Economical Quality Control Policies for a Single Cause System

We consider four types of process control procedures; variables control charts, attributes control charts, a never-inspect policy, and a regular inspection policy consisting of periodic process reset and/or repair. Using a designed experiment, we compare the optimal economic designs associated with these policies for a practical range of costs and other system parameters. We find that the regular inspection policy is economically optimal in many configurations. Moreover, we find that the type of policy that yields minimum cost depends primarily on the expected magnitude of the process shift, the relative cost of variable versus attribute sampling, and the expected search time for an assignable cause. Some general guidelines for the appropriate type of control procedure for use in practice are given.     

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.     

Optimization for condition-based maintenance with semi-Markov decision process

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs. In this paper, we have built the semi-Markov decision process (SMDP) for the maintenance policy optimization of condition-based preventive maintenance problems, and have presented the approach for joint optimization of inspection rate and maintenance policy. Through numerical examples, the improvement of this method is compared with the scheme, which optimizes only over the inspection rate. We also find that under a special case when the deterioration rate at each failure stage is the same, the optimal policy obtained by SMDP algorithm is a dynamic threshold-type scheme with threshold value depending on the inspection rate.     

An improved ordering policy for continuous review inventory systems with arbitrary inter-demand time distributions

In this paper, we revisit the optimality of (s,S) policies in continuous review inventory models where demand forms a renewal process. We explain why when orders are placed at demand epochs, (s,S) policies are not optimal in general, and propose a simple but practical ordering policy by introducing a delay in order placement as a policy parameter. Under our proposed policy, the operating characteristics of such systems can be evaluated using the existing results in the literature. In order to demonstrate the effectiveness of our policy, we restrict our analysis to a special class of inventory systems where demand follows a counting process, fixed ordering costs are negligible and leadtimes are constant. We derive expressions for the operating characteristics of such systems under our policy and present insights on the behavior of the policy parameters which minimize the average total cost rate under our policy. Using these results, we develop an efficient heuristic for computing the policy parameters. Finally, we investigate the effectiveness of our policy in comparison to policies which place orders only at demand epochs. The results of our numerical experiment indicate that our policy can result in a significant savings.     

Design of an integrated quality assurance strategy in production systems

High-quality of products is a critical issue for manufacturers to maintain their competitiveness in global markets. For this reason, more attention has been paid by operations managers and academics to the design of quality assurance strategies, acceptance sampling plans and inspection allocation problems. In the last decades, international research has studied and introduced several models and approaches to investigate these issues. The purpose of this paper is to provide a new methodology for designing and selecting correct integrated quality assurance strategies, defining cost models for acceptance policies and inspection station configurations. Generally, high-quality of items is guaranteed by avoiding defects, mainly caused by non-conforming components, resulting from instantaneous and standard infant mortality. Thus, an optimal acceptance policy is defined in order to reduce the instantaneous infant mortality defects. A closed-form equation has been introduced to determine easily and quickly the optimal percentage of checked items. Furthermore, a more convenient inspection station configuration is determined in order to minimise the expected total cost, composed of testing, inspection and penalty cost elements. The innovative concept of defect rate as an inspection time variable dependent has been introduced. The impact of different economic and survival parameters on designing inspection policies is also investigated. Finally, a real-life case study demonstrates the applicability of this methodology in real production systems and several considerations are reported about the future research, that the authors will carry out.     

Integrated maintenance and production control of a deteriorating production system

We consider a make-to-stock production/inventory system consisting of a single deteriorating machine which produces a single item. We formulate the integrated decisions of maintenance and production using a Markov Decision Process. The optimal dynamic policy is shown to have a rather complex structure which leads us to consider more implementable policies. We present a double-threshold policy and derive exact and approximate methods for evaluating the performance of this policy and computing its optimal parameters. A detailed numerical study demonstrates that the proposed policy and our approximate method for computing its parameters perform extremely well. Finally, we show that policies which do not address maintenance and production control decisions in an integrated manner can perform rather badly.     

ON THE USE OF BUFFER INVENTORIES TO MINIMIZE COSTS WITH AN UNRELIABLE MACHINE

In this paper, we discuss the problem of quality control with an unreliable machine which produces defects at a rate of Λ₀, per unit when in-control and a rate of Lambda; ₁, when out-of-control (where Λ₁ Λ ₀). Every h time periods, we sample n units, count the number of defects, and (using a process based on a Shewart c-chart) test the hypothesis that the machine is in control by comparing the total number of defects to an upper control limit (UCL). More important, we introduce the concept that a buffer inventory which immediately follows the unreliable machine may reduce expected total costs. This buffer serves to delay the movement of items from the unreliable machine to the next stage of the production process. In this way, we can isolate and repair most defective items before they are embedded in a product downstream or sold to customers where repair is more costly. To search for the optimal control policy, we find bounds for n, h, and UCL; given values for these variables, we show how the optimal buffer size can be determined directly. Numerical results illustrate the magnitude of potential savings.     

