Optimal tool replacement with product quality deterioration and random tool failure

Operating the machine with a deteriorated cutting tool often leads to poor product quality performance and high risk of tool failure. Replacing the degraded tool is an effective measure to reduce product quality loss and chance of tool failure. Excessive tool replacements, however, may increase the production capacity loss and tool replacement cost. Taking these factors into consideration, this paper presents an approach for determining the optimal tool replacement time for cutting process. It assumes that the product quality deteriorates as cutting tool wears and tool failure occurs randomly during the cutting process. A product quality failure rate model is developed to characterise the deterioration of product quality during the cutting process, and the product quality loss is estimated based on this model. Weibull distribution is employed to describe the stochastic tool life. A tool replacement model is proposed based on balancing the product quality loss, penalty cost for possible tool failure, production capacity loss and tool replacement cost. Sensitivity analysis of the optimal tool replacement decision is presented.     

Optimal cutting tool replacement based on tool wear status

In this paper, we develop an optimal tool replacement model based on the actual tool wear status. In this model, we consider separately the probability distribution of the tool capacity obtained under testing conditions and the tool capacity consumption by the workpieces. Special cases with exponential distribution for tool capacity consumption and in which one tool can process many workpieces are solved.     

Optimal control of a deteriorating process with a quadratic loss function

This paper considers the optimal determination of the length of the production run and the initial setting of a process that exhibits a linear drift that can start at a random point in time. Quadratic off‐target costs and time‐based costs of maintenance and salvage value are included in the formulation. The model includes other models proposed in the literature as particular cases. Numerical examples are provided to illustrate the application of the proposed model. Copyright © 2001 John Wiley & Sons, Ltd.     

Oscillators with symmetric and asymmetric quadratic nonlinearity

In this paper, oscillators with asymmetric and symmetric quadratic nonlinearity are compared. Both oscillators are modeled as ordinary second-order differential equations with strong quadratic nonlinearities: one with positive quadratic term and the second with a quadratic term which changes the sign. Solutions for both equations are obtained in the form of Jacobi elliptic functions. For the asymmetric oscillator, conditions for the periodic motion are determined, while for the symmetric oscillator a new approximate solution procedure based on averaging is developed. Obtained results are tested on an optomechanical system where the motion of a cantilever in the intracavity field is oscillatory. Two types of quadratic nonlinearities in the system are investigated: symmetric and asymmetric. The advantage and disadvantage of both models is discussed. The analytical procedure suggested in the paper is applied. The obtained solution agrees well with a numerical one.     

Process setup adjustment with quadratic loss

A classic adjustment method, the harmonic adjustment rule, minimizes expected quadratic loss where adjustments are easy and cheap, and the items produced during the adjustment process should be as close to target as possible. This paper generalizes the harmonic adjustment rule by explicitly taking into account measurement and adjustment costs. The generalization is static, in that adjustments are performed at predetermined points. An optimal model and a near-optimal approximation, in which adjustments are spaced roughly according to a geometric sequence, are presented. Skipping small adjustments dynamically may offer further savings, but dynamic models require further research.     

Optimal replacement with non-monotone failure rates

Summary The state of a system, which is subject to random failure, is described by a Markov process. Preventive replacements are possible at any stopping time. If the failure rate is not a monotone function, the optimal replacement policy that minimizes long run cost per unit time is in general no control limit rule. Conditions are given, under which the optimal policy can be determined.

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Zusammenfassung Der Zustand eines Systems werde bis zu seinem Ausfall durch einen Markov Prozeß beschrieben. Eine vorsorgliche Wartungserneuerung kann zu einer Stoppzeit durchgeführt werden. Ist die Ausfallrate nicht monoton, so wird die optimale Erneuerungsstrategie nach dem Durchschnittskostenprinzip i. a. keine control limit rule sein. Es werden Bedingungen angegeben, unter denen eine optimale Politik bestimmt werden kann.

     

Optimal asymmetric tolerance design

An asymmetric tolerance design occurs when deviation (from the ideal target) of a quality characteristic in one direction is more harmful than in the opposite direction. Asymmetric tolerances are common in many manufacturing processes. Traditionally, the designer of a manufactured component either would choose the smaller tolerance as the tolerance for both sides of the ideal target, or would set a process mean at the middle of the tolerances. Both methods fail to minimize the expected value of Taguchi's societal quality losses when the quality loss function is asymmetric. Linear and quadratic quality loss functions are considered to determine the optimal value of a process mean that minimizes the expected value of the quality loss function. Also, a quality loss model involving a pokayoke defect prevention procedure is investigated.     

On unbiased Lehmann-estimators of a variance of an exponential distribution with quadratic loss function

Summary Lehmann in [4] has generalised the notion of the unbiased estimator with respect to the assumed loss function. In [5] Singh considered admissible estimators of function λ^-r of unknown parameter λ of gamma distribution with density ,x> 0, whereb-known parameter, for loss function . Goodmann in [1] choosing three loss functions of different shape found unbiased Lehmann-estimators, of the variance σ² of the normal distribution. In particular for quadratic loss function he took weight of the formK(σ²)=C andK(σ²)=(σ²)^-2 only. In this work we obtained the class of all unbiased Lehmanns-estimators of the variance λ² of the exponential distribution, among estimators of the form functions of the sufficient statistics-with quadratic loss function with weight of the form ,C>0.

