Measuring the Process Yield for Circular Profiles

Two indices C_p(circular) and C_pk(circular) based on the functional method have been proposed to measure the process capability of circular profiles. However, these two indices only provide potential capability and a lower bound on the process yield, respectively. In this paper, we develop a new yield index S_pk(circular) for circular profiles. This index provides an exact measure of process yield. The asymptotic normal distribution of the estimated index is derived. The statistical inferences such as hypothesis testing, confidence interval, and lower confidence interval can be easily constructed. A simulation study is conducted to assess the performance of the proposed method. The simulation results confirm that the estimates are close to the true value and the coverage rates of the confidence intervals are greater than the 95% lower limit of the stated nominal in most cases. One real data set is used to illustrate the applicability of the proposed method. Copyright © 2013 John Wiley & Sons, Ltd.     

Efficient methods for comparing two process yields – strategies on supplier selection

Selecting an appropriate supplier can substantially reduce purchasing costs, decrease production lead time, increase customer satisfaction, and strengthen corporate competitiveness. Thus, an effective approach to alleviate the problem of supplier selection is essential. Numerous studies have indicated that quality is the most critical and fundamental factor for supplier selection and evaluation, among various criteria. This study provides several methods for selecting the superior supplier based on the commonly used quality criterion, process yield. Four tests for comparing two yield-measure indices, based on the normal approximation and generalised confidence intervals method, are presented and compared. This paper provides recommendations for selecting efficient methods, based on the simulation results of test size and selection power. An example is also presented to illustrate the applicability of these methods.     

Yield‐Based Capability Index for Evaluating the Performance of Multivariate Manufacturing Process

Process capability indices (PCIs) have been widely used in the manufacturing industry providing numerical measures on process precision, accuracy and performance. Capability indices measures for processes with a single characteristic have been investigated extensively. However, an industrial product may have more than one quality characteristic. In order to establish performance measures for evaluating the capability of a multivariate manufacturing process, multivariate PCIs should be introduced. In this paper, we analyze the relationship between PCI and process yield. The PCI EC_pk is proposed based on the idea of six sigma strategy, and there is a one‐to‐one relationship between EC_pk index and process yield. Following the same, idea we propose a PCI MEC_pk to measure processes with multiple characteristics. MEC_pk index can evaluate the overall process yield of both one‐sided and two‐sided processes. We also analyze the effect of covariance matrix on overall process yield and suggest a solution for improving overall process yield. Copyright © 2013 John Wiley & Sons, Ltd.     

Effect of Testing Normality on Estimating Process Capability Indices

Process capability indices are used to measure whether a manufacturing process meets the specifications. The studies of these indices are usually based on the assumption that the process follows a normal distribution. These include the indices C_p, C_pk, C_pm, and C_pmk. When the investigator is uncertain whether the process follows a normal distribution, a test of normality may be used to resolve the uncertainty. If the test accepts the null hypothesis that the process follows a normal distribution, the investigator uses C_p, C_pk, C_pm, or C_pmk. If the test rejects the null hypothesis, the investigator uses indices under non-normal distributions. Therefore the test of normality is a preliminary test that determines the form of the distribution and the index to use. In this paper we study the effect of the preliminary test of normality on the estimation of the four process capability indices mentioned above.     

Process capability analysis for an entire product

Process capability indices (PCIs) are powerful means of studying the process ability for manufacturing a product that meets specifications. Several capability indices including C p , C pu , C pl and C pk have been widely used in manufacturing industry to provide common quantitative measures on process potential and performance. The formulas for these indices are easily understood and can be straightforwardly applied. However, those process capability indices are inappropriate for asymmetric tolerances and could not be applied to evaluate multiprocess products. Based on C p , C pu , C pl and C pk , this research aims to develop one process capability analysis chart (PCAC) for precisely measuring an entire product composed of symmetric tolerances, asymmetric tolerances, larger-the-better and smaller-the-better characteristics. The process capability analysis chart evaluates the capabilities of multi-process products and provides chances for continuous improvement on the manufacturing process.     

Measuring the Process Yield for Simple Linear Profiles with one‐Sided Specification

Profile monitoring is mainly for checking the stability of the relationship between response and explanatory variables over time based on observed data. Linear profiles are common in calibration applications. In this study, we develop two new indices for measuring the process yield for simple linear profiles with one‐sided specification. The asymptotic distribution of the estimated index is provided. The approximate lower confidence bound for the true process yield is also obtained and used to determine whether the process yield meets the quality requirement. A simulation study is conducted to assess the performance of the proposed method. The results show that the coverage rates of the confidence intervals for all simulated cases are greater than the 95% lower limit of the stated nominal value. One real example is used to illustrate the applicability of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Process capability indices for a regularly adjusted process

Process capability indices are widely used in industry to achieve and maintain a high-quality level of manufactured items. The successful application of process capability indices requires the process to be stationary. This is not the case for trended processes with regular adjustment, which are very common in manufacturing processes. An interesting and important question is how to define and interpret the process capability for such a process. In this paper, the traditional process capability indices are modified for these trended processes. Two different sources of process variation, one from the process trend, the other from random variation, are identified and used to develop new process capability indices. Based on these new indices, we show that the capability of trended processes can be improved through periodic adjustment to its maximum achievable value. We also develop the procedures to determine the adjustment frequency to meet any prespecified requirements on the capability index or on the process yield.     

