The construction and application of Six Sigma quality indices

Process quality is the primary factor in facilitating product sales. In accordance with the concept of Six Sigma, numerous studies have employed process capability indices for the determination of process quality levels. Unfortunately, existing indices present only a range of quality levels rather than a specific quality level value. This paper aims to propose Six Sigma quality indices for the assessment of quality levels associated with unilateral as well as bilateral specifications. To ensure the reliability in process assessment, we employ the lower confidence limit of the indices to serve as a standard and develop a process quality analysis chart for the simultaneous evaluation of larger-the-better, smaller-the-better and nominal-the-best quality characteristics with the aim of identifying the causes of sub-standard quality. The resulting chart also provides a valuable reference by which to guide efforts aimed at improvement. Finally, we present three cases and numerical experiments to demonstrate the practical applicability of the proposed method.     

Testing and analysing capability performance for products with multiple characteristics

Process capability analysis is a vital part of an overall quality improvement programme. Numerous techniques and tools have been proposed for process capability analysis. Among these, indices and charts of process capability are simple and effective tools and widely used in the manufacturing industry. Many scholars have revealed numerous valuable aspects of previously developed tools and methods. Due to the rising demands of product quality, the current tools and methods are insufficient for enabling managers to make informed decisions. To address this gap, this study proposes a hypothesis testing procedure which determines whether the process capabilities satisfy the target level. Furthermore, this study proposes an integrated quality test chart (IQTC), which can display the process potential and performance for an entire product with smaller-the-better, larger-the-better and nominal-the-best specifications. The proposed procedure and IQTC incorporate the quality-level concept of the Six Sigma model and can be used to quantitate the relationships among the quality level, capability indices and process yield. They can be applied to assist managers in measuring, monitoring, analysing and improving process performance in a timely manner which will help ensure that the quality levels of their products meet customer demands. Finally, an example is provided to illustrate how to use the proposed procedure and IQTC.     

Two-phase selection framework that considers production costs of suppliers and quality requirements of buyers

Buyers are faced with selecting the optimal supplier, while suppliers are left to consider production costs. In this study, we developed a two-phase selection framework that allows buyers to evaluate the performance of suppliers while taking production costs into account for value maximisation. This scheme is a win-win solution capable of promoting long-term relationships between buyers and suppliers. Under the assumption of normality, the first phase involves constructing a new Six Sigma quality capability analysis chart (SSQCAC) which takes production costs into account. The objective is to evaluate all potential suppliers using the 100?×?(1–α)% upper confidence limit (UCL) of an integrated Six Sigma quality index (SSQI) Q_PIh when dealing with products with smaller-the-better (STB), larger-the-better (LTB), or nominal-the-best (NTB) quality characteristics. According to interval estimation theory, this method can have a significant impact on the consumption of resources; i.e. the production costs of the supplier can be decreased by reducing the production quality to below that required by the buyer. The proposed method also filters out unsuitable suppliers in order to simplify the decision problem and reduce computational demands and operational risks/costs without compromising the quality of the final product. In the second phase, a detailed analysis is conducted using Euclidean distance measure to select the optimal supplier from among the remaining candidates. We conducted a real-world case study to evaluate the efficacy of the proposed method. We also conducted comparisons with existing methods to demonstrate the advantages of the proposed method and its managerial implications. Suggestions for future study are also provided.     

Capability measures for processes with multiple characteristics

Process capability indices, such as , , and , have been widely used in the manufacturing industry providing numerical measures on process precision, process accuracy, and process performance. Capability measures for processes with a single characteristic have been investigated extensively. However, capability measures for processes with multiple characteristics are comparatively neglected. In this paper, we consider a generalization of the yield index proposed by Boyles, for processes with multiple characteristics. We establish a relationship between the generalization and the process yield. We also develop a control chart based on the proposed generalization, which displays all the characteristic measures in one single chart. Using the chart, the engineers can effectively monitor and control the performance of all process characteristics simultaneously. Copyright © 2003 John Wiley & Sons, Ltd.     

