Integration of process monitoring,quality control and maintenance in an M/G/1 queue-like production system

For an unreliable production system, process monitoring, quality control, and maintenance are essential activities for assuring the proper operation of the production system and for managing the quality of the system's outputs. Although these activities are interrelated, they are seldom studied simultaneously. This paper interrelates and synthesizes the economic design of these activities and the management of an unreliable production system described in terms of an M/G/1 queue. A mathematical model is developed to determine the optimal policies of these activities when both the quality and quantity issues in the system are considered. Then, managerial insights are provided regarding the role and interrelationship of these activities. Finally, hypothetical data are used to illustrate the impact of these activities on the operating characteristics of the production system     

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.     

An optimal multi-machine replacement policy in a serially dependent production system

Here we investigate the serially dependent, multi-machine replacement problem. Given a planning horizon with T periods, M machines of T+ 1 possible vintages, costs for machine operations, machine replacements, and shutdown times, we investigate a linear programming reformulation which involves half the variables and a factor of T fewer constraints than earlier forms. Only T binary variables are necessary, a factor of M fewer than currently employed by heuristic procedures on alternate formulations. Specialized monotone cost structures are no longer necessary, thus extending the class of problems which can be solved efficiently. Computations done using the reformulation's linear programming relaxation on randomly generated problems typically produced integer solutions without branching, even in problems with 75 machines and 15 time periods. In situations where exact optimal solutions are required, the reformulation partially remedies the slow convergence witnessed in earlier studies using branch and bound techniques.     

An optimal geometric process model for a cold standby repairable system

In this paper a cold standby repairable system consisting of two identical components and one repairman is studied. Assume that each component after repair is not ‘as good as new'. Under this assumption, by using a geometric process, we consider a replacement policy N based on the number of repairs of component 1. Our problem is to determine an optimal replacement policy N* such that the long-run expected reward per unit time is maximized. The explicit expression of the long-run expected reward per unit time is derived and the corresponding optimal repair replacement policy can be determined analytically or numerically. Finally, a numerical example is given.     

An economic off-line quality control approach for unstable production processes

An economic off-line inspection/disposition approach is proposed, which incorporates manufacturing variation. This approach includes a new inspection algorithm for inspections based on cost minimization and utilizing a specified confidence level for identifying in-control items. This approach addresses two situations not addressed in previous papers: (i) the last unit in the batch is conforming; (ii) inspection time is non-negligible. Advantages are that there is no need to record the original position of each unit, the impact of manufacturing variation is reduced and non-negligible inspection times can be easily incorporated. Comparisons of this approach to other approaches are provided.     

The stochastic optimal model of continuous production process control

This work is the result of an investigation undertaken by the author during his stay in the U.S.S.R. The elaborated algorithm of electrolysis process control proved to be effective and the calculating procedure uncomplicated.

This approach may be used for analysing and designing control systems in a wide class of continuous processes, which are dealt with in investigating activities, in the manufacturing sphere and information exchange, etc.     

An optimal control model for continuous time production and setup scheduling

This paper concerns a new approach to continuous time optimal scheduling problems for a large class of manufacturing systems. The proposed approach states the problem in terms of optimal control with setup and production rates controllable on one hierarchical level. This allows for the traditional disadvantages of the two-level problem consideration (one level for defining the target production rates, and the other for scheduling the setup changes) to be avoided and stable control strategies to be obtained. Analysis of the maximum principle results in setup conditions of the optimal schedule and special regimes to which the optimal tends between subsequent setups. Based on these results, a numerical method is developed to define the sequence of the special regimes and the timing for getting into and out of them. An example illustrates the effectiveness of the approach.     

Integrated model for determining the optimal initial settings of the process mean and the optimal production run assuming quadratic loss functions

Chen and Chung (1996 Chen, SL and Chung, KJ. 1996. Determining the optimal production run and the most profitable process mean for a production process. International Journal of Production Research, 34: 2051–2058.  ) addressed the problem of the joint determination of the optimal process mean and production run for an industrial process. Their study considered a product with an upper and a lower specification limit. The optimal process mean and optimal production run were obtained by balancing the profit of meeting and not meeting the specification limits. However, Chen and Chung did not consider the quality cost for the product within the specification limits. The present paper revisits the problem and incorporates the quality cost by introducing a Taguchi loss function for determining simultaneously the optimal process mean and production run. As per Chen and Chung, the present paper assumes a 100% inspection scheme. It also investigates the differences between Chen and Chung's approach and the Reward Theorem approach. A sample inspection scheme is also proposed. Numerical examples are provided to demonstrate the application of the model. A sensitivity analysis of the model is provided. Some new directions for further research are also outlined.     

