Economic optimization of off-line inspection with rework consideration

This paper addresses issues relating to off-line inspection with rework consideration. We develop a mathematical model to determine the first unit inspected and the average number to be inspected in a batch, assuming the involvement of a quality-control department with a standard procedure. Numerical analyses are used to simulate the effect of changes in the various parameters on the optimal solution when the probability of a transition between states follows the discrete Weibull distribution.     

Economic off-line quality control strategy with two types of inspection errors

A commonly used quality control method is to inspect products to identify their quality and to perform the related disposition of acceptance, salvage or rejection based on the findings. While the issue of finding the most economical inspection/disposition policy has been studied for a batch of units produced from an unreliable system, previous studies assumed the inspections to be perfect. In this study, we further extend the inspection/disposition model to consider two types of inspection errors in order to facilitate the adaptation of this economic inspection/disposition model to real world applications. We first describe an inspection/disposition policy for the two types of inspection errors and then obtain the related mathematical formulae. An algorithm is presented for determining the optimal inspection/disposition policy. Finally, numerical examples are given to illustrate the effect of inspection errors on the optimal inspection/disposition policy under the following three quality control policies: cost minimizing, zero-defects and perfect information policy.     

Economic optimization of off-line inspection in a process that also produces non-conforming units when in control and conforming units when out of control

A finite batch of units is produced by a process subject to random failures. The process starts from the in-control state and may shift, while producing a unit, to the out of control state. We consider the case that inspection is conducted after all the units of the batch have been produced, when the production order of the units is preserved. Most research has assumed that while in the in-control state, the process produces only conforming units and in the out of control state, it produces only non-conforming ones. In our research we relax this assumption, i.e. we consider that in the in-control state the process may also produce non-conforming units and in the out of control state, it may also produce conforming ones. Using dynamic programming, we develop an optimal inspection/disposition policy that finds which units to inspect and how to dispose of uninspected units in order to minimize the expected cost, which includes inspection and penalty costs due to classification errors. In addition to the optimal policy, we develop several heuristic policies since the computational complexity of the dynamic programming calculations is O(3^N)$\mathrm{O}(3^N)$. We then perform computational studies to check the behavior of the optimal and heuristic policies and also to compare the latter policies.     

Economic design of inspection procedures using guard band when measurement errors are present

One of the most important aspects in designing production systems is implementing an adequate inspection procedure to ensure the product quality. Our literature study indicates that two important questions still remain unanswered. First, most of the previous studies on inspection procedures are mainly concerned with how to evaluate and analyze the adequacy of inspection procedures during a production stage. Although the issue of the adequacy of inspection procedures at this point is clearly important, many production processes may better benefit from designing enhanced inspection procedures during an early design stage. Second, the majority of previous studies do not incorporate possible economic impacts of measurement errors when inspection procedures need to be designed. More extensive efforts in designing inspection procedures need to be investigated based on economic considerations. Two approaches, the use of guard band and the selection of inspection precision level, are simultaneously examined for designing economic inspection procedures. By incorporating these two approaches, this paper proposes an optimization scheme for economic design of inspection procedures. A numerical example along with sensitivity analysis demonstrates the applicability of the proposed model.     

Bayesian inspection model with the negative binomial prior in the presence of inspection errors

One of the basic assumptions in Bayesian inspection models is that we have some prior knowledge about the number of defects in a certain product or software system. The prior knowledge can be often described as a probability distribution (e.g., Poisson distribution). In the paper, we propose three conditions that should be put forth as desirable properties for a prior probability distribution of the number of defects in the product. We review various prior probability distributions and test if they meet those conditions. The negative binomial distribution is found to be the only one that satisfies all the desirable conditions. With the negative binomial prior, we analyze the effects of various parameters on the Bayesian estimate of the number of undetected errors still remaining in the product.     

