Imperfect inspection of a multi-attribute deteriorating production system?a continuous time model (original) (raw)
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A NEW MODEL FOR PRODUCTION, INSPECTION, AND MAINTENANCE: MODEL VALIDATION AND CASE STUDY
Journal Paper, 2020
A model is developed to integrate production planning, preventive maintenance, and process/product quality inspection decisions. The integrated model objective is to minimize the total costs of the three decisions that are subjected to constraints of production availability, preventive maintenance economical limitations, and system reliability constraints. Genetic Algorithms and Mixed Integer Linear Program are utilized to solve such complicated problems with constraints considered. An extensive literature review has been presented. The integration of the production, preventive maintenance, and quality decisions in one integrated model is rare so that further investigations and real case study applications in the industry fields are needed. The proposed model and solution method are compared and validated with four models and methodologies from literature. A case study demonstrates the significant improvements of the model results on a real practical industrial application, which also validates the proposed model.
Modeling cost benefit analysis of inspection in a production line
International Journal of Production Economics, 2014
Production management aims to maximize profit by increasing salable output while reducing the cost related with inspection, where inspection is defined as the measurement and quality assessment of items produced. This study is based on a semiconductor production line with consecutive deteriorating machines. Each machine is inspected via the items it produces and an inspection result triggers a machine's repair, if needed. Inspection related cost includes fixed and variable cost of inspection capacity, Yield Loss Cost generated due to unsalable throughput, and delivery delay cost caused by inspection flow-time. The effects of inspection capacity and inspection rate on cost are investigated using analytical and simulation models. Under a given inspection capacity, Yield Loss Cost decreases with growing inspection rate until a minimum is reached, and then starts to increase with further growing rate. This increase is explained by the impact of higher load on the inspection facility, which prolongs the inspection response time. Thus, an optimal inspection rate can be derived for a given inspection capacity. It will be shown that the higher the capacity, the higher the optimal rate, and the lower the yield loss. Determination of optimal inspection capacity considers the capacity cost against the other costs and minimizes the total expected inspection related costs.
IEEE Access
Over the past 20 years, integrated decision making for production systems has gained the interest of researchers and practitioners. Many studies have shown that integrated decision making can lead to substantial amount of savings. Yet, a few research work has been conducted on the areas of integrated maintenance, production and quality in dynamic environments. This paper provides an integrated multiperiod, maintenance, production and quality-inspection scheduling model, which is formulated as a Markov decision process. The model minimizes the total expected maintenance, production and quality inspection costs. The structural properties of the proposed model are mathematically investigated and with using sensitivity analysis, practical insights are also provided. We mathematically provide conditions to guarantee that the optimal inspection policy is monotone non-decreasing in the state of the machine. Furthermore, we show that the optimal production policy decreases by one unit as the state of inventory increases by one unit. Sensitivity analysis demonstrates that the production parameters affect both, maintenance and inspection decisions. In addition, the maintenance parameters affect inspection decisions. Finally, it is found that among the inspection parameters (i.e., cost-of-inspection and inspection-errors), type-II error mainly affects maintenance decisions. INDEX TERMS Decision making under uncertainty, integrated production, maintenance and quality, inspection errors, Markov decision process.
Inspection scheduling for imperfect production processes under free repair warranty contract
European Journal of Operational Research, 2007
The paper considers scheduling of inspections for imperfect production processes where the process shift time from an 'in-control' state to an 'out-of-control' state is assumed to follow an arbitrary probability distribution with an increasing failure (hazard) rate and the products are sold with a free repair warranty (FRW) contract. During each production run, the process is monitored through inspections to assess its state. If at any inspection the process is found in 'out-of-control' state, then restoration is performed. The model is formulated under two different inspection policies: (i) no action is taken during a production run unless the system is discovered in an 'out-of-control' state by inspection and (ii) preventive repair action is undertaken once the 'in-control' state of the process is detected by inspection. The expected sum of pre-sale and post-sale costs per unit item is taken as a criterion of optimality. We propose a computational algorithm to determine the optimal inspection policy numerically, as it is quite hard to derive analytically. To ease the computational difficulties, we further employ an approximate method which determines a suboptimal inspection policy. A comparison between the optimal and suboptimal inspection policies is made and the impact of FRW on the optimal inspection policy is investigated in a numerical example.
