Maintenance scheduling of a manufacturing system subject to deterioration

This paper presents an integrated model for the joint determination of both optimal inspection strategy and optimal repair policy for a manufacturing system whose resulting output is subject to system state. An appropriate maintenance strategy is essential to optimize revenue from a manufacturing system which is in continuous operation and subject to deterioration. The optimum policy balances the amount of maintenance required to increase availability against the loss of revenue arising from the down time: insufficient maintenance leads to an increase in the number of defective items, low profit and low maintenance cost; excessive maintenance results in a reduction in the proportion of defective items, high profit and high maintenance cost. In this paper, an intensity control model adapted to partial information provides an optimal inspection intensity and repair degree of the system as an optimal control process to yield maximum revenue. The solution is obtained through formulating an equivalent deterministic Hamilton-Jacobi equation. A numerical example is provided to illustrate the behavior of the optimal control process. The optimal control process determines a solution to both optimum inspection frequency and optimal replacement policy which results in an optimal production run length of the system.     

DETERMINATION OF THE OPTIMAL PROCESS MEAN WHEN INSPECTION IS BASED ON A CORRELATED VARIABLE

Consider a production process where items are produced continuously. A lower limit is specified for the quality characteristic of interest, and an item is defective if its value of the quality characteristic is smaller than the specification limit. The process mean (target value) may be set higher to reduce the costs incurred by producing defective items. Using a higher process mean, however, results in a higher production cost when production cost is an increasing function of the quality characteristic. An inspection procedure is used to screen outgoing items from the defective ones. In this paper, we consider a situation where inspection is based on a surrogate variable instead of the quality characteristic of interest. A model is developed to jointly determine the most economical process mean and the inspection specification limit.     

Integrated production quality and condition-based maintenance optimisation for a stochastically deteriorating manufacturing system

This paper investigates the problem of optimally integrating production quality and condition-based maintenance in a stochastically deteriorating single- product, single-machine production system. Inspections are periodically performed on the system to assess its actual degradation status. The system is considered to be in ‘fail mode’ whenever its degradation level exceeds a predetermined threshold. The proportion of non-conforming items, those that are produced during the time interval where the degradation is beyond the specification threshold, are replaced either via overtime production or spot market purchases. To optimise preventive maintenance costs and at the same time reduce production of non-conforming items, the degradation of the system must be optimally monitored so that preventive maintenance is carried out at appropriate time intervals. In this paper, an integrated optimisation model is developed to determine the optimal inspection cycle and the degradation threshold level, beyond which preventive maintenance should be carried out, while minimising the sum of inspection and maintenance costs, in addition to the production of non-conforming items and inventory costs. An expression for the total expected cost rate over an infinite time horizon is developed and solution method for the resulting model is discussed. Numerical experiments are provided to illustrate the proposed approach.     

Joint optimisation of production,maintenance and quality for batch production system subject to varying operational conditions

This paper considers the integration problem of production, maintenance and quality for a capacitated lot-sizing production system subject to deterioration. The effects of varying operational conditions from batch to batch on system reliability and product quality are modelled by proportional hazards models, resulting in non-monotonic failure rate and defect rate. After each batch production, imperfect preventive maintenance (PM) is determined to mitigate the system deterioration, and inspection is taken to sort nonconforming items in the finished goods. Once the cumulative number of nonconforming items exceeds a predetermined threshold, an overhaul is performed to renew the system. An integrated model for optimising production plan, PM plan and overhaul strategy is developed to minimise the total cost while satisfying all product demands. A genetic algorithm is proposed to solve the integrated model efficiently. Numerical results validate the rationality of the model with varying operational conditions consideration and its applicability in economic benefits.     

