Selecting a supplier by fuzzy evaluation of capability indices C pm

A process capability index C_pm that fits nominal-the-best type quality characteristics is an effective tool for assessing process capability since the index can adequately reflect a centring process capability and process yield. A valuable method using C_p estimators was developed by Chou [7] for practitioners to use to determine whether or not two processes have equal capability. However index C_p failed to measure process yield and process centring with bilateral specifications and in addition, more than two suppliers can be selected in an actual application. This study proposes a fuzzy inference method to select the best among the competing suppliers based on an estimated capability index of C_pm calculated from sampled data. This method has the advantages of fuzzy systems where a grade can be obtained instead of a more specific exact evaluation result. An illustrated example of colour STN displays demonstrates that the proposed method is effective and feasible for the evaluation of competing process capability.     

模糊综合评判在机械设备评价中的应用

针对机械设备评价中存在的大量模糊因素,介绍模糊综合评判方法,并对塔设备的综合性能进行评判。     

Measuring process yield based on the capability index Cpm

Process capability indices C_p, C_a, C_pk and C_pm have been proposed to the manufacturing industry as capability measures based on various criteria including variation, departure, yield, and loss. It has been noted in recent quality research and capability analysis literature that both the C_pk and C_pm indices provide the same lower bounds on process yield, that is, Yield2(3C_pk)-1=2(3C_pm)-1. In this paper, we investigate the behaviour of the actual process yield in terms of the number of nonconformities (in ppm) for processes with a fixed index value of C_pk=C_pm, but with different degrees of process centring, which can be expressed as a function of the capability index C_a. The results illustrate that it is advantageous to use the index C_pm over the index C_pk when measuring process capability, since C_pm provides better customer protection. This revised version was published online in October 2004 with a correction to the issue number.     

The evaluation of process capability for a machining center

The machining center methodology is widely applied to production systems within the fast-developing processing industry. The automated machining center can simultaneously perform certain processes, such as milling, drilling, boring, and reaming, on the same machine at the same time, and manufactures limited quantities of multiple-type products. These products usually have numerically important quality characteristics with high accuracy. However, a machining center is unable to measure process capability on its own. Thus, we reflect the process capability of a machining center by measuring the quality characteristics of its processing products. In this paper, we propose the three integrated process capability indices (PCIs) C _p^mc, C _a^mc, and C _pm^mc to evaluate the integrated process precision, accuracy, and actual capability respectively. Furthermore, we develop a process capability monitoring figure (PCMF), which not only displays the status of the process precision and accuracy by the color management method [1], but it also forecasts the integrated process capability of the next productive time (batch) through the analysis of time series. Using the PCMF, engineers will be assisted with tasks such as monitoring the process quality, deciding the period of the borer’s replacement, and designing the process parameters.     

The measurement of a process capability for folded normal process data

There are two approaches to estimate the nonconforming percentage and process capability indices which are commonly used to measure the ability of a process to manufacture products meeting a required specification. The most commonly used approaches are based on the assumption that the process is normally distributed. If the process is not normal with a skewed distribution, but normal-based techniques are used to estimate process capability indices or fraction nonconforming, serious errors can result. Basically, non-normal process data, such as folded normal process data, is common in mechanical industries. In this paper, we propose one procedure to evaluate the process capability from folded normal data, by solving the true process mean and process standard deviation of the underlying normal distribution. A numerical result based on the proposed approach is illustrated.     

Testing manufacturing performance based on capability index C pm

The loss-based process capability index C_pm, sometimes called the Taguchi index, has been proposed to the manufacturing industry to measure process performance. In this paper, we propose a method to assess the performance of a normally distributed process. We implement the theory of testing hypothesis using the natural estimator of C_pm, and provide an efficient program to calculate the p-values. We also provide tables of the critical values for some commonly used capability requirements. Based on the test, we develop a simple step-by-step procedure for in-plant applications.     

西格玛水平与过程能力指数关系模型探讨

通过对质量特性过程的波动和概率分布的研究,结合对不合格品率的系统分析,给出西格玛水平和过程能力指数的详细计算方法,建立西格玛水平、过程能力指数及不合格品率之间的联系,拓展六西格玛管理的研究内容,给企业管理层提供了质量评价决策依据.     

Measuring manufacturing capability based on lower confidence bounds of C pmk applied to current transmitter process

Several process capability indices, including C_p, C_pk, and C_pm, have been proposed to provide numerical measures on manufacturing potential and actual performance. Combining the advantages of those indices, a more advanced index C_pmk is proposed, taking the process variation, centre of the specification tolerance, and the proximity to the target value into account, which has been shown to be a useful capability index for manufacturing processes with two-sided specification limits. In this paper, we consider the estimation of C_pmk, and we develop an efficient algorithm to compute the lower confidence bounds on C_pmk based on the estimation, which presents a measure on the minimum manufacturing capability of the process based on the sample data. We also provide tables for practitioners to use in measuring their processes. A real-world example of current transmitters taken from a microelectronics device manufacturing process is investigated to illustrate the applicability of the proposed approach. Our implementation of the existing statistical theory for manufacturing capability assessment bridges the gap between the theoretical development and the in-plant applications.     

