A pseudo-boolean approach to determining least cost tolerances

Kim, Sunn Ho; Knott, Kenneth

doi:10.1080/00207548808947848

Cited by 26 publications

(6 citation statements)

References 5 publications

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“…They chose a discrete combinatorial optimization technique for the optimization. Kim and Knott (1988) suggested that the methods proposed by Wilde (1975) and Ostwald and Huang (1977) could be combined to provide an improved approach. The suggested pseudo-Boolean approach allowed simplifications through a number of questions that could be asked by designers and manufacturing engineers.…”

Section: Tolerance Allocationmentioning

confidence: 99%

Discrete tolerance allocation for product families

Lööf¹,

Söderberg²

2012

Engineering Optimization

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Section: Tolerance Allocationmentioning

confidence: 99%

Discrete tolerance allocation for product families

Lööf¹,

Söderberg²

2012

Engineering Optimization

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“…Therefore, both and are neglected from the state-space model. From (8) and (9), an input-output relation can be obtained as (10) where the state transition matrix is defined as (11) Calculating variance/covariance for both sides of (10), we have (12) where and represent the covariance matrices of and , respectively; and . .…”

Section: A State-space Modeling Of Process Dimensional Variation Promentioning

confidence: 99%

Integration of Process-Oriented Tolerancing and Maintenance Planning in Design of Multistation Manufacturing Processes

Chen

Ding

Jin

et al. 2006

IEEE Trans. Automat. Sci. Eng.

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Manufacturing systems are inherently imperfect both statically and dynamically. Tolerance and maintenance design are two major tools to address the static and dynamic imperfection of manufacturing processes (i.e., inherent process imperfection and tooling deterioration, respectively). Yet, traditionally, tolerance and maintenance designs have been studied separately to address these two critical areas of manufacturing systems. This paper presents an integrated framework of tolerance and maintenance design for multistation manufacturing processes. Two nonlinear optimization problems are formulated to minimize the overall average production cost in the long run, which includes the tolerance cost of tooling fabrication, maintenance cost, and the overall loss of quality (as a part of the objective function or as a constraint function). The proposed methodology is illustrated, analyzed, and further discussed in the context of a multistation automotive body assembly process. Extensive numerical analyses are conducted to demonstrate the efficiency of the developed methodology. Given various cost components and time horizons, the integrated design scheme is compared with traditional design schemes in terms of cost efficiency, offering new insights into the interrelation between manufacturing process maintenance and tolerancing in the context of the product life cycle.Note to Practitioners-With intensified competition as a result of economic globalization, quality and cost have become crucial factors to the success of any manufacturing industry. Decisions in the process design phase, such as process tolerance assignment and maintenance planning, play a substantial role for overall manufacturing quality and costs. Tolerance of process variables determines the inherent variation level of a manufacturing process. Preventive maintenance oversees and controls process degradation and its resulting deterioration on product quality. Significant tooling and operational costs result from both tolerancing and maintenance activities. Traditionally, tolerancing and maintenance decision-making have been studied separately. Tolerancing was mainly conducted during the design stage; while maintenance policy was often determined after a manufacturing system was designed and installed. However, tolerancing of process variables and maintenance decision-making policy are interconnected in modern manufacturing systems. Intuitively, tight initial tolerances specified on process variables are able to reduce the frequency of conducting maintenance during production, since the process can accommodate more deterioration to reduce maintenance cost; but they take a toll on tolerance cost. On the other hand, loose initial tolerances specified on process variables can lower design cost but increase the frequency of maintenance during production. Hence, there is a critical need to strike a balance between the tolerance cost of tooling fabrication and the maintenance cost of tooling replacement. This paper presents a new framework to integrate tolerance ...

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“…The authors made use of Balas' algorithm for solution and claimed to achieve good computational efficiency by eliminating a large number of infeasible solutions. Kim and Knott [8] proposed a methodology for simplification of the original tolerance design problem by reformulating it to one involving a reduced number of variables and constraints. Lee and Woo [9] attempted both linear and non-linear tolerance design problems by proposing a zero-one integer programming formulation with the aid of what is termed the reliability index.…”

Section: Literature Reviewmentioning

confidence: 99%

Comparative study of genetic algorithm and simulated annealing for optimal tolerance design formulated with discrete and continuous variables

Sing

Jain

2005

Proceedings of the Institution of Mechanical Engineers, Part B:

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Optimal tolerance design has been the focus of extensive research for a few decades. This has resulted in several formulations and solution algorithms for systematic tolerance design considering various aspects. Availability of different alternative manufacturing processes or machines for realization of a dimension is frequently encountered. In such cases optimal tolerance design must also consider optimal selection of a set of manufacturing processes or machines as appropriate. Such a non-linear multivariate optimal tolerance design problem results in a combinatorial and multi-modal solution space. Optimal solution of this advanced tolerance design problem is difficult using traditional optimization techniques. The problem formulation becomes more complex with simultaneous selection of design and manufacturing tolerances. The focus of the current research is on the optimal solution of this advanced and complex tolerance design problem. Genetic algorithm and simulated annealing as non-traditional global optimization techniques have been used to obtain the solution. Application of the solution techniques has been demonstrated with the help of appropriate examples. Comparison of the results establishes that the genetic algorithm is the superior of the two approaches.

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A pseudo-boolean approach to determining least cost tolerances

Cited by 26 publications

References 5 publications

Discrete tolerance allocation for product families

Discrete tolerance allocation for product families

Integration of Process-Oriented Tolerancing and Maintenance Planning in Design of Multistation Manufacturing Processes

Comparative study of genetic algorithm and simulated annealing for optimal tolerance design formulated with discrete and continuous variables

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