Multi-objective optimization of reliability-redundancy allocation problem for multi-type production systems considering redundancy strategies

https://doi.org/10.1016/j.ress.2019.106681Get rights and content

Highlights

  • A new model of multi-type production systems that generalizes the manufacturing systems with multiple switchable production lines is developed.

  • A binary matrix is used to describe the composition of each production line of the multi-type production system.

  • RRAP considering redundancy strategies (either active or cold standby) is modeled for enhancing the reliabilities of different production lines.

  • A NSGA-II is developed to solve the RRAP for the multi-type production system.

Abstract

This paper innovatively proposes a new model of multi-type production system which can process different types of production. The multi-type production system consists of several independent sequentially ordered subsystems which undertaking different tasks. Different types of production require different manufacturing lines: required subsystems will be powered on, while others powered off. The system can switch into different production line based on detection results. A binary matrix is suggested to describe the composition of each production line of the multi-type production system. Reliability-redundancy allocation on each subsystem is considered for achieving higher reliabilities of different production lines. The reliability-redundancy allocation problem for the proposed multi-type production system is essentially multi-objective subject to resource constraints. This paper formulates the multi-objective optimization problem and considers the optimal redundancy strategy, either active or cold standby. The exact reliabilities of cold standby redundant subsystems with imperfect detector/switch are determined by introducing an approach based on continuous time Markov chain. Then, a multi-objective evolutionary algorithm is suggested to solve the proposed reliability-redundancy allocation problem. Finally, numerical examples are presented to illustrate the proposed methods.

Introduction

In many practical industrial applications, a manufacturing or production system is usually constructed using several specific functional stations [1] or subsystems, and can process multiple types of production by choosing or setting up different production lines appropriately. Each production line in a manufacturing system consists of a specific sequence of stations or subsystems. Multiple production lines are known to be beneficial for manufacturing systems with higher efficiency and flexibility [2,3]. A great deal of research has been devoted to studying or evaluating the performance of systems with multiple production lines since Chen & Lan [2] came up with the concept of multiple-production-line system. In [2], a maximal profit flow model was proposed to reach the optimal design of multiple-production-line system, but the whole system was assumed to make a same type of product during the manufacturing process. Lan [3] proposed a mathematical model to design a manufacturing system consisting of multiple production lines in parallel with further considering the production deadline. Lin & Chang [4] modeled a manufacturing system as a manufacturing network with multiple production lines and provided the evaluation method of system reliability, two scenarios (identical vs. distinct production lines in parallel producing the same product type) were fully discussed in their work. Lin & Chang [1] proposed a novel technique to measure the performance of a manufacturing system considering stochastic capacities and multiple production lines, they also discussed the aforementioned two scenarios. References [5,6] focused on the flowshop scheduling problems of multiple production lines for the precast production and the reinforced precast concrete components, respectively.

However, in these existing studies of multiple production lines, references [1], [2], [3], [4] only considered manufacturing systems processing a same production type, while references [5,6] mainly emphasised on the optimization approaches for scheduling problems. The modelling and optimal designing of certain systems which can process different types of production are rarely discussed. Hence, in this paper, a new model of multi-type production system is proposed to investigate such cases. The considered multi-type production system consists of several independent subsystems. Each subsystem undertakes different task or processes unique operation. These subsystems can be regarded as linearly arranged based on working procedures. Different types of production may be processed by different manufacturing lines which consists of a sequence of selected subsystems: the required subsystems will be powered on, while others powered off. As shown in Fig. 1, the multi-type production system can switch into different manufacturing lines by detecting the types of production. For each type of production, the reliability of corresponding production line equals to the reliability of the “series system” consisting of the subsystems connected to power source. The introduction of this new model of multi-type production system is motivated by the following examples.

Pharmaceutical processing system: consider a pharmaceutical plant consists of various subunits, such as weighting machine, shifter machine, mass mixer, granulator, fluid bed dryer, blender, compression machine, coating machine, and etc. [7]. All these subunits are arranged in series. This system can process different types of raw materials. Some subunits of this system are necessary for all types of raw materials, such as weighting machine, fluid bed dryer and so on, while some other subunits are not required for certain raw materials. Hence, when processing a same type of raw materials, the subunits which are not required can be shut down temporarily.

Service system: consider a service center which consists of several specific functional stations. All these stations can be regarded as positioned in series. For different clients who come to this center to seek for different types of service, they do not need to visit every functional station from beginning to end, and they can skip some stations which are not required.

