Reliability Models of Complex Systems for Robots and Automation

Hamed Fazlollahtabar, Seyed Taghi Akhavan Niaki

• Publisher: CRC Press
• Year: 2017
• eBook ISBN: 9781351337328
• Topic: Technology & Engineering
• Subtopic: Industrial Design
• Index: Technology & Engineering

Availability of a system is a crucial factor for planning and optimization. The concept is more challenging for modern systems such as robots and autonomous systems consisting of a complex configuration of components. As complex systems have become global and essential in today's society, their reliable design and the determination of their availability have turned into a very important task for managers and engineers.

Reliability Models of Complex Systems for Robots and Automation offers different models and approaches for reliability evaluation and optimization of a complex autonomous system. Comprehensive fault tree analysis on the critical components of industrial robots and its integration with the reliability block diagram approach is designed in order to investigate the robot system reliability. The cost and hazard decision tree are integrated for the first time in an approach to evaluate the reliability of a complex system.

• Considers a complex production system composing of several autonomous robots
• Develops binary state reliability evaluation model for a complex system
• Introduces new concepts of hazard decision tree
• Proposes fault tree and reliability block diagram for complex robotic systems
• Develops stochastic process based reliability evaluation and optimization models

Today's competitive world with increasing customer demands for highly reliable products makes reliability engineering a more challenging task. Reliability analysis is one of the main tools to ensure agreed delivery deadlines which in turn maintains certainty in real tangible factors such as customer goodwill and company reputation.

1
Introduction and Background

1.1Overview

Today’s competitive world with increasing customer demands for highly reliable products makes reliability engineering a challenging task. Reliability analysis is one of the main tools to ensure agreed delivery deadlines are met, which in turn maintains certainty intangible factors such as customer goodwill and company reputation (Jardine, 1998). Downtime often leads to both tangible and intangible losses. These losses may be due to some unreliable components; thus, an effective strategy needs to be framed for maintenance, replacement, and design changes needed for those components (Ross, 1970; Billinton and Allan, 1983; O’Connor, 2002).

The design for reliability is an important research area, specifically in the early design phase of product development. In fact, reliability should be designed and built into products and systems at their earliest development stages. Reliability-targeted design is the most economical approach to minimize the life cycle costs of the product or system, based on which one can achieve better product or system reliability at much lower costs. Otherwise, the majority of life cycle costs are locked in phases other than design and development; poor reliability consideration at the design stage can have implications later on in the product life. If reliability analysis is applied during the conceptual design phase, its impact will be more remarkable on the design process, producing high-quality products (Soleimani and Pourgol-Mohammad, 2014). In other words, a structure reliable in concept is less expensive than a structure that is not reliable in concept, even with improvement at a later phase of the design process (Avontuur and van der Werff, 2001). Moreover, reliability analysis in the conceptual design process leads to more optimal structures than its application at the end of the design process (Avontuur, 2000).

In problems of maintenance optimization, it is convenient to assume that repairs are equivalent to replacements, and those systems or objects are, therefore, brought back to an as-good-as-new state after each repair. Standard results in renewal theory may then be applied for determining optimal maintenance policies. In practice, there are many situations in which this assumption cannot be made. The quintessential problem with imperfect maintenance is how to model it. In many cases, it is very difficult to assess by how much a partial repair will improve the condition of a system or object, and it is equally difficult to assess how such a repair influences the rate of deterioration. Kallen (2011) proposed a superposition of the renewal process that is used to model the effect of imperfect maintenance. It constituted a different modeling approach than the more common use of a virtual age process.

Nishijima (2007) addressed the issue of optimization of reliability acceptance criteria for components of complex engineered systems with a given criterion for an acceptable system risk. To this end, they first described how complex engineered systems may be modeled hierarchically using Bayesian probabilistic networks. The Bayesian probabilistic network serves as a function that relates the reliability acceptance criteria of the individual components of the system to the risk acceptance criteria of the system. Thereafter, a constrained optimization problem is formulated for the optimization of the component reliabilities. In this optimization problem, the system risk acceptance criteria define the constraint, and the expected utility from the system is considered the objective function.

During the design phase of a product, reliability engineers are called upon to evaluate the reliability of the system. The question of how to meet a reliability goal for the system arises when the estimated reliability is inadequate. This then becomes a reliability allocation problem at the component level. Mettas (2000) estimated a general model for the minimum reliability requirement of multiple components within a system that will yield to the ultimate reliability of the system. The model consisted of two parts. The first part was a nonlinear programming formulation of the allocation problem. The second part was a cost function formulation to be used in the nonlinear programming algorithm, where a general behavior of the cost as a function of a component’s reliability was assumed.