A Production and Maintenance Planning Model with Restoration Cost Dependent on Detection Delay

In this paper, the joint problem of production planning and maintenance schedule is studied under the realistic assumption that the cost of process restoration is a function of the detection delay and the existence of shortages in the system. The detection delay is defined as the elapsed time since the production process has deteriorated until it is identified by some inspection procedure and repaired. Since production planning and maintenance problems have usually been studied as separate problems, this paper is an attempt to develop a formal framework for the joint problem. We have developed sufficient conditions for the optimality of the commonly used equal-interval maintenance schedule. The conditions are found to be a function of parameters such as the cost of defective items, the mean time for system deterioration, and the form of the restoration cost function. For specific restoration cost functions such as linear and exponential, an efficient solution procedure is presented for the simultaneous determination of the number of maintenance inspections in a production run, the length of the production run and consequently the economic manufacturing quantity, and the maximum level of backorders. A numerical example illustrates the use of this procedure and the differences between the optimal cost obtained by this procedure and the cost obtained by using the classical economic manufacturing quantity model.     

Dependability and performance stochastic modelling of a two-unit repairable production system with preventive maintenance

In this paper, a two-unit multistate repairable production system is considered in which preventive maintenance (PM) is implemented in order to improve its dependability and performance. A general model is provided for the production system using a semi-Markov process, for examining system’s limiting behaviour. Apart from combining redundancy with PM, we introduce scenarios like imperfect and failed maintenance which are usually met in real life production systems. For the proposed model, we calculate the availability, the mean time to failure and the total operational cost and we formulate optimisation problems settled with respect to the system’s inspection times. The main aim of our work is to determine the optimal inspection times and consequently the optimal PM policies to be adopted in order to optimise system’s dependability and performance.     

A sensitivity analysis of an integrated model for joint determination of economic design of $\overline{x}$‐control charts,economic production quantity and production run length for a deteriorating production system

This study presents an integrated model for the joint economic design of ‐control charts and maintenance schedules and, simultaneously, determines the economic production quantity and production run length for a deteriorating production system. The operating state of the production process is classified as either in control or out of control. In the latter state, the process produces some defective items. An ‐control chart is used to monitor the process mean. Both uniform and non‐uniform inspection schemes are adopted. Inspection and maintenance are performed simultaneously. Replacement cost is assumed to be very high. The process failure mechanism is assumed to follow a general probability distribution with an increasing failure rate. The concept of a truncated production cycle is introduced. The production cycle begins when a new component is installed and ends with a repair after the detection of a failure or after a specified number of inspection intervals, , whichever occurs first. The effects of preventive maintenance on quality control are discussed. Numerical examples are provided to evaluate the performance of the model. Sensitivity analyses are conducted to study the effects of various model parameters. Copyright © 2002 John Wiley & Sons, Ltd.     

Optimal production run length and inspection schedules in a deteriorating production process

This paper presents an economic manufacturing quantity model which determines an optimal production run length and inspection schedules simultaneously in a deteriorating production process. It is assumed that a production process is subject to a random deterioration from the in-control state to the out-of-control state and, thus, produces some proportion of defective items. An optimal production run length and an optimal number of inspections are derived, and unique properties of the proposed model are discussed. A numerical experiment is carried out to examine the behavior of the proposed model and compare the proposed model to an existing model.     

A new inspection sampling plan under capacity constraints and multiple shifts

Various SPC models have been widely deployed in the quality control of different production systems. This paper considers a new design of SPC model with associated decision rules to control a process that produces items in finite lots and has a variance shift as well as a mean shift. Under both an inspection capacity constraint and a false alarm rate constraint, an inspection sampling plan that maximizes the yield of production is developed. Numerical examples are presented to illustrate and evaluate the approach. A semi-economic approach that computes the optimal quantity of inspection capacity is also presented.     

An Application of Sampling Inspection to Corrective Plan for Semi-Markov Production Process

A corrective plan for the maintenance of production process whose capability is deteriorating in service is given. The special analysis by sampling inspection of a lot production is proposed for the semi-Markov model of production process. The result in the present paper is a generalization of previous conclusions based on the Markov model. Dynamic characteristics from the initial state to the corrected state of production process are also analyzed with Graphical Evaluation and Review Technique (GERT). It is shown furthermore that information on the improvement of process capability can be obtained from the sensitivity analysis.     