Bayesian approach for measuring EEPROM process capability based on the one-sided indices CPU and CPL

The purpose of process capability analysis is to provide numerical measures on whether a process is capable of reproducing items meeting the manufacturing specifications. Capability analyses have received considerable recent research attention and increased usage in process assessments and purchasing decisions. Most existing research works on capability analysis focus on estimating and testing process capability based on the traditional distribution frequency approach. In this paper, we propose a Bayesian approach based on the indices C_PU and C_PL to measure EEPROM process capability, in which the specifications are one-sided rather than two-sided. We obtain the credible intervals of C_PU and C_PL and develop a Bayesian procedure for capability testing. The posterior probability p, for which the process under investigation is capable, is derived. The credible interval is a Bayesian analog of the classical lower confidence interval. A process satisfies the manufacturing capability requirements if all the points in the credible interval are greater than the pre-specified capability level w. To make this Bayesian procedure practical for in-plant applications, a real example of an EEPROM manufacturing process is investigated, demonstrating how the Bayesian procedure can be applied to actual data collected in the factories.     

The study of cost-tolerance model by incorporating process capability index into product lifecycle cost

To reduce the cost of manufacturing systems, many studies of cost minimization have been performed. Since tolerance design significantly affects the manufacturers’ cost, the optimization of cost-tolerance allocation will be an important issue for reducing these costs. Costs incurred in a product life-cycle include manufacturing cost and quality loss. However, most cost-tolerance optimization models frequently ignore the concept of quality loss and may not lead to an accurate analysis of the tolerance. Until now, process capability analysis has been the tool used to evaluate the adequacy of a production tool in meeting a quality target. Hence, the concept of process capability analysis should be included into the cost-tolerance optimization model. In this study, a flexible cost-tolerance optimization model will be constructed by integrating the process capability index into the product life-cycle cost function. The constructed cost-tolerance optimization model simultaneously considers the manufacturing cost of the components, the process capability of the manufacturing operations, and the quality loss of products. The decision-maker can apply the proposed cost-tolerance optimization model to determine a reasonable tolerance with minimum total cost including consideration of the process capability .     

Contract manufacturer selection by using the process incapability index C pp

In the competitive global business environment, enterprises should effectively respond to and satisfy customer needs. Outsourcing manufacturing is an effective method of adjusting the flexibility of production capability. To ensure final product quality, evaluating and selecting a contract manufacturer is essential. Process capability indices are extensively adopted in manufacturing to determine whether a process meets capability requirements. This study attempts to determine the score index R_i and then apply it to assess the process performance of contract manufacturer by using the process incapability index C _pp . The formulae for C _pp and R_i are simple to understand and to apply. The procedure developed in this paper is also an easy and convenient tool for practitioners to assess contract manufacturer quality performance and make more reliable decisions regarding contract manufacturer.     

Application of the generalized folded-normal distribution to the process capability measures

A generalized folded distribution arises when deviations are measured and the weighted magnitude is recorded, where the weight depends on the degree and the direction (sign) of the deviation. When the underlying distribution is normal, the resulting distribution is referred to as the generalized folded-normal distribution. In this paper, we derive explicit forms of the cumulative distribution function and the probability density function of the generalized folded-normal distribution, and calculate the expected value and the variance. An application of the generalized folded-normal distribution to the process capability measures is illustrated.     

Bootstrap approach for estimating process quality yield with application to light emitting diodes

Process capability indices have been widely used by quality professionals for measuring process performance. Although process yield is the most common criterion used in the manufacturing industry for measuring process performance, a more advanced measurement formula Y_q, called quality yield index, has been proposed as an alternative measure of process performance. Quality yield can be viewed as the classical process yield minus the truncated expected relative process loss, within the specifications, which focuses on customer satisfaction. By taking customer loss into consideration, the advantage of using the quality-yield measure as process performance is that the formula can be applied to processes with arbitrary distributions. Unfortunately, statistical properties of the estimated Y_q are mathematically intractable. Therefore, capability testing cannot be performed. In this paper, a nonparametric but computer intensive method called bootstrap is used to obtain a lower confidence bound on quality yield for capability testing purposes. Simulation studies are conducted to examine the sampling distribution of the estimated Y_q. An application using the index Y_q for the light emitting diode manufacturing process is presented for illustration purposes.     

The process modelling of epoxy dispensing for microchip encapsulation using fuzzy linear regression with fuzzy intervals

Epoxy dispensing is a popular way to perform microchip encapsulation for chip-on-board (COB) packages. However, the determination of the proper process parameters setting for a satisfactory encapsulation quality is difficult due to the complex behaviour of the encapsulant during the dispensing process and the inherent fuzziness of epoxy dispensing systems. Sometimes, the observed values from the process may be irregular. In conventional regression models, deviations between the observed values and the estimated values are supposed to have a probability distribution. However, when data is scattered, the obtained regression model has too wide of a possibility range. These deviations in processes such as epoxy dispensing can be regarded as system fuzziness that can be dealt with satisfactorily using a fuzzy regression method. In this paper, the fuzzy linear regression concept with fuzzy intervals and its application to the process modelling of epoxy dispensing for microchip encapsulation are described. Two fuzzy regression models, expressing the correlation between various process parameters and the two quality characteristics, respectively, were developed. Validation experiments were performed to demonstrate the effectiveness of the method for process modelling.     

