Joint optimisation of production,maintenance and quality for batch production system subject to varying operational conditions

This paper considers the integration problem of production, maintenance and quality for a capacitated lot-sizing production system subject to deterioration. The effects of varying operational conditions from batch to batch on system reliability and product quality are modelled by proportional hazards models, resulting in non-monotonic failure rate and defect rate. After each batch production, imperfect preventive maintenance (PM) is determined to mitigate the system deterioration, and inspection is taken to sort nonconforming items in the finished goods. Once the cumulative number of nonconforming items exceeds a predetermined threshold, an overhaul is performed to renew the system. An integrated model for optimising production plan, PM plan and overhaul strategy is developed to minimise the total cost while satisfying all product demands. A genetic algorithm is proposed to solve the integrated model efficiently. Numerical results validate the rationality of the model with varying operational conditions consideration and its applicability in economic benefits.     

Designing two mixed quick switching sampling plans for linear profiles

This study compares two proposed mixed quick switching sampling (QSS) plans for linear profiles as the quality characteristic. For the QSS plans, we recommend a binomial attribute plan for normal inspection and then a variable sampling plan for tightened inspection based on capability index C_puA of linear profiles with one-sided specifications. The difference between the two proposed QSS plans is in the tightened inspection. Tightened inspection of the first proposed plan is a single sampling using C_puA index, but tightened inspection of the second plan is a multiple dependent state repetitive (MDSR) plan based on C_puA index. The optimal parameters are obtained by nonlinear optimization. Simulation study for selecting parameters is conducted with various combinations of specified acceptable quality level (AQL), limited quality level (LQL), producer's risk, and consumer's risk. Simulation results confirm that the second proposed QSS plan which applies variable MDSR at tightened inspection performs better than another proposed plan. Hence, the approach of the second proposed plan is demonstrated in an illustrative example.     

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.     

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.     

Inspection resource assignment in a multistage manufacturing system with an inspection error model

Producing high-quality products at low cost is always one concern for a multi-stage manufacturing system. That is, production costs and inspection efficiency should receive equal importance. Inspection planning to allocate inspection stations should then be performed to manage limited inspection resources during process planning. Product quality and the possible costs can then be concurrently considered when evaluating a manufacturing plan. Except for finite inspection station classes, the limited number of inspection stations of each inspection station class is considered to solve the inspection allocation problem in this research. Rather than utilizing a constant inspection error or a specified inspection error probability distribution determined by previous observations, the inspection allocation problem is solved using relative cost models in which the inspection error model is embedded. The inspection allocation problem can then be solved by practically reflecting the inspection error when tolerances are rapidly changed to satisfy customer requirements. Since determining the optimal inspection allocation plan seems impractical as the problem size becomes quite large, two heuristic methods have been developed by considering the defective rate, manufacturing cost and earliest stage priority in this research. The performance of each method is measured in comparison with the enumeration method that generates the optimal solution. A feasible manufacturing plan can then be determined and confirmed during process planning by concurrently solving the inspection allocation problem.     

Dependent Mixed and Mixed Repetitive Sampling Plans for Linear Profiles

In this paper, we present two new dependent mixed sampling plans and a mixed repetitive sampling plan based on the process yield index for linear profiles. A mixed sampling plan includes two stages; the first stage is a combined test by variables and by attributes, and the second stage is tested by attributes only. The first plan is based on the traditional mixed sampling scheme without marginal quality, and the second plan is based on the modified mixed sampling scheme with marginal quality. If a lot is very bad, the probability it can be rejected with the small initial sample is higher for dependent mixed sampling with marginal quality. We compare dependent mixed plans with other types of double sampling plans; the former outperforms the others with respect to average sample number. Additionally, the number of profiles required in the first stage is much smaller than in the second stage. When the inspection is costly and destructive, a mixed repetitive sampling plan includes one stage that combines the inspection by attributes and by variables and allows resampling in some conditions. We compare the mixed repetitive sampling plan with the repetitive sampling plans by attributes and by variables. The probability of acceptance using the mixed repetitive sampling plan performs better than the repetitive sampling plans by attributes and by variables. Three examples are used to illustrate the proposed methods. Copyright © 2017 John Wiley & Sons, Ltd.     