Economic design of a complete inspection plan with feedback control

This paper studies production control with complete inspection where every finished product is subject to variable inspection. Two process states, in-control and out-of-control, are assumed. If the inspection signals that the process is out of control, remedial action is taken to restore the process to the in-control state. Inspected items are either accepted with a quality cost or reworked according to the observed quality characteristic. Specification limits and action limits are derived from an economic model.     

The optimal production and quality policy for the vendor in a trade

Arranging an inspection schedule for the production process and taking inspection and burn-in tests to screen out defective items in a production lot before items are shipped to the buyer are widely used by the vendor, such that the defective percentage in an outgoing batch satisfies the quality requirement specified in the contract between them. For an inspection schedule, the number of inspections and the length of time intervals between two inspections are influential to both the precision of detecting the manufacturing process and the inspection cost. As to the inspection test, it is not perfect, so there are two types of errors (Types I and II). Nevertheless, compared with inspection test, burn-in is usually costly. Hence, how to make a suitable trade-off between these three treatments (i.e., inspection schedule, inspection test, and burn-in test) such that the outgoing batch satisfies the purchaser's quality requirement with low cost is an important issue. The main purpose of this paper is to deal with the problem of determining the optimal inspection schedule and the optimal mixed policy of inspection and burn-in, where the average outgoing quality is used as the measure of quality. More specifically, by using the criterion of maximizing the expected profit that the vendor makes in a trade, a nonlinear programming problem is built to determine (a) the number of inspections undertaken in the production process, (b) the times at which the production process is inspected, (c) the total number of items that the vendor should produce (or the production run time), (d) the number of items for inspection, the number of items for burn-in, and the number of items that need neither inspection or burn-in, and (e) the optimal burn-in time for those needing burn-in testing. An example is provided to illustrate the proposed method.     

Economic Design And Control of Monitoring Mechanisms in Automated Production Systems

Monitoring production processes to assure product quality has been a major managerial and control problem. These processes are subject to shifts to “out-of-control” states, resulting in the production of defective items. Inspection as well as restoration capabilities are necessary to provide early detection and correction of these shifts in the process. This paper considers the costs of different policies for providing these detection and restoration capabilities. These policies amount to periodic or continuous inspection of the production process with perfect information, and continuous or periodic availability of maintenance facilities. The optimal operation of each policy is studied. Comparative analyses are conducted with different specifications of key parameters such as the rate of shift of the process and the cost of producing defective items. These analyses enable the derivation of the optimal policy when only ranges of the values of these parameters are known.     

A general approach to modeling CUSUM charts for a proportion

This paper considers two CUmulative SUM (CUSUM) charts for monitoring a process when items from the process are inspected and classified into one of two categories, namely defective or non-defective. The purpose of this type of process monitoring is to detect changes in the proportion p of items in the first category. The first CUSUM chart considered is based on the binomial variables resulting from counting the total number of defective items in samples of n items. A point is plotted on this binomial CUSUM chart after n items have been inspected. The second CUSUM chart considered is based on the Bernoulli observations corresponding to the inspection of the individual items in the samples. A point is plotted on this Bernoulli CUSUM chart after each individual inspection, without waiting until the end of a sample. The main objective of the paper is to evaluate the statistical properties of these two CUSUM charts under a general model for process sampling and for the occurrence of special causes that change the value of p. This model applies to situations in which there are inspection periods when n items are inspected and non-inspection periods when no inspection is done. This model assumes that there is a positive time between individual inspection results, and that a change in p can occur anywhere within an inspection period or a non-inspection period. This includes the possibility that a shift can occur during the time that a sample of n items is being taken. This model is more general and often more realistic than the simpler model usually used to evaluate properties of control charts. Under our model, it is shown that there is little difference between the binomial CUSUM chart and the Bernoulli CUSUM chart, in terms of the expected time required to detect small and moderate shifts in p, but the Bernoulli CUSUM chart is better for detecting large shifts in p. It is shown that it is best to choose a relatively small sample size when applying the CUSUM charts. As expected, the CUSUM charts are substantially faster than the traditional Shewhart p-chart for detecting small shifts in p. But, surprisingly, the CUSUM charts are also better than the p-chart for detecting large shifts in p.     