Utilizing the information theory of entropy to solve an off-line inspection problem

This study presents an off-line inspection problem for a batch produced from a process subject to random failures and exhibiting manufacturing variations. The objective of this paper is to develop an inspection policy in which units should be inspected in a particular order to find the transition unit in the batch under a required confidence level. This study develops an algorithm to compute the expected number of inspections. This approach uses the information theory of entropy to select an un-inspected unit to be inspected, and effectively minimizes the uncertainty of the transition unit in the production batch. A numerical example illustrates the proposed off-line inspection policy, and the effects of model parameters on the expected inspection number are investigated. The numerical example in this study indicates that full inspection is required when the required confidence level is one or the process has larger manufacturing variations.     

Accounting for inspection errors and change in maintenance behaviour

We propose a way to account for inspection errors in a particularframework. We consider a situation where the lifetime of a systemdepends essentially of a particular part. A deterioration ofthis part is regarded as an unacceptable state for the safetyof the system and a major renewal is deemed necessary. Thusthe statistical analysis of the deterioration time distributionof this part is of primary interest for the preventive maintenanceof the system. In this context, we faced the following problem.In the early life of the system, unwarranted renewals of thepart are decided upon, caused by overly cautious behaviour.Such unnecessary renewals make the statistical analysis of deteriorationtime data difficult and can induce and underestimation of themean life of the part. To overcome this difficulty, we proposeto regard the problem as an incomplete data model. We presentits estimation under the maximum likelihood methodology. Numericalexperiments show that this approach eliminates the pessimisticbias in the estimation of the mean life of the part. We alsopresent a Bayesian analysis of the problem which can be usefulin a small sample setting.     

Economic design of a complete inspection plan with interactive quality improvement

Consider the monitoring of an ongoing production process subject to complete inspection. Inferior quality products are either reworked or scrapped to assure good outgoing quality. Whenever the quality characteristic of a product exceeds a predetermined action limit, remedial action is taken to restore the process to an in-control state. In addition, the decision maker has a learning opportunity to improve the process by investing in resources to identify and eliminate the causes of deviation from the target quality. Taking a learning action would improve the mean value of the quality characteristic of items produced in an out-of-control state. This paper proposes a cost model to determine the optimal number of learning actions to be taken and the optimal action limit. The model considers the trade-off between quality cost and process improvement cost.     

AT&T准则下完全检验的最优设计

本文研究了完全检验的质量控制问题,将广泛用于X-控制图的AT&T准则应用于完全检验,并根据完全检验的特点,提出一种新的最优模型,数值实验结果表明AT&T准则下的完全检验优于传统的完全检验.     

Two optimization models of the optimum inspection problem

This paper deals with establishing an optimum inspection schedule for systems that are subject to random failure and where the failure can be detected only through an inspection. The paper reviews ‘classical’ optimum checking policies. Two new optimization models are proposed to find the optimum sequence of inspection times. Theoretical analysis and numerical examples show that the optimum inspection time sequence derived from the proposed models is relatively accurate, robust, and computationally simple.     

质量控制中完全检验的一种最优设计

本文提出质量控制中完全检验的一种最优设计。所谓完全检验 ,也就是 1 0 0 %检验 ,是指生产出来的每一个产品都要经过检验。生产过程中有两种生产状态 :控制状态和失控状态。当一个产品的质量特征值超过预定的控制界限 ,就立即对生产过程进行检查 ,一旦发现生产失控 ,马上采取调整措施使生产恢复正常。检验后的产品按其质量特征值接受或者重新制作。根据本文所建立的质量成本模型 ,我们可以得到最优的产品质量的规格界限和控制界限 ,对实际企业的生产有积极的指导作用。     

AT&T准则下完全检验的最优设计(英文)

本文研究了完全检验的质量控制问题,将广泛用于X-控制图的AT＆amp;T准则应用于完全检验,并根据完全检验的特点,提出一种新的最优模型,数值实验结果表明AT＆amp;T准则下的完全检验优于传统的完全检验。     

Playing off-line games with bounded rationality

We study a two-person zero-sum game where players simultaneously choose sequences of actions, and the overall payoff is the average of a one-shot payoff over the joint sequence. We consider the maxmin value of the game played in pure strategies by boundedly rational players and model bounded rationality by introducing complexity limitations. First we define the complexity of a sequence by its smallest period (a nonperiodic sequence being of infinite complexity) and study the maxmin of the game where player 1 is restricted to strategies with complexity at most n and player 2 is restricted to strategies with complexity at most m. We study the asymptotics of this value and a complete characterization in the matching pennies case. We extend the analysis of matching pennies to strategies with bounded recall.     