Determining the optimal production–maintenance policy with inspection errors: using a Markov chain
Computers & Operations Research, 2003
Lee and Park examine the e ects of an imperfect production process on the optimal production-inventory policy. They consider an imperfect production process which can go out of control after an exponentially distributed production time and then produce some proportion of defective items. The defective item cost is equivalent to the reworking cost and the warranty cost. Some maintenance-inspection mechanisms are introduced to monitor and restore the process to enhance process reliability and thereby lower the number of defective items produced. However, in many situations, a deteriorating production system possesses an increasing failure rate. In general, such a process will not be as good as new after maintenance but will be younger than its real age. Besides, Lee and Park did not investigate the possibility of imperfect inspection based on consideration of type I and type II errors. In this paper, we consider the e ects of general time to shift distributions, two types of process inspection errors and general repair policy on the optimal production=inspection=maintenance policy. A mathematical model representing the expected average cost is developed using a Markov chain to jointly determine the production cycle, process inspection intervals, and maintenance level. An optimal production=inspection=maintenance policy is determined by minimizing the expected average cost. A numerical example is given to illustrate the use of the method. Based on this proposed Markov structure model, some process-related assumptions such as maintenance that can cause the system to go out of control and that the random results of general repairs can also be easily relaxed, and they are described in the section of model extensions. An extended production-maintenance model for a deteriorating production system is established.
A discounted integrated inspection-maintenance model for a single deteriorating production facility
International Transactions in Operational Research, 2006
In this paper, we address the problem of determining optimum inspection schedules for a single deteriorating production system with a predetermined replacement cycle. It is assumed that, at different discrete points in time over the fixed planning horizon, the facility is inspected to detect its operating state and then it goes over an imperfect preventive maintenance routine to enhance its operating performance. Moreover, the facility undergoes minimal repair once detected in an ''out-of-control'' state. We also adopt the concept of discounted cash flow analysis to account properly for the effect of time value of money on the inspection policies. Under these settings, we formulate the discounted integrated inspectionmaintenance problem as a dynamic programming model with general time to failure distribution. After illustrating the model with a numerical example, we perform sensitivity analysis to investigate the effects of some input parameters on the expected present worth and the number of inspections.
Monitoring process for attributes with quality deterioration and diagnosis errors
Applied Stochastic Models in Business and Industry, 2007
The aim of this paper is to present an online economical quality-control procedure for attributes in a process subject to quality deterioration after random shift and misclassification errors during inspections. The process starts in control (State I) and, in a random time, it shifts to out of control (State II). Once at State II, the non-conforming fraction increases according to a non-decreasing function (z), where z is the number of items produced after a shift. The monitoring procedure consists of inspecting a single item at every m produced items, which is examined r times independently to decide its condition. Once an inspected item is declared non-conforming, the process is stopped and adjusted. A direct search technique is used to find the optimum parameters which minimize the expected cost function. The proposed model is illustrated by a numerical example.
We consider a system with three possible states, good, defective and failed. Failures are detected as soon as they occur; the defective state, which is only revealed by inspection, does not prevent the system from fulfilling the function for which it was designed. We present a maintenance model consisting of periodic inspections to check the state of the system, in which inspections are subject to error. At a false positive inspection the system is unnecessarily replaced; at a false negative inspection a defect remains unrevealed with reliability implications for future operation. The model is illustrated with an example from the railways. In this context, we suppose that system lifetime is heterogeneous so that the time the system spends in the defective state is a random variable from a mixed distribution. We determine under what circumstances the cost of maintenance cannot be justified by its efficacy, and suggest that when there is the possibility that replacement is poorly executed (lifetime heterogeneity) the natural response to imperfect inspection of increasing the inspection frequency can be counter-productive.
2014
We study the problem of determining the frequency of quality control inspections in a tortilla and bread & bakery manufacturer producing pizzas. We first perform statistical analysis of failure data obtained from a real automated pizza production line. Based on this data, we develop a simple model of a quality inspector who visits several such lines and his goal is to allocate the number of his/her visits to the different workstations of the lines so as minimize the total production time of undetected, defective products.