Economic optimization of off-line inspection

In this paper we solve the problem of determining the optimal inspection/disposition policy for a finite batch of items produced by a machine that is subject to random breakdowns. In particular, we identify which units should be inspected and in which order so as to minimize costs. The operational implications of the optimal policy are analyzed with a selected set of numerical results. We place special emphasis on three different policies: the cost minimizing policy; the policy of perfect information, i.e., we insist on determining the quality of each unit; and the policy of zero-defects,i.e., we insist that all accepted units are known to conform to specifications, allowing the rejection of units of unknown quality. We also show how the optimal inspection/disposition policy is incorporated into the optimization of the batch size.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute 'approximately optimal' base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

Exploring inventory systems sensitive to shrinkage – analysis of a periodic review inventory under a service level constraint

Motivated by empirical evidence, this article focuses on the behaviour of a store inventory exposed to inventory record inaccuracy. The inventory, controlled by an infinite horizon, single-stage, single-product periodic-review policy, is subject to shrinkage errors that cause a difference between the physical and information system inventory levels. We model a set of scenarios depending on the technology available to track shrinkage in the store. In scenarios where a technology such as Radio Frequency IDentification (RFID) is not used, inventory is controlled by estimating the expected shrinkage rate. We assume that an inspection process is performed at a regular frequency of N selling periods. We analyse two situations that permit management of the joint ordering and inspection policy based on the information the inventory manager has on shrinkage errors. A comparison between these two situations permits us to analyse the impact of shrinkage errors and the value of taking into account the inventory inaccuracy issue when optimising the inventory and inspection policies. The deployment of the RFID technology produces two benefits: total visibility of the shrinkage rate and the elimination of shrinkage errors. A comparison of the scenarios enables us to evaluate the economic impact of inventory record inaccuracies, which can be significant, particularly in systems with a poor estimation of the error parameter as well as with a high inspection cost.     

Integrated approach to part scheduling and inspection policies for a job shop manufacturing system

The quality of a product greatly depends on the quality of its components. This requires that manufacturing specifications have to be met in the manufacturing environment and as a consequence inspection stations are present in many manufacturing systems and inspection policies must be adopted. One problem, which has been widely investigated, concerns the detection of the inspection points in the hypothesis that the action to be taken is known when a defective part is detected. If different jobs are to be produced, then operation scheduling becomes yet another complex problem needing to be solved. And while the problem of scheduling has received a great amount of attention from researchers, to our knowledge the interaction between the two problems has not been treated in job-shop environment. In the present paper three different control policies are preliminarily examined: they differ both in terms of the number of operations that are inspected, and with regard to the type of intervention carried out on detection of a defect. Each control policy affects the optimal inspection locations, which, in their turn, influence operation scheduling. As will be shown in the present paper, a sequential decision process based on separate optimization steps can lead to very poor final results. For this reason, an integrated approach is proposed, in an attempt to identify an optimal solution using a genetic algorithm.     

Base-stock control for single-product tandem make-to-stock systems

In this paper, we consider a multiple-stage tandem production/inventory system producing a single product. Processing time at each stage is assumed to have a general stationary processing time distribution. The cost of holding work-in-process (WIP) inventory is different at each stage. Therefore, decisions on when to release work to the system as well as when to transfer WIP from one stage to another need to be made. We formulate this problem of release/production control as a Markov decision process. However, the optimal policy is rather complex, making its implementation impracticable in practice. We therefore investigate the performance of simple base stock policies. Our approach aggregates several stages into one and uses a simple approximation to compute approximately optimal base stock levels. We present the results of a simulation study that tests the performance of our approximation in estimating the best base stock levels, and the performance of base stock policies as compared with the optimal policy.     

Scheduling policies,batch sizes,and manufacturing lead times

In this paper we examine the impact of scheduling policies on batch sizing decisions in a multi-item production system. We also investigate the joint effect of scheduling policies and batch sizing decisions on production lead times. In particular we compare the performance of a first-come-first-served (FCFS) policy with that of a group scheduling (GS) policy and study the effect of each on the optimal batch size. We show that a GS policy can lead to significant performance gains, as measured by reduced lead times and higher production rates, relative to the FCFS policy, and characterize conditions under which these gains are realized. We also study the impact of the GS policy on other system operating parameters. In particular we find that using a GS policy eliminates the need for batching, preserves system capacity despite the presence of setups, and accommodates higher product mix variety. These results are shown to be very different from those obtained for the FCFS policy and to have important implications for the management and control of multi-item production facilities.     

An Annotated Bibliography on Methods for Non-linear least Squares Computations Including Test Problems

An optimal inspection policy will inspect either every item produced or no item when (a) product characteristics are well modeled as iid and (b) overall inspection cost is a sum of individually and identically determined costs for each of the items encountered. This result is widlsly known for special cases such as iid Bernoulli product characteristics with single-sample lot acceptance-sampling plans. We show that the result holds true much more generally and over a much wider class of inspection plans, even when independent inspection errors are possible. We examine the assumptions that lead to all-or-none optimality and discuss the practil:al meaning of all-or-none results to practitioners. Examples are given to demonstrate that both “other” cost structures and “informative” inspections (i.e., lack of independence) can lead to optimal policies that are not of the all-or-none type.     

