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.     

Mathematical Probability in the Natural Sciences

Presidential address given at Symposium III of the XVIIIe Congress International des Sciences Pharmaceutiques, organized jointly by the Scientific Section of the International Pharmaceutical Federation and the Section Adolphe Quetelet—Brussels, 8–15 September, 1958. This address will also appear in Metrika, 1959.     

Minimum Average Total Inspection Plans for Variables Sampling, Indexed by Average Outgoing Quality Limit

Dodge and Romig's 1944 volume Sampling Inspection Tables provided, among other procedures, sampling inspection plans for attributes inspection which were indexed by average outgoing quality limit. These tabulated plans guaranteed that when rejected lots are appropriately treated, the long-term average outgoing product quality would not exceed the average outgoing quality limit (AOQL) index of the plan. In addition, the plans were structured so that when the submitted quality level was at the indicated level of process average, the total amount of inspection would be minimized. In this article, plans are presented that match the AOQL, lot size, and process average parameters of the Dodge and Romig plans, but are based on variables sampling rather than attributes sampling. It is assumed that the distribution of the measured characteristic is Normal. Although measurements data are usually more difficult to obtain than attributes data and more calculation is involved in using the plans, the sample sizes are generally substantially smaller. The exception to this is for unknown standard deviation plans, higher AOQL index, and process average near the listed AOQL. It would be presumed that in present-day applications, plans involving low levels of both process average and AOQL would be most widely used.     

Economic Design of CSP-1 Plan Under the Dependent Production Process and Linear Inspection Cost

Chen and Chou presented the economic design of type I continuous sampling plan (CSP-1 plan) under the linear inspection cost. However, it can be argued that the production process is seldom independent. In this paper, we further propose the problem concerning the economic design of CSP-1 plan under the dependent production process and linear inspection cost. A solution procedure is developed to find the unique combination (i*, f*) that will meet the average outgoing quality limit (AOQL) requirement while also minimizing the total expected cost per unit produced during one inspection cycle.     

An economic model for determining the optimal quality and process control policy in a queue-like production system

This paper interrelates and synthesizes the economic design of quality and process control policy and the management of a production system described in terms of an M/G/X queue. A mathematical model is developed to determine the optimal quality and process control policy when both the quality and quantity issues in the production system are considered. The optimal control policy is defined as the one that maximizes the expected profit per unit time over an infinite horizon. Hypothetical data is used to illustrate the impact of on-line control policies on the operating characteristics of the production process.

For a given control policy, it is shown that the expected profit per unit time of the production system can be increased by either improving the reliability of the production system, increasing the arrival rate of incoming jobs, increasing the system's processing rate, or shortening the system's shutdown time. The results also indicate that the larger the performance difference between the in-control and the out-of-control states, the greater the amount of effort should be involved in quality and process control. Finally, it is important for the capacity design of a production system to take into account the requirrments for both quality control and process adjustment.     

The optimal production and shipment policy for the single-vendor singlebuyer integrated production-inventory problem

This paper considers the problem of a vendor (manufacturer) supplying a product to a buyer (customer). The vendor manufactures the product in batches at a finite rate and ships the output to the buyer. The buyer then consumes the product at a fixed rate. The objective is to minimize the mean total cost per unit time of manufacturing set-up, stock transfer and stock holding. Previously published work has concentrated on finding optimal solutions from within given classes of policy. We derive the structure of the globally-optimal solution, set out an algorithm for obtaining it and illustrate the process with two numerical examples.     

A study of a two-phase inspection policy for a preparedness system with a defective state and heterogeneous lifetime

This paper considers an inspection policy for a single component protection or preparedness system, in which the component arises from a heterogeneous population. At any point in time, the system may be in one of three states, good, defective or failed. The system is only required in an emergency, and in order to ensure high availability of the system on-demand, the system undergoes a sequence of inspections. Inspection determines the system state, so that if a transition from the good state occurs between inspections it is not revealed until subsequent inspection. When a defect or failure is revealed, the component is replaced. At the final inspection the component is replaced. We suppose that a component may be either weak or strong, so that the time in the good state has a distribution that is a mixture. In these circumstances, the efficacy of a two-phase inspection policy, with an anticipated high inspection frequency in early life and low inspection frequency in later life, is considered using availability and cost criteria. The policy is investigated in the context of a valve in a natural gas supply network. If the lifetime distributions in the mixture are quite distinct, then cost savings of the order of 5% can be achieved by using the two-phase policy in place of the simpler single phase policy. Furthermore, only if the mean time in the defective state is small or the required availability is very high does the two-phase policy tend to mimic a burn-in policy.     