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Resumen Lehmann en su trabajo [4] generalizó la idea del estimador sin vías en relación a la aceptación de la función de pérdidas. En el trabajo [5] Singh considera de estimadores admisibles para la función λ^-r parámetro desconocido λ de la distribución de gamma, de densidad ,x>0,b>0 parámetro conocido, de la función de pérdidas resulta . Goodman en su trabajo [1] acumulando 3 formas diferentes de funciones de pérdidas encontró estimadores sin biases en el sentido de Lehmann de la variancia de σ² de una distribución normal, en particular para la función de pérdidas con los pesos, solo de la formaK(σ²)=C,K(σ²)=(σ²)^-2. En su trabajo distinguida la clase de todos los estimadores sin biases obtenidos en el sentido de Lehmann de la variancia λ² en la distribución exponencial, entre los estimadores de forma así pues de la función estadística suficiente— por una función de pérdidas al cuadrado con los pesos de la forma ,C>0. Palabras y frases. Estimador sin vías en el sentido de Lehmann, función de pérdidas, riesgo mínimo, suficiente estadística.

     

Optimal tooling policy for a tool switching problem of a flexible machine with automatic tool transporter

This paper addresses a tool switching problem of a flexible machine with the objective of minimizing the frequency of movements of the tool transporter. A flexible machine must process a set of parts with its production sequence already prescribed. It is assumed that the tool magazine cannot hold enough tools for the parts. Thus, tools may have to be switched between two successive parts in the part sequence. Tools that are required but unavailable at the magazine are transferred from the tool crib by an automatic tool transporter with a limited carrying capacity. We suggest an optimal tooling policy utilizing the concept of early insertions of tools and show the effects of early insertions through computational tests on randomly generated test problems.     

Optimal replacement and overhaul decisions with imperfect maintenance and warranty contracts

In this article, we develop a model to help a maintenance decision making situation of a given equipment. We propose a novel model to determine optimal life-cycle duration and intervals between overhauls by minimizing global maintenance costs. We consider a situation where the costumer, which owns the equipment, may negotiate a better warranty contract by offering an improved preventive maintenance program for the equipment. The equipment receives three kind of actions: repairs, overhauls, and replacement. An overhaul represents an imperfect maintenance action, that is, the failure rate is improved but not a point that the equipment is as good as new. Corrective maintenance actions are minimal, in the sense that the failure rate after each repair is the same as before the failure. The proposed strategy surpasses others seen in the literature since it considers at the same time the warranty negotiation situation and the optimal life-cycle duration under imperfect preventive actions. We also propose a simplified approach that facilitates the task of implementing the method in standard solvers.     

Optimal replacement policy for a redundant system

Summary This paper considers the reliability of a system which consists ofn components connected in series, the i^thcomponent being supported by (m _i – 1) units in parallel and obtains the optimal policy of replacement by dynamic programming. In the case of a system consisting of identical pairs, the decision depends on the number of operable pairs. For this case sample calculations are presented.

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Zusammenfassung Wir untersuchen die Zuverlässigkeit eines Seriensystems ausn Komponenten, bei dem für diei-te Komponentem _i – 1 Reserveelemente zur Verfügung stehen. Mit Hilfe der dynamischen Optimierung bestimmen wir die optimale Ersetzungspolitik. Besteht das System aus identischen Paaren, hängt die Entscheidung von der Zahl der intakten Paare ab. Für diesen Fall geben wir beispielhaft einige numerische Ergebnisse.

     

Optimal supervisory control of a central chilled water plant with heuristic search sequential quadratic programming

A new methodology for adapting rigorous simulation programs to optimal supervisory control of a central chilled water plant is proposed in this article, which solves plant operation mode optimization and set points optimization by combining heuristic search with sequential quadratic programming. The mathematical basis of this algorithm is developed. A new derivative calculation strategy is introduced in set points optimization. This approach is applied to a central chilled water plant which consists of three chillers, two 3-cell cooling towers, three chilled water pumps and three condenser water pumps. Model verification study is performed. The optimal sequence of operation, set points of the decision variables at given load demand and weather condition are calculated. The plant performance and optimal control results are discussed.     

Optimal machining conditions with costs of quality and tool maintenance for turning

Although there is a voluminous literature on machine tool economics, the cost of machining quality has received little attention. In this paper, we develop a timedynamic economic model for single-pass turning. The model incorporates considerations on the stochastic nature of tool-life and such tool maintenance activities as tool replacement and tool regrinding. We model the quality cost of tool-cutting in terms of deviation from target roughness and deviation from target dimension. The cost of deviation is either the Taguchi type under continuous assumption or in terms of the cost to the entire workpiece under discrete assumption. The connection between quality cost and tool maintenance cost is explicitly addressed. Essentially, quality cost as well as machining cost is a function of two sets of decisions: machining conditions as defined by the choice of cutting speed and feed rate (depth of cut is a constant in single-pass operations), and the condition of the cutting tool as defined by the tool retirement and regrinding policy. The cost of tool failure is also incorporated.     