基于过程能力指数的抽样风险研究

如果将生产过程中上一道工序的加工过程（设备）视为生产者,而紧邻的下一道工序的加工过程（设备）视为使用者,则上道工序加工的零部件在通过质量抽样检验进入下道工序的过程中．就将产生抽样风险。而由抽样风险确定的抽样方案直接关系到加工过程质量控制和检验成本控制等加工效率问题。考虑到许多大批量自动生产线的检验设备已经具备在线计算过程能力指数的能力．提出了一个基于过程能力指数的抽样风险分析方法,通过计算过程能力指数,得到相应的抽样风险．进而确定合理的抽样检验方案,从而将加工过程的重要指标——过程能力指数与抽样检验方案之间建立了联系。最后,以某汽车发动机曲轴生产线加工过程为例进行了抽样风险分析。     

Economic design of offline inspections for a batch production process

We consider a batch production process that can be either stable or unstable, in which inspection is performed offline after production of the batch is completed. The quality of a batch can be estimated with a desired level of certainty by inspecting only a sample of its units. In order to minimise the expected total cost per batch, which includes the costs of inspection, of false acceptance and of false rejection, we propose an economic inspection plan in which only a fraction of the batches, rather than each batch, is inspected. We prove that the expected total cost is a strictly quasiconvex function of the inspection interval. We establish necessary and sufficient conditions for the optimal inspection interval to be finite and propose an efficient algorithm to obtain its value. We demonstrate for the case of a single-sampling plan where the proposed economic approach outperforms the common procedure of inspecting every batch, and the proposed algorithm is very efficient.     

A modified short‐run type II continuous sampling plan

In this article, a modified continuous sampling of type II is provided for finite production runs. The suggested sampling plan revises the continuous sampling plan‐2 of Yang (1983). The proposed plan places no predetermined limit on the number of items to be inspected until the second defect is detected when in partial inspection mode. A similar derivation to that of Yang is used to find an approximation to the average outgoing quality of the modified continuous sampling plan‐2 in finite production runs. Some tables are provided to aid in the selection of the clearance number and sampling fraction when the production run length and an average outgoing quality limit are given. Copyright © 2002 John Wiley & Sons, Ltd.     

The economic performance of the Shewhart t chart

In the production of small batches of customized parts, high flexibility and frequent switching of production from one product variant to another could not allow for the implementation of a control chart to monitor the process. In fact, when a short‐run production should be started, the distribution parameters of the quality characteristics to be monitored are frequentlytextitunknown and the production run is too short to get sufficient Phase I samples. To overcome this problem, the statistical properties of Shewhart t charts monitoring a short production run have been recently discussed in literature. In this paper, we investigate their economic performance: the SPC inspection cost optimization is constrained by the manufacturing and the inspection activities configuration. The decision variables of the problem include the chart design parameters and the size of batches of parts to be worked and released to the local inspection area. A numerical analysis aimed at evaluating the economic performance of the Shewhart t chart vs the Shewhart chart with known parameters has been performed. The expected economic loss associated with the implementation of the Shewhart t chart is acceptable with respect to the ‘ideal’ condition of the control chart with known parameters when the cost optimization is achieved without a statistical constraint limiting the number of expected false alarms. Finally, the effect of an erroneous initial set‐up on the correctness of the inspection cost estimation has been investigated. Copyright © 2011 John Wiley & Sons, Ltd.     