旋转超声内圆磨削砂轮变幅器的设计与试验研究

砂轮变幅器是旋转超声内圆磨削谐振系统的关键部件,其设计质量直接影响超声磨削的工艺效果。但目前内圆磨削砂轮变幅器缺乏较为完善的理论分析模型。为提高砂轮变幅器理论分析模型的通用性,基于非谐振设计理论建立了纵向谐振砂轮变幅器的理论分析模型,并利用砂轮变幅器各振动单元间的力、位移连续条件与边界条件推导了其频率方程。然后,针对频率方程进行编程求解,并通过ANSYS有限元仿真分析进行验证。最后,加工制作了纵向谐振砂轮变幅器,并开展阻抗特性分析试验、超声谐振试验和振动位移测量试验,分析了其谐振特性。试验结果表明,所研制的砂轮变幅器的谐振试验频率与理论设计频率一致,其输出端振动位移的试验值与仿真值的相对误差为7.83%,符合旋转超声内圆磨削的要求,验证了理论分析模型求解的正确性。研究结果为旋转超声内圆磨削砂轮变幅器的设计提供了便捷且有效的方法。     

The development of a target‐focused process capability index with multiple characteristics

Within an industrial manufacturing environment, Process Capability Indices (PCIs) enable engineers to assess the process performance and ultimately improve the product quality. Despite the fact that most industrial products manufactured today possess multiple quality characteristics, the vast majority of the literature within this area primarily focuses on univariate measures to assess process capability. One particular univariate index, C_pm, is widely used to account for deviations between the location of the process mean and the target value of a process. While some researchers have sought to develop multivariate analogues of C_pm, modeling the loss in quality associated with multiple quality characteristics continues to remain a challenge. This paper proposes a multivariate PCI that more appropriately estimates quality loss, while offering greater flexibility in conforming to various industrial applications, and maintaining a more realistic approach to assessing process capability. Copyright © 2010 John Wiley & Sons, Ltd.     

面向质量目标的Q控制图设计

针对大批量生产开始阶段的过程监控,提出了一种基于预定质量目标的Q控制图监控方法.其基本思路是利用面向质量目标的统计公差技术与Q控制图相结合应用,以实现大批量过程开始阶段均值和方差未知时面向质量目标的过程监控.基于质量目标建立统计公差(CP*,k*),并将该统计公差转化为基于给定置信概率的对CP和k的估计值的判定条件.通过案例分析,面向质量目标的Q控制图能够在过程保持受控状态的前提下以一定置信概率保证质量目标.     

Process True Capability Evaluation with the Consideration of Measurement System Variability and Expected Quality Loss

Process capability indices are widely computed under the assumption that the measurement system is free from errors. However, measurement variability is unavoidable and has a significant impact in process capability evaluation. From an economic point of view, Taguchi loss function is an effective tool to measure the quality loss of a product characteristic deviated from target value that is extensively used without taking into account the effect of the measurement system. This paper investigates the influence of measurement system variability on the process capability analysis through the calculation of process capability indices. A new quality loss function, integrating the measurement system errors, is developed to compute the optimal true process capability regarding to the expected mean value of the Taguchi loss function and the loss resulting from the control of the true process capability. Copyright © 2016 John Wiley & Sons, Ltd.     

An improved approach for process performance evaluation with the consideration of process yield and quality loss

In recent years, several process capability indices have received considerable research attention and increased usage in evaluating process performance and purchasing decisions in manufacturing industries. In particular, the third-generation capability index C_pmk is constructed by taking process yield and quality loss into consideration. Unfortunately, the sampling distribution of the estimated C_pmk is complicated, making the establishment of the exact confidence interval very difficult. Thus, this study applies the concept of the generalised pivotal quantity (GPQ) to derive the generalised confidence interval (GCI) for the index C_pmk. To examine the performance and the effectiveness of the GCI approach, a series of simulations is undertaken. Three types of bootstrap methods are also implemented and compared with the proposed GCI approach. The results reveal that the proposed GCI approach is superior to the three bootstrap methods since the obtained coverage rates are very close to the nominal confidence level in most of our studied cases even for small sample sizes. Therefore, this article recommends the GCI approach for evaluating process performance in real applications.     

Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss

Acceptance sampling plans have been utilised predominantly for the inspection of outgoing and incoming lots; these plans provide effective rules to vendors and buyers for making decisions on product acceptance or rejection. Multiple dependent state (MDS) sampling plans have been developed for lot sentencing and are shown to be more efficient than traditional single sampling plans. The decision criteria of MDS sampling plans are based on sample information not only from the current lot but also from preceding lots. In this study, we develop a variables MDS sampling plan for lot sentencing based on the advanced process capability index, which was developed by combining the merits of the yield-based index and loss-based index. The operating characteristic function of the developed plan is derived based on the exact sampling distribution. The determination of plan parameters is formulated as an optimisation model with non-linear constraints, where the objective is to minimise the sample size required for inspection and the constraints are set by the vendor and the buyer to satisfy the desired quality levels and allowable risks. The performance of the developed plan is examined and compared with traditional sampling plans. A step-by-step procedure is provided, and the parameters of the plan under various conditions are tabulated for practical applications.     

Modelling infant failure rate of electromechanical products with multilayered quality variations from manufacturing process

The optimisation of product infant failure rate is the most important and difficult task for continuous improvement in manufacturing; how to model the infant failure rate promptly and accurately of the complex electromechanical product in manufacturing is always a dilemma for manufacturers. Traditional methods of reliability analysis for the produced product usually rely on limited test data or field failures, the valuable information of quality variations from the manufacturing process has not been fully utilised. In this paper, a multilayered model structured by ‘part-level, component-level, system-level’ is presented to model the reliability in the form of infant failure rate by quantifying holistic quality variations from manufacturing process for electromechanical products. The mechanism through which the multilayered quality variations affect the infant failure rate is modelled analytically with a positive correlation structure. Furthermore, an integrated failure rate index is derived to model the reliability of electromechanical product in manufacturing by synthetically incorporating overall quality variations with Weibull distribution. A case study on a control board suffering from infant failures in batch production is performed. Results show that the proposed approach could be effective in assessing the infant failure rate and in diagnosing the effectiveness of quality control in manufacturing.     

Fuzzy-based analysis of process capability for assembly quality assessment in mechanical assemblies

Process capability indices are useful tools for evaluating the ability of a process to produce products that meet certain specifications. The assembly quality is dependent on the distribution of variations of assembly dimensions, which is in turn dependent on mating conditions in the mechanical assembly. Since it is often difficult to measure the assembly dimensions in the production stages, they are not considered as a direct inspection objective. Rather, the inspection and evaluation of quality is carried out by specifying whether the assembly requirements satisfy the specified limits. Therefore, we can basethe process capability indices on the assembly dimensions. In most real life cases, the observations are fuzzy. In this paper, a novel method based on fuzzy concepts for process capability analysis of assembly dimensions in mechanical assemblies is presented. According to this scheme, sample observations of manufactured variables are described as fuzzy numbers. The proposed method is able to estimate the ability of the manufacturing process in satisfying the assembly quality in the mechanical assemblies with asymmetric tolerances which have non-normal distributions. In this paper, a proper criterion based on the probability of fuzzy set to interpret the computed fuzzy results is proposed, so these results are converted to the interpretable results for making a decision to evaluate the assembly quality. Furthermore, a new fuzzy-based quantity factor for expressing the percent contributions of effective manufacturing variables on the assembly quality is presented. The application of the presented method is demonstrated through an example and its results are discussed.