A smooth nonparametric approach to process capability

The determination of the capability of a stable process using the standard process capability indices requires that the quality characteristic of interest be normally distributed. Departures from normality can result in erroneous conclusions when using these indices. In this paper we propose assessing the capability of a process using a nonparametric estimator. This estimator is based on kernel estimation of the distribution function. Bandwidth selection for this method can be based either on a normal reference distribution or on a nonparametric estimate. An example is presented that applies this proposed method to non-normal process data. The performance of the resulting estimator is then compared with the sample proportion and a normal-based estimate in a simulation study. © 1998 John Wiley & Sons, Ltd.     

Quality yield measure for processes with asymmetric tolerances

Process capability indices provide numerical measures on whether or not a process is able to produce products that meet prespecified quality targets and are often used by manufacturers to evaluate manufacturing performance. Although process yield is the primary focus of the performance criteria, a formula that combines the yield and the average process loss, called the quality yield index, has been developed. This index, the quality yield, can be viewed as the conventional process yield minus the truncated expected relative process loss within the specifications. Although cases with symmetric tolerances dominate in practical situations, cases with asymmetric tolerances can also occur. In this paper, we generalize the quality yield index for asymmetric tolerances. The generalization technique is justified, and some statistical properties of the estimated generalization are investigated. An application example on high-density light emitting diodes is also presented to illustrate the applicability of the generalization.     

A weighted variance capability index for general non‐normal processes

Process capability indices are considered to be one of the important quality measurement tools for the continuous improvement of quality and productivity. The most commonly used indices assume that process data are normally distributed. However, many studies have pointed out that the normally‐based indices are very sensitive to non‐normal processes. Therefore we propose a new process capability index applying the weighted variance control charting method for non‐normal processes to improve the measurement of process performance when the process data are non‐normally distributed. The main idea of the weighted variance method is to divide a skewed or asymmetric distribution into two normal distributions from its mean to create two new distributions which have the same mean but different standard deviations. In this paper we provide an example, a distribution generated from the Johnson family of distributions, to demonstrate how the weighted variance‐based process capability indices perform in comparison with another two non‐normal methods, namely the Clements and Johnson–Kotz–Pearn methods. This example shows that the weighted variance‐based indices are more consistent than the other two methods in estimating process fallout for non‐normal processes. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

A QUANTIFIED ASSESSMENT OF THE RELATIONSHIP BETWEEN THE RELIABILITY AND ENTROPY OF WATER DISTRIBUTION SYSTEMS

Several researchers have suggested that it might be possible to use entropy as a general performance indicator for water distribution systems. It has several advantages over other performance and reliability indices, for example, it is extremely rapid and far easier to calculate than other measures, has minimal data requirements and lends itself to direct incorporation into design optimization frameworks.

This paper summarises the first proper attempt to investigate the apparent relationship between the entropy and reliability of water distribution systems. A maximum entropy-constrained approach was used to generate designs for a sample water distribution system which, along with traditional minimum-cost designs, formed the basis of this study. By varying the layout, number of loops and links and reversing the direction of flow in some pipes, it is shown statistically that the correlation between entropy and reliability is strong. Based on the results, a new method for sizing the pipes of water distribution systems is proposed. It is quick, easy to implement, finds optimal pipe sizes, does not require non-linear programming and always guarantees a high level of reliability.     

A Bayesian Approach to Capability Testing Based on Cpk with Multiple Samples

Process capability indices provide numerical measures to compare the output of a process to client's expectations. However, most of the existing researches have used traditional distribution frequency method by using a single sample due to assess process capability. An alternative to this approach is to use the Bayesian method. In this paper, we utilize a Bayesian approach based on subsamples to check process capability via capability index C_pk. As a new suggestion, we used the informative normal prior distribution and the characteristics of sufficient statistic of the parameter to drive the posterior distribution. The capability test is done, and the posterior probability p, for which the process under investigation is capable, is derived both based on the most popular index C_pk. Finally, a numerical example is given to clarify the method. Copyright © 2013 John Wiley & Sons, Ltd.     

