Design of product specifications and control policies in a single-stage production system

Screening (100%-inspection) is a common practice in quality engineering. Traditional screening procedures seek upper and lower specification limits for a quality characteristic associated with some product, such that the total quality cost per item is minimized. This practice ignores the effect of parts rejection on product lead times, inventory carrying costs, shortage costs, throughput, and, eventually, total profit rate of the system. In this paper, a single-stage production system is considered and two control policies arc determined jointly with the inspection plans. Numerical experiments indicate that such co-ordinated policies achieve a better performance than independently determined quality and production control policies     

Optimisation design of attribute control charts for multi-station manufacturing system subjected to quality shifts

The qualities of products are a major concern in any production system; thus implementing efficient inspection policies is of great importance to reduce quality-related costs. This article addresses the problem of finding optimal inspection policies for the multi-station manufacturing system (MMS) subjected to quality shifts to minimise total quality-related cost. Each station of the MMS may stay at either in-control condition or out-of-control condition, which may lead to different nonconforming product rates. Markov chain method is used to calculate the steady-state probability distribution (SSPD). Based on the SSPD, the cost structure of this MMS is analysed. The economical optimisation model of attribute control charts (ACCs) is then established, in which the decision variables are the control chart parameters: sampling interval, sample size and control limit. The ACCs optimisation model is resolved by the proposed integrated algorithm combining heuristic rule and tabu search. This approach is verified through an application case taken from a mobile phone shell production company. The results of comparative analysis show that the proposed model is much more economical than both the current outgoing inspection strategy and the regular np control chart. The sensitivity analysis of four input parameters is also conducted.     

Simulation of an integrated age replacement and spare provisioning policy using SLAM

This paper presents a SLAM simulation model for determining a jointly optimal age replacement and spare part provisioning policy. The policy, referred to as a stocking policy, is formulated by combining age replacement policy with a continuous review (s, S) type inventory policy, where s is the stock reorder level and S is the maximum stock level. The optimal values of the decision variables are obtained by minimizing the total cost of replacement and inventory. The simulation procedure outlined in the paper can be used to model any operating situation having either a single item or a number of identical items. Results from a number of case problems specifically constructed by 5-factor second order rotatory design have been presented and the effects of different cost elements, item failure characteristics and lead time characteristics have been highlighted. For all case problems, optimal (s, S) policies to support the Barlow-Proschan age policy have also been determined. Simulation results clearly indicate the separate optimizations of replacement and spare provisioning policies do not ensure global optimality when total system cost has to be minimized.     

Optimal inspection of a finite population

This article presents a method for determining an optimal quality control (QC) inspection frequency for a manufacturing process where a specified number of items will be produced and where, if the process goes out of control and generates a defective item, it stays out of control. In addition, there is a QC inspection procedure than can detect a defective item. The frequency of inspection is based on minimizing the total cost. The total cost includes the cost of QC inspections plus the cost of manufacturing defective items. In this application the cost of manufacturing defective items is, after identifying a defective item, the cost of checking previously manufactured items until it is determined when the process went out of control, i.e., until a good item is found.     

The Effects of Inspection Error on a Complete Inspection Plan

In a complete inspection plan, every incoming item is subject to variable inspection. If the inspection result indicates that an item fails to meet predetermined specification limits, the item is reworked so that its quality characteristic is exactly equal to the target value. The specification limits are determined by the tradeoff among the cost incurred by imperfect quality, cost of rework and cost of inspection. The economic and statistical effects of inspection error on the complete inspection plan are investigated. Two models with considerations of inspection error are developed under different rework schemes, then compared with the model without inspection error consideration.     

Minimum Cost 100% Inspection Systems with Inspection Error

A field failure in certain products has the potential to cause human suffering and/or loss of life. To the manufacturer, these failures will result in a significant external failure cost. In this paper, cost minimization models are developed to determine an optimal inspection system for multiple 100% attribute inspections with inspection error. An example involving the visual inspection of a braze joint in a cardiac biopsy device is presented to illustrate the use of the models. A key result is that a system requiring an item to pass every inspection in order to be shipped to a customer is not always the best alternative. Examples illustrating the sensitivity of the model results to key cost and operational parameters are shown.     

Condition-based inspection scheme for condition-based maintenance

In condition-based maintenance (CBM) with periodic inspection, the item is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on minimisation of long-run average maintenance costs per unit time due to preventive and failure replacements. It is assumed that inspections are performed at equal time intervals and that the corresponding cost is negligible. However, in many practical situations where CBM is implemented, e.g. manufacturing processes, inspections require labours, specific test devices, and sometimes suspension of operations. Thus, when inspection cost is considerable, it is reasonable to inspect less frequently during the time the item is in healthier states, and, more frequently as time passes and/or the item degrades, namely, a condition-based inspection scheme. This paper proposes a novel two-phase approach for determination of replacement threshold and a condition-based inspection scheme for CBM. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, then, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure to obtain a cost-effective condition-based inspection scheme. The proposed approach can be utilised in many CBM applications. For the sake of simplicity of presentation, the approach is illustrated through a simplified case study already reported by some researchers referenced in the paper.     