An optimal inspection and diagnosis policy for a multi-mode system

This paper considers a multi-mode system that is inspected periodically, and the period of inspection is a random variable. The system has three modes: normal (N), abnormal (A) and failure (F), where F is a self-announcing mode whereas, N and A are non-self-announcing and operating modes. When the system is operating, it is inspected once every random time T to make sure whether it is in N or A until it attains F, or until it is detected to be in A. Each inspection consists in measuring a value taken by a diagnostic parameter. The diagnostic parameter, which is a random variable, has a close relation with the operating modes. If it is found to have exceeded a certain critical value, a preventive maintenance (or repair) is performed. By using the supplementary variable technique, the reliability indices and an optimal inspection and diagnosis policy for the system are obtained.     

An optimal cart moving policy for a flexible manufacturing system

A flexible manufacturing system is composed of many stations such as a load/unload station, a set of workstations, and a common buffer, that are linked together with a material handling system. Each workstation consists of a limited input buffer, a single machine and a limited output buffer. The material handling system consists of a single cart moving parts in the system according to the process paths required by the parts. A part is blocked when it is moved to a workstation but cannot enter the workstation. The function of the common buffer is to temporarily store blocked parts. A blocked part is treated in accordance with a flexible manufacturing system blocking mechanism. We model the flexible manufacturing system by a closed queueing network with the flexible manufacturing system blocking mechanism and a block-dependent static Markov part routing. An optimal cart moving policy that maximizes the expected system throughput is formulated as an undiscounted semi-Markov decision process. Several properties of the optimization problem are characterized. A loop approach is developed for finding an optimal policy. An example is given to illustrate the methodology, and investigate its convergence.     

An integrated material flow system approach for determining the economic production quantity (EPQ)

Traditionally, the analysis of material flow systems has focused on each of the individual components of the system separately (i.e. material handling, production lot size, unit load size, flow path, layout, space, etc). Even though each component is difficult to address on its own, it is imperative that they be addressed concurrently due to their interactions. This paper explores the relationships between the components in the material flow system with respect to determining the economic production quantity (EPQ). This is in contrast to the traditional EPQ model, which considers only set-up cost, inventory cost, and demand, while ignoring other material flow system issues. A multi-item economic production quantity model under a storage space limit is considered with respect to material handling equipment selection and requirements, unit load size, and flow path selection. The integrated material flow system problem is mathematically formulated as a large scale, nonlinear integer programming model, and a heuristic solution procedure is developed. The impact of using an integrated approach to determine the EPQ is illustrated and solutions are compared to both a lower bound and a traditional sequential approach. It is found that an integrated approach provides consistent and significant improvement in the overall solution quality.     

An optimal batch size for an imperfect production system with quality assurance and rework

We consider a manufacturing system which receives raw material from a supplier, processes it, and delivers it to the customer periodically. The system considered is imperfect and produces defectives at a constant rate. The finished product can only be delivered if the whole lot is quality-certified. Hence, defectives have to be reworked, and the whole lot quality-checked within the cycle. Three different scenarios are considered, viz. (a) a single lot of raw material for multiple lot of finished product and delivery of the product in multiple instalments, (b) a single lot of raw material for a multiple lot of finished product and delivery of the product in a single instalment, and (c) lot-for-lot and delivery of finished product in single instalment. A total cost equation is developed for each model, and the optimal ordering quantities are evaluated. The results found are encouraging and quite simple to use for practical purposes.     

An optimal control problem in estimating the optimal control force for the force vibration system

An optimal control problem for the force vibration system based on the iterative regularization method, i.e. the conjugate gradient method (CGM), is examined to estimate the optimal control force in a damped system having time‐dependent system parameters such that the desire (or design) system displacements can be satisfied. It is assumed that no prior information is available on the functional form of the unknown control function in the present study, thus, it is classified as the function estimation. Numerical simulations are performed to test the validity of the present algorithm by using different types of the desire system displacements. Results show that an excellent estimation on the optimal control force can be obtained with arbitrary initial guesses within a couple of second's CPU time at Pentium III‐500 MHz PC. Copyright © 2001 John Wiley & Sons, Ltd.     