Optimal burn-in time under cumulative free replacement warranty

In this paper, optimal burn-in time to minimize the total mean cost, which is the sum of manufacturing cost with burn-in and cumulative warranty-related cost, is studied. When the products with cumulative warranty have high failure rate in the early period (infant mortality period), burn-in procedure is considered to eliminate the early product failures. After burn-in, the posterior product life distribution and the cumulative warranty-related cost are dependent on burn-in time; long burn-in period decreases the warranty-related cost, but it increases the manufacturing cost. The paper provides a methodology to obtain the total mean cost under burn-in and cumulative warranty. Properties of the optimal burn-in time are analyzed here. Numerical examples and sensitivity analysis are used to demonstrate the applicability of the methodology derived in the paper.     

Optimal design approach for eco-efficient machine tool bed

An optimal design approach of machine tool bed with the aim of obtaining an eco-efficient machine structure is studied. The suggested method includes three phases. The first is the layout design optimization of stiffener plates inside bed. In order to improve the design efficiency, a simplified design model called fiber model is suggested, and the layout of the stiffener plates inside bed is optimized by changing a 3-dimensional topology design optimization problem to a 2-dimensional problem. The second is the detailed sizing optimization of stiffener plates and supporting blocks under the structure based on the initial optimal model resulted from phase one. Finally, a topology design optimization process is implemented to obtain a reasonable distribution of manufacturing holes in bed structure. By considering the manufacturing requirement, an optimal bed structure is obtained. The validity of the suggested method is confirmed by a typical cylindrical grinding machine tool bed, and the result shows that the suggested method is effective, and the optimal structure has much better mechanical and economical performance by comparing with the original structures.     

Optimal replacement of ageing equipment using geometric programming

Geometric programming (GP) is suggested as an analytical tool for solving a certain class of replacement problems with an infinite time horizon. The GP solution method is described and explained through the formulation and solution of a typical replacement problem. A numerical example is presented to illustrate how the theories of GP are applied for the analysis of replacement decisions of equipment due to age and wear. We also discuss the aspect of sensitivity analysis based on the GP approach.     

Optimal periodic replacement for a deteriorating production system with inspection and minimal repair

Here we discuss an inspection policy model for a deteriorating production system with minimal repair. A minimal repair is resorted to as and when the system is found to be in a failed state during an inspection unless it is apre-set overhaul/replacement time in which case the system is overhauled or replaced. Using a dynamic programming formulation, and assuming that the cost of minimal repair is a non-decreasing function of age, we arrive at the optimal inspection time that maximizes the profit per unit time for a given overhaul/replacement time. The procedure is then extended to determine the optimal periodic overhaul/replacement time and the corresponding optimal number of inspections and their schedule.     

The efficiency range of economical cutting conditions and tool replacement under the age replacement strategy

This paper presents models for calculating the optimal cutting feed rate, spindle speed, and age of preventive tool replacement for a standalone cutting machine. The optimal cutting conditions are determined and analysed for three different objective functions: minimum expected cycle time, minimum expected cost per unit, and maximum expected profit-rate, under the Age Replacement Strategy (ARS) and assuming that the tool-life distribution function is Normal. We show that the first two objective functions are separable, and present an efficient, one-dimensional search procedure for the optimization. A definition of the efficiency ranges of feed rate and standard age of tool replacement is suggested for the ARS, which improves the efficiency range defined in the literature for the Failure Replacement Strategy (FRS).     

Optimal maintenance—replacement policy under imperfect maintenance

During a given planning period, in order to have the system working at or below a fixed failure rate, it may be necessary to replace the system to minimize the expected total cost. Preventive maintenance (PM) or replacement should be performed whenever the system reaches the maximum failure rate. This paper formulates a cost model and a branching algorithm to determine the number of PM interventions to be performed between each replacement and the number of such replacements during the planning period to minimize the expected total cost. Adjustment of the failure rate for the system degradation after each PM intervention and inflationary trends in cost factors are also incorporated. Numerical illustration and computational times have been presented.     

Optimal replacement policy and inspection interval for condition-based maintenance

In condition-based maintenance (CBM), replacement policy is often defined as a rule for replacement or leaving an item (or a system) in operation until the next inspection, depending on monitoring results. The criterion for determining the optimal threshold for replacement, also known as optimal control limit, is to minimise the average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. On the one hand, higher frequency of inspections provides more information about the condition of the system and, thus, maintenance actions are performed more effectively, namely, unnecessary preventive replacements are avoided and the number of replacements due to failure is reduced. Consequently, the cost associated to failure and preventive replacements are decreased. On the other hand, in many real cases, inspections require labour, specific test devices, and sometimes suspension of the operations and, thus, as the number of inspections increase, the inspection cost also increases. In this paper, preventive and failure replacement costs as well as inspection cost are taken into account to determine the optimal control limit and the optimal inspection interval simultaneously. The proposed approach is illustrated through a numerical example.