Dynamic quality control in assembly systems

We study an assembly system, in which each end product consists of two different components. The components are produced in batches, with possible defective units. The proportion of defective units in each batch is itself a random variable, known only in terms of its distribution. Defective units can be identified and corrected through an inspection-repair procedure, before final assembly taking place. We are concerned with developing an optimal inspection policy that minimizes the total expected cost due to inspection, repair, and warranty. Particularly, we focus on policies that have simple threshold structures and a near-optimal performance.     

The Study of Cost Rate for Multiple Cold Standby System Replacement Policies

We consider a replacement policy for a multiple-component cold-standby system,and atfer we analyze this plicy,we want to get the mean total cost rate and the preventive policy to make it the lowest.In this system,the failure rate of the component in poeration is constant,and the inspection will control all the processes of the operation.The system is inspected at random points over time to determine whether it is to be replaced.During the process,the replacement decision is based on the number of failed components at the time of inspection.     

Control of a manufacturing system with random product yield and downward substitutability

We consider a manufacturing system where the quality of the end product is uncertain and is graded into one of several quality levels after production. We assume stochastic demand for each quality level, stochastic production times, and random quality yields. We also assume downward substitutability (i.e., customers who require a given product will be satisfied by a higher quality product at the same price). The firm produces to stock and has the option to refuse satisfying customers even when it has items in stock. We formulate this problem as a Markov Decision Process in the context of a simple M/M/1 make-to-stock queue with multiple customer classes to gain insight into the following questions: (i) how does the firm decide when to produce more units (i.e., what is the optimal production policy?) and (ii) how does the firm decide when to accept/reject orders and when to satisfy customers demanding lower quality products using higher quality products? In the case of two product classes, we completely characterize the structure of the optimal production and acceptance/substitution policies. However, the structure of the optimal policy is complicated and we therefore develop a simple heuristic policy for any number of classes which performs very well. We finally extend our heuristic to the system where production occurs in batches of size of larger than one, the system where there is a setup cost for initiating production, and the case where processing time distribution is Erlang.     

Estimating manufacturing cycle time and throughput in flow shops with process drift and inspection

Process drift is a common occurrence in many manufacturing processes where machines become dirty (leading to more contamination) or processing parameters degrade, negatively affecting system performance. Statistical process control tracks process quality to determine when the process has gone out of control (has drifted beyond its specifications). This paper considers the case where parts examined at a downstream inspection station are used to determine when the upstream process is out of control. The manufacturing cycle time from the out of control process to the downstream inspection process influences the detection time that elapses until the out of control process is noticed and repaired. Because an out of control process produces more bad parts, the detection time affects the number of good parts produced and the throughput of the manufacturing system. This situation is common in many industries but no models of the phenomena exist. This paper presents a novel manufacturing system model based on queueing network approximations for estimating the manufacturing cycle time and throughput of such systems. These are important performance measures since they influence economic measures such as inventory costs and revenue. The model can be used for a variety of system design and analysis tasks. In particular, the model can be used to evaluate the placement of inspection stations in a process flow.     

A data-driven maintenance policy for railway wheelset based on survival analysis and Markov decision process

Wheelsets absorb a significant part of the maintenance budget of any train operating company. Although wheel wear has been an extensively discussed topic in the literature, wear rates are very rarely characterized by using degradation data in a real-world case study aimed at identifying optimal maintenance policies including both degradation and recovery modeling. Furthermore, wheel defects, which impose an additional challenge to the modeling of the lifecycle of the wheels, are usually considered separately in the literature. In this study, conducted at a Portuguese train operating company, 17 years of inspection data are used to estimate wheel wear rates and survival curves, which are further incorporated into a Markov decision process (MDP) model. A bidimensional framework considering discrete intervals of wheel diameter along with a quantitative variable (kilometers since last turning/renewal) is used to represent the possible wheel states, while the probability of a defect interfering with the wheel maintenance schedule is modeled by contemplating survival curves derived from a Cox proportional-hazards model. Optimal results in terms of minimal cost policy are discussed in the context of the MDP, but a more realistic and easy-to-implement policy fixing one of the parameters is compared with the optimal policy. Results showed that in practice train operating companies might benefit from using the easy-to-implement policy, which has an associated long-run average cost only about 1% higher than the one suggested by the optimal decision map.     

Economic design of dual-sampling-interval policies for X¯ charts with and without run rules

Recent studies show that the dual-sampling-interval (DSI) policies of X¯ control chart yield a smaller average time to signal (ATS) than Shewhart's classical fixed-sampling-interval (FSI) policy for off-target processes. An economic design approach for DSI policies has not been addressed in the literature. In this paper we develop a comprehensive cost model for DSI policies with and without run rules and steady-state performance. The expression for the unit cost of quality is used as the objective function in optimal design of DSI policy parameters. The design process and the sensitivities of some of the model input parameters are exposed through numerical examples.