In the exact method, there are two classes for the computation of network reliability. The first class deals with the enumeration of all the minimum paths or cuts. A path is a subset of components (edges and/or vertices) that guarantees the source and the sink to be connected if all the components of this subset are functioning. A path is minimal if a subset of elements in the path, which is also a path, does not exist. A cut is a subset of components (edges and/or vertices) whose failure disconnects the source and the sink. A cut is minimal if a subset of elements in the cut, which is also a cut, does not exist (Hariri and Raghavendra, 1987; Ahmad, 1988). The probabilistic evaluation uses the inclusion–exclusion or sum-of-disjoint-products methods because this enumeration provides nondisjoint events. Numerous works about these kinds of methods have been presented in the literature (Lucet and Manouvrier, 1999). In the second class, the algorithms are based on graph topology. In the first process, we reduce the size of the graph by removing some structures, namely, polygon-to-chain (Choi and Jun, 1985) and delta-to-star reductions (Gadani, 1981). By this, we will be able to compute the reliability in linear time and the reduction will result in a single edge. The idea is to decompose the problem into one failed and another functioning (Carlier and Lucet, 1996). The same was confirmed by Theologou and Carlier (1991) for dense networks. Satyanarayana and Chang (1983) and Wood (1985) have shown that factoring algorithms with reductions are more efficient at solving this problem than the classical path or cut enumeration methods.

Statistical modeling has been paramount for the quality control and maintenance of repairable production systems. It allows to reduce costs and to prevent the occurrence of undesirable events. At the same time, it provides support for enhancing production levels and the longevity of components. The generalized renewal process (GRP) is a powerful statistical formalism for modeling repairable systems. It enables one to evaluate the quality of the performed interventions as well as to forecast the time for undesirable events to occur (Felix de Oliveira et al., 2016).

In GRP reliability analysis for repairable systems, the Monte Carlo (MC) simulation method is often used, instead of the numerical method, to estimate model parameters because of the complexity and difficulty of developing a mathematically tractable probabilistic model. Wang and Yang (2012) proposed a nonlinear programming formulation based on the conditional Weibull distribution for repairable systems, using negative log-likelihood as an objective function and adding inequality constraints to model parameters to estimate the restoration factor for the Kijima-type GRP model. This method minimized the negative log-likelihood directly and avoided solving the complex system of equations. Numerical studies on NC machine tools were analyzed by the proposed approach. The results showed that the GRP model is superior to the ordinary renewal process (ORP).

An important characteristic of the GRP, which is of great practical interest, is the generalized renewal equation, which represents the expected cumulative number of recurrent events as a function of time. Just like in an ORP, the problem is that the generalized renewal equation does not have a closed form solution, unless the underlying event times are exponentially distributed. The MC solution, although exhaustive, is computationally demanding. Yevkin and Krivtsov (2012) offered a simple-to-implement (in an Excel spreadsheet) approximate solution, when the underlying failure-time distribution is Weibull. The accuracy of the proposed solution was in the neighborhood of 2%, when compared to the respective MC solution.

Many models and methodologies are available to deal with imperfect repair for repairable systems. Initial attempts at modeling imperfect repair using the (p, q) rule that defined the two extremities of imperfect repair—perfect renewal and minimal repair—were effectively extended by Kijima and Sumita. They developed a generalized renewal theory from the renewal theory in the context of imperfect repair and applied it to repairable systems with the concept of virtual age. Since this pioneering work, much of imperfect repair modeling literature builds up on Kijima’s models based on the GRP. Tanwar et al. (2014) conducted a survey for imperfect repair of repairable systems using the GRP based on arithmetic reduction of age (ARA) and arithmetic reduction of intensity (ARI) concepts in general and Kijima models in particular. In addition to the theoretical development of Kijima models and its extensions, the review highlighted their applications such as designing maintenance policies based on the concept of ARA.

van der Weide and Pandey (2015) presented a stochastic approach to analyze instantaneous unavailability of standby safety equipment caused by latent failures. The problem of unavailability analysis was formulated as a stochastic alternating renewal process without any restrictions on the form of the probability distribution assigned to time to failure and repair duration. An integral equation for point unavailability was derived and numerically solved for a given maintenance policy.