Another Look at the Process Capability Index

Process capability indices (PCIs) have been widely used in manufacturing industries. In this paper, we take a very specific view that a proper value of the process capacity index (PCI) represents the true yield of the process. Following this logic, a universal PCI, C_y, is proposed and derived. The superiority of the new PCI is presented in theory and demonstrated through examples. Copyright © 2005 John Wiley & Sons, Ltd.     

Multiple comparisons with the best for supplier selection with linear profiles

In some manufacturing processes, the quality of a process or product is characterised by a linear profile. Comparing the process yield of multiple suppliers with linear profiles is an important task in supplier evaluation. In this study, we consider linear profiles with two-sided specifications and present the multiple comparisons with the best method based on the process yield index to select the best supplier. A subset contains the best supplier determined from the confidence interval of the difference between the process yield indices of the unknown best supplier and all of the suppliers. A simulation study is used to conduct the statistical power analysis. The results confirm that the larger the number of levels or the number of profiles, the larger the power of test. The simulation results indicate that our proposed method can effectively identify the best supplier. Two real examples are used to illustrate the applications of our proposed method.     

An alternative approach to test process capability for unilateral specification with subsamples

Process capability indices are useful management tools, which provide common quantitative measures on manufacturing capability and production quality. The indices C_PU and C_PL are designed specifically for processes with one-sided manufacturing specifications. The majority of the results obtained so far related to the distributional properties of the estimated capability indices were derived based on the assumption of possessing a single sample. However, a common practice in process control is to estimate the process capability indices by using the past ‘in control’ data from several subsamples. In order to use previous in-control data from multiple subsamples to make correct decisions regarding process capability, the distribution of the estimated capability index based on multiple subsamples should be available. In this paper, we develop a capability testing procedure with one-sided specifications using a Bayesian approach based on subsamples collected over time from an in-control process. By applying the proposed testing procedure, the practitioners can make reliable decisions to determine whether their processes meet the pre-set capability requirement when a daily based or weekly based production control plan is implemented for monitoring process stability.     

Design based failure analysis and yield improvement in CMOS-circuits

In this paper we show that defect simulation is a basis for yield enhancement strategies. These strategies involve identification of the yield detractors (i.e. identification of spot defect characteristics) and yield oriented layout design, which uses information about defects. Information about key yield detractors can be obtained in a time and cost efficient manner using defect simulation. By comparison of process variants and of SRAMs with different layouts, the sensitivity of the method for process changes as well as for design differences is illustrated. This leads to the conclusion that the defect and yield simulation tools can be used for yield oriented design. The enormous cost and time savings demonstrated in this work give a signal to enforce the introduction of design based failure simulation methods into the yield learning process.     

Re-evaluating the process capability indices for non-normal distributions

Classical process capability indices (PCIs) C _p , C _pu , C _pl and C _pk can indicate the potential process capability accurately when the quality characteristic of the product is normally distributed. When the process has a non-normal distribution, classical PCIs will be inappropriate and can misled the assessment of process capability. Zwick (1995), Schneider and Pruett (1995-96) and Tong and Chen (1998) proposed various PCIs for non-normal distributions. This paper compares the accuracy of these indices for several selected non-normal distributions based on the proportion of non-conformity of manufactured product. The results indicate that these PCIs lead to a larger number of errors in various combinations of shape parameters and specification limits. Therefore, this paper proposes three indices, S _pu , S _pl and S _pk , which can reflect accurately the proportion of nonconformity in either normal or non-normal distributions.     

Generalized confidence intervals for assessing process capability of multiple production lines

Process capability indices (PCIs) have become popular as unit‐less measures on whether a process is capable of reproducing items meeting the quality requirement. A reliable approach for testing process capability is to establish an interval estimate, for which we can assert that it contains the true PCI value with a reasonable degree of certainty. However, the construction of such an interval estimate is not trivial, since the distribution of the commonly used C_pk index involves unknown parameters. In this paper, we adopt the concept of generalized confidence intervals and generalized pivotal quantities to derive the generalized lower confidence bounds for providing critical information on process performance. Two practical applications in the area of process capability were considered, they include (i) assessing whether a process under investigation is capable and (ii) providing the lowest performance of the manufacturing processes from several production lines or several suppliers for quality assurance. The applicability of the derived results is also illustrated with examples. Copyright © 2008 John Wiley & Sons, Ltd.     

A Quantified Model for Facility Site Selection-Application to a Multiplant Location Problem

Present location theory ranges from lists of subjective factors to be used as guidelines on the one hand to mathematical models utilizing only monetary factors on the other. A void has existed with respect to using all relevant location information in a comprehensive location model. Such a model is presented in this paper. All factors, both subjective and those quantifiable, are evaluated, converted to consistent, dimensionless indices, and then combined to yield the location measure of a given site. These location measures may be used to select a single location or may serve as input to a second model which solves a multiplant location problem. The entire process has been programmed in FORTRAN IV and is currently in use.