Auto-loading system: consider a modern automatic artillery which is compatible with different types of ammunition. The auto-loading system, consisting of various functional modules, needs to automatically detect and transport required ammunition to the gun barrel. For the ammunition with different size, weight, shape, and location, the auto-loading system needs to activate different functional modules to complete a series of actions. Some of these functional modules, such as the hydro-cylinder and motor, are necessary for all types of ammunition, while some other modules, such as inhibiting devices, are activated only as needed.

A variety of other practical systems also fit this model, for example, heating system, transportation system, and etc. These complex multi-type production systems exhibit hierarchical design structures and the reliabilities of such systems during design stage can be improved by enhancing the reliabilities of components in subsystems or allocating appropriate redundancies at component level [8,9]. Both ways usually increase the resources (cost, volume, weight, etc.). Generally, there are two different reliability optimization problems: (a) the redundancy allocation problem (RAP); (b) the reliability–redundancy allocation problem (RRAP). In RAPs, there are discrete component choices with known characteristics such as reliability, cost, and weight, where the aim is to find the optimal number of redundant components allocated to each subsystem in order to maximise the overall system reliability subject to resource limitations. While RRAPs involve the simultaneously selection of components reliabilities and redundancy levels. In RRAPs, the component reliability is not given but treated as a design variable while the component cost, weight, volume, and etc. are defined in advance as increasing nonlinear functions of component reliability [9,10].

In recent years, the technique of reliability-redundancy allocation is widely studied for various systems with different considerations on either the optimization techniques or the redundancy strategies. Garg et al. [11] solved a RRAP with nonlinear resource constraints by applying an efficient two-phase approach, of which the first phase is an algorithm based on artificial bee colony while the second phase is an improvement procedure. Ardakan and Hamadani [10] considered the mixed-integer non-linear optimization of RRAP with using a cold-standby strategy for redundant components, they developed a bi-objective RRAP and solved it by using a non-dominated sorting genetic algorithm II (NSGA-II). Garg et al. [12] also developed a bi-objective RRAP for a series-parallel system in fuzzy environment, the bi-objective problem was converted to single objective by using intersection (minimum) aggregation operator considering the preferences of decision makers in the form of weights. Huang [13] proposed a particle-based simplified swarm optimization algorithm to solve RRAPs for four benchmark systems, but he only considered active redundancies. Raouf and Pourtakdoust [14] studied a multi-objective RRAP of a two-stage launch vehicle for maximizing the system reliability while minimizing the launch vehicle cost. They considered three groups of design variables, namely the component reliability, system redundancy level, and the type of components. Garg [15,16] solved the RRAPs of series–parallel systems under nonlinear resource constraints by using the cuckoo search algorithm and the biogeography-based optimization algorithm, respectively. Kim and Kim [17] investigated an advanced RRAP with considering either active or cold standby redundancy strategy, and suggested an exact reliability function for a cold standby redundant subsystem with an imperfect detector/switch. Kim [18] presented new reliability models for k-out-of-n systems using a structured continuous-time Markov chain, and studied both RAP and RRAP for the considered system. Ardakan et al. [19] implemented a novel mixed strategy in the RRAP and showed that the new strategy outperforms the active and standby strategies on benchmark problems. Ghavidel et al. [20] developed an efficient improved hybrid Jaya algorithm for solving various types of nonlinear mixed-integer RRAPs. Muhuri et al. [21] proposed a new model for the multi-objective RRAP considering interval type-2 fuzzy uncertainties in the component parameters and solved the problem using NSGA-II. Ardakan and Rezvan [22] investigated a cold-standby RRAP and formulated the allocation problem in a bi-objective model, they also suggested a NSGA-II to solve the multi-objective problem. Yeh [23] proposed a new boundary simplified swarm optimization algorithm by integrating a novel self- boundary search and a two-variable update mechanism in solving RRAPs, so as to balance the exploration and exploitation ability. Therefore, subsequent to aforementioned studies of RRAPs, this paper tries to investigate the RRAP for the newly proposed multi-type production systems, aiming to achieve higher reliabilities of each production lines.