Developing a model‐based sampling plan

Statistical process modeling is widely used in industry for forecasting the production outcomes, for process control and for process optimization. Applying a prediction model in a production process allows the user to calibrate/predict the mean of the distribution of the process outcomes and to partition the overall variation in the distribution of the process outcomes into explained (by the model) and unexplained (residuals) variations; thus, reducing the unexplained variability. The additional information about the process behavior can be used prior to the sampling procedure and may help to reduce the required sample size to classify a lot. This research focuses on the development of a model‐based sampling plan based ontextitCpk (process capability index). It is an extension of a multistage acceptance sampling plan also based on Cpk (Negrin et al., Quality Engineering 2009; 21 :306–318; Quality and Reliability Engineering International 2011; 27 :3–14). The advantage of this sampling plan is that the sample size needed depends directly and quantitatively on the quality of the process (Cpk), whereas other sampling plans such as MIL‐STD‐414 (Sampling Procedures and Tables for Inspection by Variables for Percent Defective, Department of Defense, Washington, DC, 1957.) use only qualitative measures. The objective of this paper is to further refine the needed sample size by using a predictive model for the lot's expectation. We developed model‐based sample size formulae which depend directly on the quality of the prediction model (as measured by R²) and adjust the ‘not model‐based’ multistage sampling plan developed in Negrin et al. (Quality Engineering 2009; 21 :306–318; Quality and Reliability Engineering International 2011; 27 :3–14) accordingly. A simulation study was conducted to compare between the model‐based and the ‘not model‐based’ sampling plans. It is found that when R² = 0, the model‐based and ‘not model‐based’ sampling plans require the same sample sizes in order to classify the lots. However, as R² becomes larger, the sample size required by the model‐based sampling plan becomes smaller than the one required by the ‘not model‐based’ sampling plan. In addition, it is found that the reduction of the sample size achieved by the model‐based sampling plan becomes more significant as Cpk tends to 1 and can be achieved without increasing the proportion of the classification errors. Finally, the suggested sampling plan was applied with areal data set from a chemicals manufacturing process for illustration. Copyright © 2011 John Wiley & Sons, Ltd.     

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.     

A new inspection sampling plan under capacity constraints and multiple shifts

Various SPC models have been widely deployed in the quality control of different production systems. This paper considers a new design of SPC model with associated decision rules to control a process that produces items in finite lots and has a variance shift as well as a mean shift. Under both an inspection capacity constraint and a false alarm rate constraint, an inspection sampling plan that maximizes the yield of production is developed. Numerical examples are presented to illustrate and evaluate the approach. A semi-economic approach that computes the optimal quantity of inspection capacity is also presented.     

A methodology for risk-based inspection planning of oil and gas pipes based on fuzzy logic framework

In an efficient and effective pipe integrity management programme, maintenance engineers often use the risk-based inspection (RBI) and maintenance strategy. Unfortunately, the calculation of risk is a daunting task because in order to calculate the risk of failure, a maintenance engineer needs to predict the rate of growth of a defect, the effect of the defect on the integrity of the structure and the consequence of failure. Unfortunately precise calculation for either of these parts is quite difficult.Fuzzy logic is a mathematical tool suitable for handling imprecise information in the real world. The benefit of this approach lies in its ability to include personal experiences along with acceptable deterministic models in the calculation. The structure of the model also allows easy calibration of the model to suit a particular plant condition. This approach can thus help to reduce the dependence upon the precise data, allow modelling even when a phenomenon is incompletely understood, and reduce the difficulties arising due to the complex computation required by more traditional methods.This paper presents a proposed methodology, based on fuzzy logic framework, for the establishment of an RBI programme for pipes. The paper also presents in detail a section of the methodology that can be used for calculating the estimated rate of CO₂ corrosion in carbon steel pipes. In this technique the plant operating parameters (temperature, gas and liquid flow rates, total pressure, CO₂ partial pressure and pH) are taken as fuzzy variables and used to calculate the Predicted Rate of Corrosion. The inspected rate of corrosion and the efficiency of inspection are also considered as fuzzy variables and are used to calculate Trust in Inspection Results and Trust in Predicted Results. By combining all the modules an estimated rate of corrosion is calculated. This estimated rate of corrosion can then be used for developing the risk-based inspection programme.     

