Chapter 4 - Review on mechanical system reliability models

<div class="section abstract"><div class="htmlview paragraph">A study of the cockpit information system architecture of current single-engine single-pilot aircraft was performed to establish a baseline for the evaluation of the reliability of new cockpit systems being developed through the Advanced General Aviation Transport Experiments (AGATE) program. That study defines a “typical” General Aviation (GA) cockpit information system architecture consisting of 38 components making up 32 subsystems. It also developed a reliability (fault tree) model for the system and utilized a proprietary analysis tool to compute system reliability.</div><div class="htmlview paragraph">Fault tree reliability models have gained wide acceptance since their introduction in the 1960’s to analyze the probability of success of military defense systems. Fault trees use logic gates to express the relationships between failures of the components and resulting failures of subsystems and of the system.</div><div class="htmlview paragraph">In a subsequent study an analytical model corresponding to the specific cockpit system reliability model was developed and implemented in a spreadsheet format. In addition to the system reliability equation, all of the subsystem reliability equations were also derived. From the analytic reliability model, the sensitivities of all of the subsystem and system reliabilities to changes in the component reliabilities were derived. These equations were also implemented in the spreadsheet tool. The resulting tool allows a user to modify the component reliability parameters and compute and display the system and subsystem reliabilities and the sensitivities of these reliabilities to changes in the component reliabilities.</div><div class="htmlview paragraph">This paper describes the single-engine single-pilot aircraft cockpit information system reliability model, explains the derivation of the analytical model for reliability and sensitivity computation, discusses the insight obtained from the analytical model, and presents the application of the spreadsheet tool.</div></div>

The current research of reliability allocation of CNC lathes always treat CNC lathes as independent series systems. However, CNC lathes are complex systems in the actual situation. Failure correlation is rarely considered when reliability allocation is conducted. In this paper, drawbacks of reliability model based on failure independence assumption are illustrated, after which, reliability model of CNC lathes considering failure correlation of subsystems is established based on Copula theory, which is an improvement of traditional reliability model of series systems. As the failure time of CNC lathes often obeys Weibull or exponential distribution, Gumbel Copula is selected to build correlation model. After that, a reliability allocation method considering failure correlation is analyzed based on the model established before. Reliability goal is set first and then failure rates are allocated to subsystems according to the allocation vector through solving the correlation model. Reliability allocation is conducted for t = 1. A real case of a CNC lathe and a numerical case are presented together to illustrate the advantages of the reliability model established considering failure correlation and the corresponding allocation method. It shows that the model accords to facts and real working condition more, and failure rates allocated to all the subsystems are increased to some extent. This research proposes a reliability allocation method which takes failure correlation among subsystems of CNC lathes into consideration, and costs for design and manufacture could be decreased.

In consideration of some drawbacks of stochastic reliability method in theoretical and practical aspects, as well as the existence of insufficient and vague data in actual equipments design, the possbilistic reliability models of typically general systems are constructed in this paper. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of system reliability models is simplified without loss of the nature of the problems to be solved, and proofs and calculations of possibilistic reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward than the traditional ones. The detailed application examples in system reliability analysis verify a possibilistic design framework on the general reliability models background, which provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.

System reliability of a manufacturing process should address effects of both the manufacturing system (MS) component reliability, and the product quality. In a multi-station manufacturing process (MMP), the degradation of MS components at an upstream station can cause the deterioration of the downstream product quality. At the same time, the system component reliability can be affected by the deterioration of the incoming product quality of upstream stations. This kind of quality & reliability interaction characteristics can be observed in many manufacturing processes such as machining, assembly, and stamping. However, there is no available model to describe this complex relationship between product quality, and MS component reliability. This paper, considering the unique complex characteristics of MMP, proposes a new concept of quality & reliability chain (QR-Chain) effect to describe the complex propagation relationship of the interaction between MS component reliability, and product quality across all stations. Based on this, a general QR-chain model for MMP is proposed to integrate the product quality with the MS component reliability information for system reliability analysis. For evaluation of system reliability, both the exact analytic solution, and a simpler upper bound solution are provided. The upper bound is proved to be equal to the exact solution if the product quality does not have self-improvement, which is generally true in many MMP. Therefore, the developed QR-chain model, and its upper bound solution can be applied to many MMP.

5 - Reliability of Large Multi-State Systems

In this paper, a polygonal k ‐out‐of‐ n :F system reliability model is established, where subsystems may share components within the polygon. Components are exposed to a combination of extreme shocks and δ ‐shock. The reliability of each subsystem's components is modeled using a phase‐type distribution and Markov chain approach, with component reliability being incorporated into subsystem reliability calculations. Disjoint cases are classified based on the number of failed components in shared regions to derive the shared component failure probability matrix and the initial probability distribution. Using the transfer matrix and transition rate matrix, the overall system reliability is determined through the Markov chain embedding approach. For this model, the total cost function of the system was determined by calculating the cost functions of different scenarios and different subsystems, and the optimal maintenance time for the system was obtained. The effectiveness of the method is verified by taking the unmanned aerial vehicle swarm working in a harsh environment as an example.

Reliability allocation is a very important problem during early design and development phases of a system. There are several reliability allocation techniques which are used to achieve the target reliability. The feasibility of objectives (FOO) technique is one of them that is widely used to perform system reliability allocation. But this technique has two fundamental shortcomings. The first is the measurement scale and the second is that it does not consider the order weight of the reliability allocation factors. The prioritization of the factors is also an important topic in decision making. Practically, all factors in multi-criteria decision making (MCDM) are not in the same priority level. Hence, in decision making situation, it is usual for decision makers to consider different priority factors. So, considering the prioritization of the factors, a reliability allocation method is proposed here to overcome the shortcomings of the FOO technique. Also, a case study on reliability allocation in airborne radar system is considered here to verify the efficiency of the proposed approach. Finally, the results are calculated in different optimistic and pessimistic view point and compared with the FOO technique. This comparison exhibits the advantages and supremacy of the proposed approach.