一种新的模糊神经网络及在化工过程控制系统的应用研究

本文提出一种新的采用补偿模糊算子的神经网络,它使控制系统具有更强的适应性和鲁棒性。该系统不仅能够自适应地调整隶属度函数。而且能够动态优化模糊规则,将其应用于化学反应器（CSTR）的控制中。仿真实验表明该网络的良好性能。     

Using normal approximation for calculating the p-value in assessing process capability index Cpk

When a process is in a perfect state of statistical control, the process capability indices are widely used to measure the capability of the process to manufacture items within the required tolerance. Most evaluations on process capability indices focus on point estimates, which may result in unreliable assessments of process performance. The index C_pk has been used in various manufacturing industries to provide a quantitative measurement of the performance of the manufacturing. In this paper, based on the theory of statistical hypothesis testing, we propose a procedure on assessing C_pk index for practitioners to use in determining whether a given process as capable. Applying Hamakers approximation, the testing procedure can be adequately derived from a normal distribution approximation, which avoids the more complicated non-central t-distribution. The provided approach is easy to use and the decision making is more reliable.     

Using target costing concept in loss function and process capability indices to set up goal control limits

This paper depicts the relationship among the loss function, process capability indices and control charts to establish goal control limits by extending the target costing concept. The specification limits derived from the reflected normal loss function is linked through the C _pm value, computed either directly from the raw data or given by management or engineers, to conventional control charts to obtain goal control limits. The target value can be taken into consideration directly. The advantages of applying the target costing philosophy are also discussed. This paper explains, from a quantitative approach, that reducing process variation is not enough to solve quality problems. In fact, reducing process variation should be used along with bringing the process mean to the target value.A list of symbols K: The maximum-loss parameter in the reflected normal loss function - : The shape parameter in the reflected normal loss function, /4 - T: The target value - : The distance from the target value to the point where K first occurs (tolerance or specification limit) - E(L(y)): The expected loss associated with the reflected normal loss function - : The average value (mean) of a population - : The standard deviation of a population - _T : The standard deviation from the target value of a population - : The estimated standard deviation of - : The new process standard deviation when 2 are applied - n: The sample size of the subgroup - d ₂: The parameter used to estimate , determined by n - D ₄, D ₃, and A ₂: The parameters in and R control charts, determined by n - c ₄: the parameter used to estimate , determined by n - B ₄, B ₃, and A ₃: The parameters in and S control charts, determined by n - L(y): The general loss function - L ₁(y): The general loss function when the quality improvement is implemented - h: The parameter used to determine L ₁(y), where L ₁(y)=hK - f(y): The probability density function     

C pm MPPAC for manufacturing quality control applied to the precision voltage reference process

The multiprocess performance analysis chart (MPPAC) based on the process capability index C_pm, called C_pm MPPAC, is developed for analysing the manufacturing quality of a group of processes in a multiple process environment. The C_pm MPPAC conveys critical information of multiple processes regarding the departure of the process and process variability from one single chart. Existing research works on MPPAC are restricted to obtaining quality information from one single sample of each process ignoring sampling errors. The information provided from existing MPPAC charts, therefore, is unreliable and misleading and results in incorrect decisions. In this paper, we consider the natural estimator of C_pm based on multiple samples. Based on the natural estimator of C_pm, we consider the sampling errors by providing an explicit formula with the Matlab program to obtain the estimation accuracy of the C_pm. We tabulate the sampling accuracy of C_pm for sample size determination so that the engineers/practitioners can use it for their in-plant applications. An example of multiple precision voltage reference (PVR) processes is presented to illustrate the applicability of C_pm MPPAC for manufacturing quality control.     

Evaluating measurement and process capabilities by GR&R with four quality measures

This paper proposes a procedure for assessing a measurement system and manufacturing process capabilities using Gage Repeatability and Reproducibility (GR&R) designed experiments with four quality measures. In this procedure, a GR&R study is conducted to obtain replicate measurements on units by several different operators. The gage and part variance components are then estimated by conducting analysis of variance (ANOVA) on the GR&R measurement observations. Finally, the acceptance and rejection criteria of the precision-to-tolerance ratio (PTR), signal-to-noise ratio (SNR), discrimination ratio (DR), and process capability index (C_p or C_pk), are employed to assess the measurement and process capabilities. Three previously studied case studies are provided for illustration; in all of which the procedure provided efficient capability assessments at minimal computational and statistical efforts. In conclusion, the procedure proposed in this research using GR&R designed experiments provides valuable procedure and helpful guidelines to quality and production managers in assessing the capabilities of a measurement system and manufacturing process, and deciding the needed actions for improving performance.