Alem Tabriz et al. (2015) considered both failure rates as internal factors and the shocks as an external factor to develop age-based replacement models in order to determine the optimal replacement cycle. As a result, according to system reliability, maintenance costs of the system were minimized. Analysis of results showed all models provided optimal replacement cycle, and at this time, the cost rate of the system, by considering the reliability rate, is minimal. Also, with an increase of one to two units, the reliability rate increases much higher than the cost.

1.2Reliability Engineering

Among its many interpretations, the term reliability most commonly refers to the ability of a device or system to perform a task successfully when required. More formally, it is described as the probability of proper functioning at a given time and under specified operating conditions. Mathematically, the reliability function is defined by

(1.1) $$R\left(t\right)=P\left(T>t\right);\forall t\ge 0,$$

where T is a nonnegative random variable representing the device or system lifetime. For a system composed of at least two components, the system reliability is determined by the reliability of the individual components and the relationships among them. These relationships can be depicted using a reliability block diagram (RBD). While simple systems are usually represented by RBDs with components in either a series or a parallel configuration, the RBDs of complex systems cannot be reduced to series, parallel, or series–parallel configurations. In a series system, all components must function satisfactorily in order for the system to operate. For a parallel system to operate, at least one component must function correctly.

There are some techniques available in the literature that can be employed to determine a mathematical expression denoting the reliability of a system in terms of the reliabilities of its components. In these techniques, it is assumed that the reliabilities of the components have been determined using standard (or accelerated) life data analysis techniques, so that the reliability function for each component is known. Having this component-level reliability information available, it then becomes necessary to determine how these component reliability values are combined to determine the reliability function of the overall system.

Reliability assessment is a systematic implementation through the design, testing, production, storage, and usage phases of a product or system. It is a process of analyzing and confirming the reliability of a system and its components (Hwang et al., 1981; Zio and Pedroni, 2009; Levitin and Lisnianski, 2013). Reliability evaluation includes both qualitative and quantitative analytical techniques to model and predict system reliability throughout the product/system life cycle. There are basically four aspects of the technical contents of system reliability assessment, including reliability modeling, reliability data collection and processing, unit reliability assessment, and system reliability synthesis. To obtain the reliability of a complex system, the reliability model should be built to describe the failure logic relationship between the whole system and its compositions. In recent decades, various reliability modeling methods have been developed for complex systems (Mi et al., 2016), where some static and dynamic modeling techniques, such as RBD model, fault tree (FT) model, binary decision diagrams (BDD) model, Markov model (Li et al., 2012), dynamic fault tree (DFT) model (Li et al., 2013), and Petri net model (Huang et al., 2010), have been applied.

The DFT model, first proposed by Dugan et al. (1992, 2000), is a mature and important method in the reliability analysis of dynamic systems (Hao et al., 2014). In this regard, Rao et al. (2009) presented an approach to solve dynamic gates, which can be used to alleviate the state space explosion problem. Considering the interactive repeated events in different dynamic gates, Merle et al. (2010) developed a new analytical method to solve DFTs with priority dynamic gates and repeated events. In addition, approximate DFT calculations were presented by Lindhe et al. (2012) based on a Markovian approach, which was used for water supply risk modeling performed by standard MC simulations. To overcome the limitations caused by the increasing size of FTs in traditional reliability assessment, Chiacchio et al. (2013) proposed a Weibull-based composition approach for large DFTs to reduce the computational effort. Mo (2014) developed a multivalue, decision-diagram-based DFT analysis method to analyze the reliability of large dynamic systems based on the state explosion and computational efficiency problems in the DFT model. Moreover, Ge et al. (2...

Table of contents

• Cover
• Halftitle Page
• Title Page
• Copyright Page
• Contents
• Preface
• Acknowledgments
• About the Authors
• 1. Introduction and Background
• 2. Fault Tree Analysis and Reliability Block Diagram
• 3. Cost and Hazard Decision Tree Models
• 4. Binary State and Bernoulli Trials Reliability Model
• 5. Binary Decision Diagram Reliability Model
• 6. Decomposition and Minimal Path and Cuts Method
• 7. Bayesian Network Reliability Model
• 8. Modified Branching Process Reliability Model
• 9. Standby Renewal Process Reliability Model
• 10. Reliability and Inspection Model
• References and Further Reading
• Index