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.     

Economic Screening of a Continuously Manufactured Product

In this paper, the problem concerning the economical screening of a continuously manufactured product is considered. Here, the cost of inspection and cost of passing defective items are assumed to be given. Our objective is to find a screening policy that minimizes the long run expected total cost per item. Similar to Klein's approach [7], we will use a Markovian sequential decision model to formulate the problem, and show how to find an optimal solution via linear programming. We will also discuss its implementation in practice and look at an illustrative example.     

Optimal Classification Of Highly-Reliable Products Whose Degradation Paths Satisfy Wiener Processes

At the research and development stage of a product, the manufacturer usually faces the problem of classifying the better and worse designs among several competing designs for each of these parts (or components). It is a great challenge for the manufacturer if these completing designs are highly reliable, since there are few (or even no) failures that would be obtained by ruing traditional life tests or accelerated life tests. In such cases, if there exist product characteristics whose degradation over time can be related to reliability, then collecting “degradation data” can provide information about product reliability. This paper proposes a systematic approach to the classification problem where the products’ degradation paths satisfy Wiener processes. First, an intuitively appealing classification rule is proposed and, then, the optimal test plan is derived by using the criterion of minimizing the total experimental cost The sample size, inspection frequency, and the termination time needed by the classification rule for each of competing designs are computed by solving a nonlinear integer programming with a minimum probability of correct classification and a maximum probability of misclassification. Finally an example is provided to illustrate the proposed method     

THE EFFECTS OF INSPECTION ERRORS TO THE IMPERFECT EMQ MODEL

The presence of Type I and Type II inspection errors may seriously affect the product quality. In this paper we incorporate them into the EMQ (Economic Manufacturing Quantity) model under the imperfect production system. We derive the expected total cost when the shift of the production process follows a general distribution and the inspection interval is arbitrary. The objective is to determine the optimal production cycle length and optimal inspection number while minimizing the total cost. Results for special shift distributions such as exponential and Weibull are established. Sensitivity analysis of the optimal production cycle length and analysis of the cost surplus for incorporating inspection errors under exponential shift distribution are also provided.     

Imperfect inspection of a multi‐attribute deteriorating production system—a continuous time model

The reliability of a multi‐attribute deteriorating production system is controlled using versatile identical inspection facilities. An attribute state is dichotomous (up designates proper function versus down). A product item is conforming if all the system attributes are up when it is produced. When a system attribute is detected as down it is restored back to an up state. Inspection of an attribute can rely on observations of the system, recently produced items, or both. Inspection policy determines the inspection capacity, frequency of inspecting each attribute and inspection schedule. These decisions involve a tradeoff between the cost of inspectors and the loss associated with the roportion of non‐conforming items due to lack of adequate inspection. Three models are introduced, analyzed and solved. In the first model, inspection and restoration are perfect, product attribute is up (down) when the system attribute is up (down), and restoration is immediate. The assumptions of perfect inspection and restoration are relaxed in the second model. The third model relaxes in addition the assumption of immediate restoration. An efficient heuristic solution scheme is provided for solving these models. Sensitivity of the solution to system parameters is studied. Numerical experiments provide some insights regarding the combined effect of imperfect production, inspection and restoration, in various conditions of inspection and restoration durations. Copyright © 2001 John Wiley & Sons Ltd.     

Integrated production planning and quality control for linear production systems under uncertainties of cycle time and finished product quality

This work considers serial production systems with several process steps and a possible quality control at final step. It deals with the problem of optimising planned lead time when the real lead time for each process is stochastic and the finished product quality is uncertain unless it is inspected. Three analytical models are proposed aiming to minimise the expected total cost, which is composed of the inventory and backlogging costs for the finished product and quality costs associated with inspection and non-conformities. These models correspond to three quality control policies: (i) without quality control, (ii) with quality control but without taking into account the inspection duration when optimising the planned lead time and (iii) with quality control and with considering the inspection duration when optimising the planned lead time. Based on the results, it can be highlighted the economic advantage of integrating quality control at the early stage of supply and production planning decisions for some cost parameters conditions. The robustness of the proposed models is also analysed regarding the variance of the probability distributions of the lead times.     

On the Optimality of a Simplified Multicharacteristic Component Inspection Model

Inspection for multicharacteristic components is an important means to assure product quality. A component is inspected with respect to its characteristics of which non-conformance of one would result in the rejection of the component. Based on a cost-minimization model developed recently by Raoul et al., this paper develops a simplified version of the model to capture the cost implication of false rejection, false acceptance and inspection of the components. The simplified model is computationally more efficient than the earlier one. Optimality of the sequencing of characteristics to be inspected is explored. Based on the simplified model, the optimal number of cycles for inspection can be readily determined. A stopping rule is developed for the search of the optimal number of cycles. Sufficient conditions for performing one cycle of inspection or no multicharacteristic inspection at all are given. Finally, the results are extended to the case where the probabilities of defectives are random.     