In this paper an analysis of component and system reliability for lattice systems is proposed when component failures are not statistically independent. We deal the case that the failure rate of a component depends on the number of the adjacent failed components. And we discuss the maintainability of the system when a failed component is replaced by a spare component. At first we discuss the approximated reliability of each component. Then we estimate the mean number of failed components. Furthermore, the system reliability is approximated by using the component reliability.

Systems with protective auxiliary component are common in engineering industry. The auxiliary components in these systems play an essential role to protect the main components from severe environment impact, however, dependence between the main and auxiliary components are usually ignored in most existing literatures. Besides, failures of auxiliary components are hidden in most systems since they do not halt the system. Therefore, inspections are necessary. In most existing studies, inspections are assumed to be perfect, which is not consistent with the reality. In this paper, a new reliability model is developed for systems with dependent main and auxiliary components under imperfect inspections. Some important indexes, such as system reliability and availability, are derived by the recursive and matrix methods, respectively. Thereafter, a numerical example is presented to illustrate the results and verify the correctness of the proposed method, in which influences of imperfect inspections are also studied by conducting sensitivity analysis on the inspection accuracy parameter.

Phased mission modelling of systems with maintenance-free operating periods using simulated Petri nets

Large‐scale agricultural machinery exhibits complex functionalities, limited test sample sizes, low fault data credibility, and urgent seasonal reliability demands, which challenge the precision of current reliability allocation methods. To better fulfill the reliability requirements of agricultural systems while accommodating industrial transformation and demand‐driven development trends in agricultural equipment, this study proposes a reliability allocation method tailored for complex agricultural machinery systems. Specifically, building upon structural–functional analysis and FMECA, an evaluation framework termed the 8B framework is established, comprising eight key indicators aligned with the characteristics of agricultural machinery. A multi‐factor maintainability definition method incorporating demand‐side response is proposed to quantify the feedback of user expectation deviations in reliability allocation. Using an improved TFN‐CRITIC‐IFM method for comprehensive weighting of the 8B framework, the weighting results are applied to the multi‐factor scoring matrix through slack factors, thereby establishing a failure rate allocation model for new products. Furthermore, a variable failure rate correction operator based on the parametric sigmoid function is introduced to characterize the dynamic approximation process of failure rate allocation results toward measured data, while avoiding excessive reliance on insufficient preliminary data with low credibility. A series system reliability allocation model considering demand‐side response and failure data correction is developed. The effectiveness of the proposed method is validated through a case study on a grain combine harvester.

In this paper, structural systems reliability analysis was used to estimate the system reliability of a typical semi-submersible based on the characteristic structure failure mechanisms under extreme wave loads. First, a three-dimensional simulation model was created for the chosen semi-submersible platform using an elastic-perfectly plastic material model, neglecting the effect of the strain hardening assumption. Then, under design wave conditions, and characteristic structural failure mechanisms of a semi-submersible platform were examined, and a system reliability model was developed based on the failure mechanism of the chosen platform. Finally, system reliability methods were used to determine the platform’s system reliability. It was discovered that the main node’s system reliability makes a significant contribution to the overall structure reliability, so it is strongly advised that the reliability of the main nodes be taken into account when determining the overall structure’s reliability. This research aims to apply reliability theory in offshore engineering and, ideally, to encourage the reliability-based design of semi-submersible platforms and other similar structures.

Analysis of common cause failure effect on system reliability in seismic PSA

Degradation of multi-component system exists widely in the field of engineering. And the degradation failure of multi-component system is due to the overall degradation of the system to a certain extent, or the degradation of component. In this paper, we focus on the reliability model of multi-component degradation system, which failure caused by degradation of component failure, was simplified and applied to the optimization model of maintenance policy. For each component of the degraded system, pure degradation and degradation increment can cause irreversible damage to it. The continuous degradation process was considered to be linear. And the degradation increment caused by the shock was considered to be cumulative. The shock was random, so that subject to Poisson distribution. The reliability model of the multi-component degradation system under the cumulative Poisson shock is complex and not easy to be applied to the maintenance model optimization model of the multi-component system. From that, this paper simplified the reliability model of multi-component degradation system under the cumulative Poisson shock. And the simplified reliability function was used as the constraint to improve the optimization model of multi-objective maintenance policy based on the reliability theory so as to facilitate its application in engineering. The feasibility of the simplified reliability model and the correctness of the improved multi-objective maintenance policy was verified by case. The influence of the change of the reliability constraint value on the whole maintenance policy was analyzed.

In reliability allocation, certain reliability values are assigned to subsystems and components to achieve the required system reliability. One big challenge in solving such reliability‐based design problems is how to handle the uncertain preferences of a decision maker on multiple attributes of interest. In this paper, we propose a new ordered weighted averaging (OWA) method based on an analytic hierarchy process to address the decision maker's uncertain preferences in reliability allocation. In the proposed OWA operator, a bi‐objective mathematical programming model considering both maximal entropy and minimal variance is transformed into a single‐objective mathematical programming model using an ideal‐point method. The maximum entropy minimal variance OWA operator takes full advantage of available information and avoids overestimating the decision maker's preferences. A detailed computational procedure is presented to facilitate the implementation of the proposed method in practice. An illustrative example about the powertrain of fuel cell vehicles is provided to demonstrate the effectiveness of this method in handling multiple attributes with uncertain preferences in reliability allocation. Copyright © 2015 John Wiley & Sons, Ltd.