A new gamma degradation process with random effect and state-dependent measurement error

In this paper, a new gamma-based degradation process with random effect is proposed that allows to account for the presence of measurement error that depends in stochastic sense on the measured degradation level. This new model extends a perturbed gamma model recently suggested in the literature, by allowing for the presence of a unit to unit variability. As the original one, the extended model is not mathematically tractable. The main features of the proposed model are illustrated. Maximum likelihood estimation of its parameters from perturbed degradation measurements is addressed. The likelihood function is formulated. Hence, a new maximization procedure that combines a particle filter and an expectation-maximization algorithm is suggested that allows to overcome the numerical issues posed by its direct maximization. Moreover, a simple algorithm based on the same particle filter method is also described that allows to compute the cumulative distribution function of the remaining useful life and the conditional probability density function of the hidden degradation level, given the past noisy measurements. Finally, two numerical applications are developed where the model parameters are estimated from two sets of perturbed degradation measurements of carbon-film resistors and fuel cell membranes. In the first example the presence of random effect is statistically significant while in the second example it is not significant. In the applications, the presence of random effect is checked via appropriate statistical procedures. In both the examples, the influence of accounting for the presence of random effect on the estimates of the cumulative distribution function of the remaining useful life of the considered units is also discussed. Obtained results demonstrate the affordability of the proposed approach and the usefulness of the proposed model.

Computer simulation of the reliability of the heat exchange surface of the steam turbine condenser

The aim of the article is to demonstrate the relationship between the adaptive regulation of the heat exchange surface to specific operating conditions of a steam turbine condenser and the reliability and availability of this surface in a specific period of time. The article exemplifies the relationship between the settings of the condenser heat exchange surface and the resulting changes in the reliability structures of this surface. The method of creating a mathematical model of reliability estimation, which is characterized by the variability of the reliability structures of the heat exchange surface in relation to specific operating conditions in a specific period of time, was indicated. Then, exemplary simulations of the adaptation of reliability structures of specific pipe systems constituting the condenser’s heat exchange surface to specific processes of operation of this condenser are presented. The simulations refer to the time-varying thermal loads of the condenser, the time-varying mean thickness of the sediments, and changes in the temperature of the cooling water at the point of its intake over time. The adaptation of certain reliability structures consists in the adaptation of specific systems of pipes through which the cooling water flows to the currently existing operating conditions of the condenser in order to maintain the desired reliability of the heat exchange surface for a specified time. This is done by enabling or disabling the flow of cooling water through a given number of pipes in specific systems under given operating conditions. On the basis of computer simulations, the reliability functions, and the availability functions of the subsystem under consideration were estimated.

Multi-objective imperfect selective maintenance optimization for series-parallel systems with stochastic mission duration

To improve the probability that an engineering system successfully completes its next mission, it is crucial to implement timely maintenance activities, especially when maintenance time or maintenance resources are limited. Taking series-parallel system as the object of study, this paper develops a multi-objective imperfect selective maintenance optimization model. Among it, during the scheduled breaks, potential maintenance actions are implemented for the components, ranging from minimal repair to replacement. Considering that the level of maintenance actions is closely related to the maintenance cost, age reduction coefficient and hazard rate adjustment coefficient are taken into account. Moreover, improved hybrid hazard rate approach is adopted to describe the reliability improvement of the components, and the mission duration is regarded as a random variable. On this basis, a nonlinear stochastic optimization model is established with dual objectives to minimize the total maintenance cost and maximize the system reliability concurrently. The fast elitist non-dominated sorting genetic algorithm (NSGA-II) is adopted to solve the model. Numerical experiments are conducted to verify the effectiveness of the proposed approach. The results indicate that the proposed model can obtain better scheduling schemes for the maintenance resources, and more flexible maintenance plans are gained.

A time-varying reliability-based robust design method considering overall efficiency of axial piston pump

Axial piston pumps (APPs) are the core energy conversion components in a hydraulic transmission system. Energy conversion efficiency is critically important for the performance and energy-saving of the pumps. In this paper, a time-varying reliability design method for the overall efficiency of APPs was established. The theoretical and practical instantaneous torque and flow rate of the whole APP were derived through comprehensive analysis of a single piston-slipper group. Moreover, as a case study, the developed model for the instantaneous overall efficiency was verified with a PPV103-10 pump from HYDAC. The time-variation of reliability for the pump was revealed by a fourth-order moment technique considering the randomness of working conditions and structure parameters, and the proposed reliability method was validated by Monte Carlo simulation. The effects of the mean values and variance sensitivity of random variables on the overall efficiency reliability were analyzed. Furthermore, the optimized time point and design variables were selected. The optimal structure parameters were obtained to meet the reliability requirement and the sensitivity of design variables was significantly reduced through the reliability-based robust design. The proposed method provides a theoretical basis for designers to improve the overall efficiency of APPs in the design stage.

Determination of optimal post-warranty variable maintenance period for repairable second-hand product based on mean residual life

Due to the increased transactions of second-hand products in the market, the optimization of maintenance strategy for the second-hand product has become very important issue to attract a great attention from many researchers of late. This paper proposes a new post-warranty strategy with a variable self-maintenance period for the second-hand product, assuming that the product is replaced by another one on the first failure following a fixed length of post-warranty self-maintenance period. During the non-renewing warranty period, the product is subject to preventive maintenance periodically at a prorated cost while only minimal repair is implemented at each failure by the dealer. The main goal of this study is to determine an optimal length of post-warranty self-maintenance period which minimizes the expected cost rate per unit time during the product’s life cycle from the user’s perspective. This approach considers not only the periodic preventive maintenance during the warranty period, but also the remaining life distribution of the product after the warranty expires, which is the significant difference of this work from many existing maintenance policies. For this purpose, we formulate the expected length of life cycle and evaluate the expected total cost incurred during the life cycle of the second-had product which is purchased at the age of [Formula: see text] The existence of the optimal self-maintenance period is proved analytically under mild conditions and the proposed maintenance model is compared with an existing model with regard to the expected cost rate. Finally, assuming that the life distribution of the product follows a Weibull distribution, the effect of relevant parameters on the optimal self-maintenance period is analyzed numerically.