When allocating redundant components to a subsystem of the proposed multi-type production system, an optimal redundancy strategy should be defined in advance. According to the failure characteristics of redundant components, there are two basic redundancy strategies namely active strategy and standby strategy [17,18,22] and other two new emerging strategies namely mixed redundancy strategy [19,[24], [25], [26], [27]] and K-mixed strategy [28,29]. For the active redundancy strategy, the redundant components are simultaneously powered on from the very beginning of the mission although only one is required at any particular time. While for the standby redundancy strategy, there are three general standby strategies: hot, cold, and warm standby. In the hot standby redundancy, component failure does not depend on whether the component is idle or in operation. In contrast with hot standby, the cold standby components are unpowered and thus do not operate until needed to replace a failed online component. In the warm standby redundancy, the components are partially affected by the operational stresses. In this manner, the likelihood of failure in the cold standby state is the lowest and has usually been assumed to be zero. The cold standby redundancy can usually provide higher system reliability than using hot standby and warm standby redundancy, especially for the large and long-term systems [30]. The mixed redundancy strategy is a combination of active and standby strategies. In mixed redundancy strategy, each subsystem uses active and standby components simultaneously. In the beginning of working process, all the active components are in operation and when the last active component fails, it will be replaced by the first standby redundant component. The subsystem fails when all the active and standby components fail. The mixed redundancy strategy has been proved superior to the basic two strategies [19]. Recently, another form of mixed redundancy strategy, called K-mixed redundancy strategy, has been suggested to eliminate the weakness caused by standby counterpart and its switching mechanism [28]. In K-mixed redundancy strategy, when the first active component fails, it will be replaced by an activated standby redundant component. This strategy keeps a specific number of components in active mode as long as possible. The latter two emerging strategies lead to higher reliability comparing to the basic two strategies and will become the research focuses in the field of redundancy allocation optimization in the near future. From the perspective of convenience for practical application, the most widely used two basic redundancy strategies are considered in our proposed new model of multi-type production system.

Furthermore, in the standby, mixed, and K-mixed redundancy strategies, all the redundant components require a fault detect/switch mechanism to identify the failure of the operating components and activate the substitutes to take over the mission task. If the fault detect/switch mechanism fails, the system will fail when the current primary component breaks down. Thus, the imperfect detector/switch must be taken into consideration for redundancy optimization. Coit [31] has discussed two distinct imperfect detector/switch cases: (i) continuous monitoring and detection, and (ii) detection and switching only at time of failure. He also presented the reliability function for the standby redundant system with imperfect detector/switch and provided the lower bound of system reliability for RAPs. Thereafter, the approach of maximizing the lower bound of system reliability has been widely used in recent studies of reliability optimization problems [10,19,24,30,[32], [33], [34], [35], [36]]. In [17], an exact reliability function for a cold standby redundant system with an imperfect detector/switch was suggested and expected to replace the approximating model in [31]. Therefore, in this paper, the continuous time Markov chain model in [17] is introduced for calculating the reliabilities of subsystems with cold standby redundant components.

For the multi-type production system proposed in this paper, either active or cold standby is considered as the redundancy strategy for achieving higher reliabilities of each manufacturing lines. The advantageous strategy depends on the reliabilities of a fault detector/switch and components, in addition to redundancy levels [17]. Constrained by recourse limitations, maximizing the reliabilities of different manufacturing lines of the multi-type production system is essentially a multi-objective RRAP. The optimal problem involves simultaneous selection of components reliabilities, redundancy levels, and redundancy strategies for each subsystem. Recently, there has been a growing research interest in the topic of multi-objective reliability modelling and optimization. The development of multi-objective evolutionary algorithms (MOEA) has also successfully evolved, producing better and more efficient algorithms, such as NSGA [37], strength Pareto evolutionary algorithm (SPEA) [38]/SPEA2 [39], Pareto archived evolution strategy [40], Pareto envelope-based selection algorithm (PESA) [41]/PESA-II [42], NSGA-II [43], niched Pareto genetic algorithm [44], multi-objective particle swarm optimization [45], MOEA based on decomposition [46], multi-objective differential evolution [47], modified ɛ-MOEA [48], and etc. Among these algorithms, the NSGA-II is one of the most widely used state-of-the-art MOEAs, which has been extensively tested and shown to be very competitive. In this paper, a NSGA-II is developed to solve the proposed RRAP for the multi-type production system.

The structure of this paper is organised as follows. In Section 2, we describe the multi-type production system, formulate the mathematical model of multi-objective RRAP, and provide approaches for calculating the subsystem reliability with either active or cold standby redundancy. Section 3 presents a NSGA-II for solving the proposed multi-objective optimization problem. Section 4 presents two numerical examples of multi-type production system, and gives the experimental results to demonstrate the efficiency of the proposed methodology through computational experiment. Finally, conclusions are presented in Section 5.

Section snippets

Assumption and notation

Before introducing the new model of multi-type production system and formulating the RRAP for the proposed system, there are several assumptions that should be described as below.

  • (1)

    All n subsystems in the proposed multi-type production system are mutually independent and sequentially ordered.

  • (2)

    All components in a subsystem are identical and have exponential distributed time-to-failure, the failed components do not damage the system and are not repaired.