An optimization approach to the reconstruction of positional DNA sequencing by hybridization with errors

Positional DNA sequencing by hybridization (PSBH) is a recently proposed enhancement of DNA sequencing by hybridization (SBH, potentially a powerful alternative to the DNA sequencing by gel electrophoresis). It has been discussed in many papers and applied to large scale sequencing by hybridization. However, the computational part of PSBH reconstruction is a difficult problem, especially for the occurrence of hybridization errors. So far the problem has not been solved well. Taking PSBH as a combinatorial optimization problem, a novel reconstruction approach to PSBH is presented in this paper. The proposed approach accepts both the negative and positive errors and can greatly reduce ambiguities in the reconstruction of PSBH. The computational experiment shows that our algorithm works satisfactorily and correctly on the test data, especially for the positive errors and k-tuple repetitions.     

Joint optimization of process target mean and tolerance limits with measurement errors under multi-decision alternatives

Determining the optimal target mean for a process has been identified as an important research area and a number of models have been proposed in the literature. This paper differs from previous studies of this problem in two ways. First, most previous studies address the process target problem through models seeking the optimal process mean using fixed tolerance settings of a process. Second, in real-world industrial settings, there are several markets often available with different price/cost structures. In this paper, we develop a model for jointly determining both the optimal process target mean and the optimal tolerance limits under the situation where there are several markets available with different price/cost structures. We then investigate the effects of measurement errors on the optimum process target and tolerance limits with multi-decision alternatives. A numerical example is given, and sensitivity analyses are also performed to study the effects of measurement errors on this model.     

两种不同系统因素影响下完全检验的最优设计

本文研究了两种不同系统因素影响下完全检验的质量最优问题 ,采用有两种不同控制界限的控制图来控制生产过程 ,并根据完全检验的特点 ,提出了一种新的最优模型。 Hui(1 991 )提出的最优模型是本文的最优模型的特殊情况 ,并且本文建立的最优模型还可推广到两种以上不同的系统因素下影响的情况     

A particle swarm algorithm for inspection optimization in serial multi-stage processes

Implementing efficient inspection policies is much important for the organizations to reduce quality related costs. In this paper, a particle swarm optimization (PSO) algorithm is proposed to determine the optimal inspection policy in serial multi-stage processes. The policy consists of three decision parameters to be optimized; i.e. the stages in which inspection occurs, tolerance of inspection, and size of sample to inspect. Total inspection cost is adopted as the performance measure of the algorithm. A numerical example is investigated in two phases, i.e. fixed sample size and sample size as a decision parameter, to ensure the practicality and validity of the proposed PSO algorithm. It is shown that PSO gives better results in comparison with two other algorithms proposed by earlier works.     

The impact of inspection errors,imperfect maintenance and minimal repairs on an imperfect production system

This paper develops an integrated model of production lot-sizing, maintenance and quality for considering the possibilities of inspection errors, preventive maintenance (PM) errors and minimal repairs for an imperfect production system with increasing hazard rates. In this study, a PM activity is imperfect in that a production system cannot be recovered as good as new and might cause the production system to shift to the out-of-control state with a certain probability. Numerical analyses are used to simulate the effect of changes in various parameters on the optimal solution for which the time that the process remains in the in-control state is assumed to follow a Weibull distribution. In addition, we investigate the effects of inspection errors and PM errors on the minimum total cost of the optimal inspection interval, inspection frequency and production quantity.