Integrated dynamic single item lot-sizing and quality inspection planning

This paper proposes an integrated model for single item dynamic lot-sizing problem and Quality Inspection Planning (QIP). The objective is to provide a model of production planning that takes into account a targeted level of outgoing quality or an Acceptable quality level (AQL) when the manufacturing system inherently generates a proportion of defectives that increases significantly when the system switches from the in-control state to the out-of-control state. The average outgoing quality of each period of time of the planning horizon is bounded as a function of the inspection capacity. The effects of integrating QIP are analysed and discussed through several experiments representing different quality control system’s parameters, i.e. inspection capacity, inspection cost and AQL. The simulation results show that it is very important to take into account the inspection process into production planning decisions. This study will help the decision-makers to negotiate service levels or react properly to given customer quality requirements based on cost and lead time parameters in addition to their process characteristics in terms of capability and stability.     

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.     

On the inspection policy of a two-component parallel system with failure interaction

In this paper we study a two-component standby system which can successfully operate upon a demand if at least one component is not failed. We assume that failures can be detected only by periodic inspections. We consider that the failure of one component can modify the (conditional) failure probability of the component still alive with probability p and do not interact with probability 1−p. For that failure interaction scheme we obtain the system reliability function for the case of staggered inspections. We compare staggered and non-staggered inspections through numerical examples considering constant hazard rates.     

On a dynamic preventive maintenance policy for a system under inspection

The purpose of this article is to propose both state and time-dependent preventive maintenance policy for a multi-state deteriorating system, which is equipped with inspection equipment(s) connected to a computer center. After the system being identified as state x at nd through computation by the computer center after inspection (or measurement) via equipment(s), one maintenance action with the minimum expected total cost since nd till Nd (where N=n+K for a fixed integer 0<K<∞) will be chosen from the set A_x of alternatives also with the help of the computer center. In real case, the expected total costs since nd till Nd will be time-dependent and so is the maintenance action chosen at nd. A numerical example is given to illustrate such a maintenance policy for a Markovian deteriorating system to describe its state dependent aspect only for simplicity reason. Due to the fact that both equipment measurement and computer computation take time, the preventive maintenance policy for a sufficiently small d may be used in fact as the one under continuous inspection.     

Quality issue in forecasting problem of production and maintenance policy for production unit

In this study, we consider an unreliable deteriorating production system that produces conforming and non-conforming products to satisfy a random demand under a given service level and during a finite horizon. The production system is subjected to a failure-prone machine. The quality of the produced products is affected by the machine deterioration since the rate of defectives increases as the deterioration increases. Preventive maintenance actions can be piloted on the production system to reduce the influence of deterioration and the defective rate. A joint control policy is based on a stochastic production and maintenance planning problem with goals to determine, firstly, the economic plan of production and secondly, the optimal maintenance strategy. The proposed jointly optimisation minimises the total cost of production, inventory, maintenance and defectives. A failure rate and quality relationship are defined to show the influence of the production rates variation on the failures rate as well as on the defective rate. A numerical example and an industrial case study are adopted to illustrate the proposed approach and a sensitivity analysis to validate the jointly optimisation.     

Determination of the optimal burn-in time and cost using an environmental stress approach: a case study in switch mode rectifier

Stress burn-in is an effective burn-in means of screening out the infant mortality components of a system which are conducted under an extremely stressful environment. While investigating stresses, screening burn-in by thermal stress, voltage stress, or mechanical shock stress, most related studies failed to develop an effective method to determine the optimal burn-in time and burn-in cost for a practical operation. Therefore, this study presents an effective procedure that adopts robust design techniques and the accelerated stress test to determine the optimal burn-in time and burn-in cost. A case study of the production of switch mode rectifier demonstrates the proposed procedure's effectiveness. Moreover, the results show that the proposed procedure generalizes well, and can screen out the early failure from material and manufacturing process.     