Optimum rectifying inspection plans

The rectifying inspection plan is a useful tool in statistical quality control (SQC) to assure the average product quality between several stages of a production line. Two optimum rectifying inspection plans are presented. They minimize either ATI (average total inspection) or AOQ (average outgoing quality) and use the other as a constraint. The definitions for both ATI and AOQ are generalized to handle the varying fraction defective of the incoming lots. A comprehensive study is conducted to compare the performance characteristics of the optimum rectifying inspection plans with several other plans. The results show that the optimum plans usually produce the best outcome and always satisfy the design specifications. Moreover, the results of a sensitivity study indicate that the optimum plans are fairly robust. Finally, a manufacturing example illustrates the applications and the managerial significance of the optimum rectifying inspection plans.     

公平关切下“前置仓模式”生鲜供应链决策与协调研究

针对由生鲜产品供应商和“前置仓模式”下的生鲜电商组成的二级供应链保鲜努力水平和“最后一公里服务”努力水平偏低的问题,从公平关切视角探究其原因。运用博弈论方法,通过建立Nash讨价还价模型,分析与比较不同公平关切情形下供应链主体的最优决策以及与之对应的收益和效用。结果表明,供应商的公平关切会降低生鲜电商保鲜努力水平和“最后一公里服务”努力水平,而且供应链成员的公平关切总是伴随着各自渠道收益比的提升和供应链总效用的损失。最后,通过设计“收益共享+成本分担”混合契约,提高电商保鲜努力水平和“最后一公里服务”努力水平,使供应链总效用达到最优。数值分析验证了相关结论。     

A process monitoring procedure based on a surrogate variable for dichotomous performance variable

A monitoring procedure using a surrogate variable is proposed for a process with a binary performance variable. Using the procedure, every item is inspected on a surrogate variable. When an item is rejected, the latest number of consecutively accepted items up to this point is compared with a predetermined number, r, to decide whether to stop the process for an investigation. The conditional distribution of the surrogate variable given the performance variable is assumed to be normal. A cost model is developed, which incorporates costs of inspection, misclassification, investigation, opportunity, and correction. We develop methods of finding the optimum r value and screening limit and analyze the effects of cost parameters on the optimal solution.     

Double-stage inspection for screening multi-characteristic items

Final product inspection of a multi-attribute product, such as in the electronic assembly industry, involves expensive facilities. The correlation among attributes may be used for reducing the efforts needed for screening the products; however, engineers without an appropriate statistical-economical analysis tools do not take risks, and they designate full inspection of each item. We propose a double stage inspection program for reducing inspection efforts. Assuming that the joint distribution is known, the conditional probability that a product is “good” may be evaluated conditional upon the observation of the product's first-stage inspected quality attributes. Then, an expected cost minimization is implemented in order to decide whether a second inspection stage is required or a classification should be based solely on the first inspection stage. The cost factors include inspection and false classification. The method is illustrated on a real data set from a particular electronic product of Motorola-Arad Ltd.     

Tools and Methods for the Improvement of Quality

In developing quality-control procedures, a step-loss function has been used implicitly or explicitly to describe consumer perceptions about product quality. A quadratic loss function has been suggested by Taguchi as an alternative to the step-loss function in measuring the loss due to imperfect product quality (cost of acceptance). In this article, Bayesian analyses of the known-standard-deviation acceptance-sampling problem are described for both the step and quadratic loss functions with three cost components—cost of inspection, cost of acceptance, and cost of rejection. A normal prior distribution is used for the lot mean. Efficient procedures for finding minimum expected cost procedures are given. For a particular example, comparisons are made of how optimal sampling plans and costs computed under the two cost structures change as the form of the prior distribution and misspecification of its mean and variance are varied. Sensitivity analyses for both cost functions show that the optimal sampling plan is robust with respect to the form of the prior distribution, as well as to misspecification of its mean and variance, if the tail specification reasonably approximates that of a normal distribution.     

Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans

The purpose of this paper is to develop a process-targeting model for a product with two quality characteristics produced by two processes in series. The first quality characteristic is determined by the setting of the first process, whereas the second quality characteristic depends on the setting of the two processes. The quality of the product is controlled by a single sample inspection plan where inspection is assumed to be error free. The objective of the model is to determine the optimal target for both processes that maximises the profit. A realistic case study is used to demonstrate the utilisation of the model. The results of applying the model indicated that the plant could improve its profit by using optimal process setting and better inspection plans parameters. In addition, sensitivity analysis was performed to study the effect of different parameters on the expected profit and optimal processes means.