A Sequential Scheme for Estimating Average Quality in a Mixed Product Production Process

A production process is assumed to produce k types of items in varying proportions and with varying defect rates. This paper proposes a sequential inspection plan which allows one to optimally allocate inspection resources so that one obtains a good estimate of average quality. The plan is fairly easy to put into practice and allows for easy modification should production characteristics change.     

Optimal economic production quantity policy for a parallel system with repair,rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.     

A Comparative Study of Continuous and Periodic Inspection Policies in Deteriorating Production Systems

Continuous or periodic inspection policies are often used to monitor the maintenance of a production process. In this paper, a comparative study of continuous and periodic inspection policies in deteriorating production systems is provided. The overall cost function is comprised of: set-up, inspection, inventory holding, defective and restoration costs. Different models, constant, linear and exponential, of restoration costs are considered. Tradeoffs between the continuous and the periodic inspection policies are analyzed, and ranges of values of system or cost parameters for which the continuous inspection policy is preferred are established.     

Optimal decision of an economic production quantity model for imperfect manufacturing under hybrid maintenance policy with shortages and partial backlogging

Considering the characteristics of the stochastic shift of the machine state and the uncertainty of the product quality of production, in this paper, we develop an optimisation decision of economic production quantity model for an imperfect manufacturing system under hybrid maintenance policy with shortages and partial backlogging. We assume that the production process is imperfect stemming from the machine reliability and the probability of out-of-control, a hybrid maintenance policy combined of emergency maintenance and preventive maintenance is executed during each production run. Three decision models based on the scenarios of machine breakdown and repair time are developed. The optimal production quantity and maintenance inspection number during each production run are solved with minimising the expected average cost of the system. Numerical examples are used to demonstrate the effectiveness and feasibility of the model. Sensitivity analysis is conducted to analyse the impacts of key parameters on the optimal decision. Some implications related to the effective and economical execution of maintenance policy for practitioners are derived.     

Risk-informed optimisation of railway tracks inspection and maintenance procedures

Nowadays, efforts are being made by the railway industry for the application of reliability-based and risk-informed approaches to maintenance optimisation of railway infrastructures, with the aim of reducing the operation and maintenance expenditures while still assuring high safety standards.In particular, in this paper, we address the use of ultrasonic inspection cars and develop a methodology for the determination of an optimal strategy for their use. A model is developed to calculate the risks and costs associated with an inspection strategy, giving credit to the realistic issues of the rail failure process and including the actual inspection and maintenance procedures followed by the railway company.A multi-objective optimisation viewpoint is adopted in an effort to optimise inspection and maintenance procedures with respect to both economical and safety-related aspects. More precisely, the objective functions here considered are such to drive the search towards solutions characterized by low expenditures and low derailment probability. The optimisation is performed by means of a genetic algorithm. The work has been carried out within a study of the Norwegian National Rail Administration (Jernbaneverket).     

Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items

For an imperfect production system, to reduce quality-related costs, a manager may consider investing capital in quality improvement. In general, the investment expense in reducing the defective rate of items is often paid by the vendor. On the other hand, the buyer may inspect the product quality as the order is received which implies it incurs an inspection cost. In a supply chain integrated system, to accomplish global optimisation, the vendor and buyer can agree to jointly invest capital to improve the imperfect production processes, and the buyer can remove the inspection programme as the defective rate reaches a certain low-level. Hence, this paper investigates the impacts of collaborative investment and inspection policies on an integrated inventory model with defective items. The objective of this study is to seek the optimal order quantity, shipping times from the vendor to the buyer per production run, and the defective rate that minimise the joint total cost per unit time. An algorithm is developed to find the optimal solution. Several numerical examples are presented to demonstrate the proposed model and solution procedure, and then several management insights are obtained from the numerical examples.