A bi-objective robust inspection planning model in a multi-stage serial production system

In this paper, we present a bi-objective mixed-integer linear programming (BOMILP) model for planning an inspection process used to detect nonconforming products and malfunctioning processors in a multi-stage serial production system. The model involves two inter-related decisions: (1) which quality characteristics need what kind of inspections (i.e. which-what decision) and (2) when the inspection of these characteristics should be performed (i.e. when decision). These decisions require a trade-off between the cost of manufacturing (i.e. production, inspection and scrap costs) and the customer satisfaction. Due to inevitable variations in manufacturing systems, a global robust BOMILP (RBOMILP) is developed to tackle the inherent uncertainty of the concerned parameters (i.e. production and inspection times, errors type I and II, misadjustment and dispersion of the process). In order to optimally solve the presented RBOMILP model, a meta-heuristic algorithm, namely differential evolution (DE) algorithm, is combined with the Taguchi and Monte Carlo methods. The proposed model and solution algorithm are validated through a real industrial case from a leading automotive industry in France.     

Integrating quality and maintenance decisions in a production-inventory model for deteriorating items

In typical production-inventory models of deteriorating items, deterioration of the production process has not been considered. In this paper, a model is proposed in which both the produced items and the production equipment deteriorate. When the production system deteriorates, it shifts to an out-of-control state and begins to produce a proportion of defective items, necessitating corrective maintenance action. A model is formulated to integrate several realistic aspects, including item and process deterioration, varying demand and production rates, quality, inspection, and maintenance. A heuristic solution algorithm is developed to determine the production and inspection schedules, and a numerical example is solved.     

配网重点物资采购抽检方案研究

针对现行配网物资采购抽检制度中存在的不同批量的产品事实上宽严程度不一致的问题,基于常用的MIL-STD-1916抽样标准,提出一种计数调整型的配网重点物资抽检方案。该抽检方案结合电网的抽检实际,在考虑科学性的基础上,兼顾电网抽检相关文件中规定的重点物资抽样检验4个“百分之百”的要求和(n|0)要求,且不加大现有抽检工作量。研究成果可以直接应用于配网物资采购抽检实际工作中。     

Process improvement versus enhanced inspection in optimized systems

This paper analyses the cost-quality implications of process improvement versus inspection enhancement for n-stage serial production processes. The analysis determines, For a given environment, the combination of process and inspection performance that minimizes the cost of each defect-Free unit produced. Insight into the process-improvement inspection-enhancement trade-off, is obtained by identifying a base-line environment and then varying key environmental parameters including: measures of production and inspection quality, functional relationships between these qualities and their costs, and penalty costs incurred by delivery of defective units to the customer. The results of the analysis are presented in the context of decisions or strategies for the immediate, short-run and long-run optimal combinations of process improvement and inspection enhancement.     

Optimal and heuristic inspection schedules for multistage production systems

Consider a single inspection facility that can be quickly switched among multiple inspection tasks. It can be used (for example) for detecting malfunction (or down state) production stages in a multistage production system. We assume that a properly working (or up state) production stage moves to a down state in any period with fixed probability. The stage then stays down until it is inspected and immediately restored back to an up state. Our purpose is to schedule inspections among the different production stages so as to maximize the fraction of good items produced. An optimal inspection schedule for a two stage production system is provided. For the general case of more than two stages, four heuristics are compared. We conclude that the proposed dynamic schedule is easy to derive, always feasible, and outperforms the static schedules.     

On tandem stochastic networks with time-deteriorating product quality

We consider an n-site tandem stochastic production network where each product moves sequentially through the sites, and the product's quality deteriorates with its sojourn time in the system. At each site the product goes through two stages: the first stage is a processing operation with a generally-distributed random duration. This operation either does or does not conclude successfully; in the latter case, the operation is repeated immediately. Once the processing operation concludes successfully, the product goes through an inspection stage lasting a generally-distributed random duration. At the end of the inspection the product's state is determined as follows: either (i) it requires additional processing and moves forward to the next site; or (ii) it is found ‘good’ and exits the network with quality value depending on its total sojourn time in the system; or (iii) it is declared ‘failed’, discarded, and exits the network with zero quality value. Two scenarios are analysed: (i) a new product enters the system only after the preceding product has exited and (ii) the network is a tandem Jackson-type system. For each scenario, we construct both time-dependent and quality-dependent performance measures. In the case where the sites can be arranged in an arbitrary order, we derive easy to implement optimal index-type policies of ordering the sites so as to maximise the quality rate of the production network.