  • (3)

    The production detect/switch device is assumed

Solution methodology

Searching the optimal solution for the RRAP (2) is a mixed-integer non-linear programming problem. The widely used method for solving such kind of multi-objective optimization problem is heuristic algorithm. A well-known MOEA, called NSGA-II, is developed herein for solving the formulated multi-objective problem. It was first proposed by Deb et al. [43] and shown to be very competitive. In this section, some customised features of NSGA-II for solving the proposed problem are presented. More

Numerical examples

In this section, we present two numerical examples to illustrate the considered problem and the proposed methodology. The RRAPs were solved by using the NSGA-II algorithm presented in section III, implemented in MATLAB R2008b on a PC with Intel Core i5-4590 CPU 3.3 Hz processor and 4GB RAM under Windows 7 operating system.

Conclusions

This paper developed a new model of multi-type production systems that generalizes the manufacturing systems with multiple switchable production lines. A binary matrix was introduced into the model to describe the structure of the multi-type production system, of which each production line consists of several required subsystems. Reliability-redundancy allocation with considering redundancy strategies (either active or cold standby) was considered for enhancing the reliabilities of different

Acknowledgements

This work was supported in part by the Science and Technology Department of Fujian Province (2018H0043) and in part by the Intelligent Manufacturing Comprehensive Standardization Project (Researches and verification for the standard of remote operation and maintenance to the key technical equipment in hazardous chemical storage area of petrochemical industry).

References (62)

  • H. Kim et al.

    Reliability–redundancy allocation problem considering optimal redundancy strategy using parallel genetic algorithm

    Reliab Eng Syst Saf

    (2017)
  • H. Kim

    Optimal reliability design of a system with k-out-of-n subsystems considering redundancy strategies

    Reliab Eng Syst Saf

    (2017)
  • Z. Ouyang et al.

    An improved particle swarm optimization algorithm for reliability-redundancy allocation problem with mixed redundancy strategy and heterogeneous components

    Reliab Eng Syst Saf

    (2019)
  • H. Gholinezhad et al.

    A new model for the redundancy allocation problem with component mixing and mixed redundancy strategy

    Reliab Eng Syst Saf

    (2017)
  • A. Peiravi et al.

    Reliability optimization of series-parallel systems with K-mixed redundancy strategy

    Reliab Eng Syst Saf

    (2019)
  • R. Tavakkoli-Moghaddam et al.

    Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm

    Reliab Eng Syst Saf

    (2008)
  • A. Chambari et al.

    A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies

    Comput Ind Eng

    (2012)
  • A. Chambari et al.

    An efficient simulated annealing algorithm for the redundancy allocation problem with a choice of redundancy strategies

    Reliab Eng Syst Saf

    (2013)
  • X. Kong et al.

    Solving the redundancy allocation problem with multiple strategy choices using a new simplified particle swarm optimization

    Reliab Eng Syst Saf

    (2015)
  • M.A. Abido

    A niched Pareto genetic algorithm for multiobjective environmental/economic dispatch

    Int J Electr Power Energy Syst

    (2003)
  • X.N. Shen et al.

    Mathematical modeling and multi-objective evolutionary algorithms applied to dynamic flexible job shop scheduling problems

    Inf Sci

    (2015)
  • A. Konak et al.

    Multi-objective optimization of linear multi-state multiple sliding window system

    Reliab Eng Syst Saf

    (2012)
  • H. Garg et al.

    Multi-objective reliability-redundancy allocation problem using particle swarm optimization

    Comput Ind Eng

    (2013)
  • G. Levitin et al.

    Influence of failure propagation on mission abort policy in heterogeneous warm standby systems

    Reliab Eng Syst Saf

    (2019)
  • H. Kim

    Parallel genetic algorithm with a knowledge base for a redundancy allocation problem considering the sequence of heterogeneous components

    Expert Syst Appl

    (2018)
  • H. Kim et al.

    Reliability models for a nonrepairable system with heterogeneous components having a phase-type time-to-failure distribution

    Reliab Eng Syst Saf

    (2017)
  • H. Garg et al.

    Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment

    Expert Syst Appl

    (2014)
  • E. Zhang et al.

    Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization

    Reliab Eng Syst Saf

    (2016)
  • H. Garg

    A hybrid pso-ga algorithm for constrained optimization problems

    Appl Math Comput

    (2016)
  • H. Garg

    A hybrid GSA-GA algorithm for constrained optimization problems

    Inf Sci

    (2019)
  • B.Y. Qu et al.

    A survey on multi-objective evolutionary algorithms for the solution of the environmental/economic dispatch problems

    Swarm Evolut Comput

    (2018)
  • Cited by (57)

    View all citing articles on Scopus
    View full text