An optimal production and shipment policy for a single-vendor single-buyer integrated system with both learning effect and deteriorating items

The collaboration of vendor and buyer is one of the key factors for successful supply chain management. The most common strategy for a collaborative system is to propose an integrated replenishment plan aimed at maintaining a win-win partnership for both vendor and buyer. The objective of this study is to develop a production and shipment model for a system that incorporates learning effect and deteriorating items and to derive an optimal joint total cost from the integrated perspective of both vendor and buyer. A simple solution procedure is presented to determine the optimal production time and number of deliveries. A numerical example is provided to illustrate the proposed model. A sensitivity analysis is conducted to study the effect of changes in the related parameters on the optimal solution. This paper shows that the proposed integrated model can result in a significant cost reduction as compared with the independent decisions made by either vendor or buyer.     

An integrated EPQ model based on a control chart for an imperfect production process

The notion of quality control is introduced into the classic economic production quantity (EPQ) model. Based on previous research, this paper contributes to an integrated EPQ model combining the concepts of statistical process control and maintenance. An imperfect production process involving three different conditions is considered. A control chart is adopted to monitor the whole process with Taguchi's loss function estimating the quality cost of each condition. A corresponding maintenance policy is planned for the machine depending on what condition it runs in. Thus the proposed EPQ model takes quality-related costs and maintenance-related costs into account other than storage costs and ordering costs already considered in the classic model. The objective of this model is to minimise the total expected production cost per production cycle while simultaneously determining the optimal parameters of control chart design, the interval between sampling, the sample size and the maintenance decision policy. The pattern search method is used to solve the problem using the MATLAB toolbox. In addition, a case study, sensitivity analysis and comparison analysis are presented to demonstrate the application of the model.     

A quality growth model and its application to initial production process control

During initial production of a new product prior to actual production, the decrease in the fraction defective of units produced can be observed as personnel gather experience and the faults in the product's design, manufacturing, etc. are removed. This paper discusses an initial production process control based on a quality growth model proposed here. The model describes a continuing reduction in the cumulative defect rate defined by the ratio of the cumulative number of defective units to that of produced units. A stopping rule is also investigated for determining when to discontinue the initial control of the production process and proceed to the actual production stage. Further, a numerical example of the application is presented.     

Determination of the optimal production run and the most profitable process mean for a production process

This paper deals with the problem of joint determination of the optimal process mean and the production run for a process. It extends the Quality Selection problem to production systems in which the process mean (target) shifts to an out-of-control state due to an assignable cause. The problem has been validated using various examples. Moreover, results indicate that an inverse relationship exists for the length of production run and the difference expected profit between in-control state and out-of-control state.     

Determination of optimal lot sizing parameters and a controllable process mean for a production system

Several mathematical models have been developed separately for determining production and recycled lot quantities to minimize total production cost and the determination of optimal process mean setting to minimize total quality cost. For a single stage discrete part production system, this paper presents a mathematical model that combines these two inter-related aspects. The production process has a controllable parameter, the process mean, which determines the output lot quality. One-sided tolerance is used to decide the quality of finished goods. Bad units are reworked before they can be reprocessed with the fresh input. For such a situation, the model determines production lot size, recycling lot quantity, and a process mean while minimizing total system cost. The model has been validated using sample data from a pharmaceutical company. Results indicate that the production lot size and the recycled quantity have an inverse relationship with process mean and, a direct relationship with process variance.     

Two-critical-number control policy for a stochastic production inventory system with partial backlogging

This paper deals with a production–inventory control model with partial backlogging, in which a reflected Brownian motion governs the inventory level variation. We consider a single storage facility with infinite capacity and assume that shortages are allowed and the total amount of stock-out is a mixture of backordering and lost sales. In addition, the production facility is controlled by a two-parameter (m, M) policy, which switches the production rate when the inventory level reaches the threshold values. The aim is to determine the optimal control parameters m and M by minimising the long-run total expected cost of the system. Some results are illustrated using numerical examples. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.     

An age-based replacement policy with non-zero repair times for a continuous production process

In this paper a case study for maintenance optimization is presented. The theoretical features of the model, an age-based replacement model taking into account non-zero repair times, are briefly discussed. The main part of the paper focuses on the application aspects of such problems like data gathering and finding the appropriate solution method. An extensive discussion of the results concludes the paper.