Joint multi-objective master production scheduling and rolling horizon policy analysis in make-to-order supply chains

This research studies multi-objective master production schedule (MPS) and advanced order commitment (AOC) in two-stage supply chains. Simulation-based experimental analysis evaluates the impact of environmental and MPS design factors on schedule cost and instability. The results provide insight into multi-objective MPS design considerations through rolling schedule policies. The study reveals that the manufacturer’s production smoothness utility coefficient and its interaction with other experimental factors considerably impact on the system’s performance. In addition, it introduces a simulation framework with embedded mixed integer programming models that could be used as a framework for future research dealing with integrated multi-stage MPS/AOC policy in a variety of planning contexts.     

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.     

The optimal consignment policy for the manufacturer under supply chain co-ordination

This study analyses an optimal consignment policy comprising a fixed fee and a per-unit commission. The manufacturer has to offer its retailers a mutually beneficial consignment scheme that affects the whole supply-chain performance. The focus is on determining the optimal consignment policy for a manufacturer and the resulting supply-chain coordination. Without loss of generality, an analytical model is developed with a closed-form solution, enabling analysis of the performance of a consignment policy. The theoretical analysis shows that the consignment with the highest supply-chain profits depends on a fixed fee and a per-unit commission. The analysis also demonstrates that a consignment policy not only generates a higher manufacturer's profit than the traditional system, but also coordinates the retailer to achieve a large supply-chain profit. As the demand is sensitive to the markdown, the consignment policy becomes more efficient, and the manufacturer's realized profit increases.     

质量技术监督应为外贸企业保驾护航

我国加入世贸后，出口企业面临技术性壁垒，质量技术监督应该发挥标准、计量、信息等优势，加强对企业应对WTO的支持。     

An optimal consignment stock production and replenishment policy with controllable lead time

This paper considers a single-vendor and single-buyer production system in which the lead-time is controllable with an extra investment under a long-term agreement between the two trading partners. The vendor produces at a finite rate, ships the outputs in lots of equal size within a production cycle, and delays those shipments for a certain period when the buyer’s inventory approaches the capacity limits. Therefore, the arrival of these shipments does not lead to an increase in the buyer’s inventory. Meanwhile, the buyer holds the payment until the complete consumption of the products. The holding cost consists of a storage component and a financial component. A joint EOQ/EPQ model is then established under cases where the buyer’s unit storage holding cost might be greater or less than that of the vendor to jointly determine the number of shipments, the size of each shipment, the number of delayed shipments, and the lead time that minimise the yearly joint total expected cost (JTEC) of the system. An efficient solution procedure is provided to solve the non-linear integer optimisation model that defined the system under consideration. A method to determine the integer global optima from the real global optima is also presented. Two numerical experiments are conducted to illustrate the procedure and the results show that considering the combined effect of adopting a consignment stock policy and lead time crashing opportunities may lead to a better result than any of these two policies considered separately.     

A bivariate optimal replacement policy for a multistate repairable system

In this paper, a deteriorating simple repairable system with k+1 states, including k failure states and one working state, is studied. It is assumed that the system after repair is not “as good as new” and the deterioration of the system is stochastic. We consider a bivariate replacement policy, denoted by (T,N), in which the system is replaced when its working age has reached T or the number of failures it has experienced has reached N, whichever occurs first. The objective is to determine the optimal replacement policy (T,N)^* such that the long-run expected profit per unit time is maximized. The explicit expression of the long-run expected profit per unit time is derived and the corresponding optimal replacement policy can be determined analytically or numerically. We prove that the optimal policy (T,N)^* is better than the optimal policy N^* for a multistate simple repairable system. We also show that a general monotone process model for a multistate simple repairable system is equivalent to a geometric process model for a two-state simple repairable system in the sense that they have the same structure for the long-run expected profit (or cost) per unit time and the same optimal policy. Finally, a numerical example is given to illustrate the theoretical results.