An improved measure of quality loss for notching processes

Nowadays, electronic products are progressively becoming thinner, lighter, and more convenient for people to use. Printed circuit boards, and especially integrated circuit (IC) substrates, are among the essential component of these products. The IC substrate not only protects circuits, fixes lines, and conducts heat, but is also the critical component that provides signal connectivity between the chip, the printed circuit boards, and other crucial parts during the packaging process. The process capability index C_pm is commonly used to assess the product quality loss for decision making in modern semiconductor packaging manufacturing. For high-definition products, packaging processes often have very strict quality requirements and thus the quality inspection procedure is time-consuming and complicated. Therefore, because of the limitation of manpower and capacity of the inspection instruments, the collected sample for quality assessment may be with small to moderate sample sizes. In this paper, we introduce an unbiased estimator for C_pm and provide a step-by-step parametric bootstrap procedure for obtaining a composite lower confidence bound on C_pm . To compare with the approaches discussed in the literature, numerical simulations are conducted under various process parameter settings. The results show that for small to moderate sample sizes, the proposed method applying the unbiased estimator has more accurate coverage rates than the existing methods. At the end of this paper, an application of quality loss assessment in notching processes is demonstrated.     

Measuring Process Yield for Nonlinear Profiles

Assuring the process capability in nonlinear profiles to meet the requirement is a very important task. This paper aims at evaluating the process yield for nonlinear profiles in manufacturing processes. We present the statistical properties of the estimated S_pkA and obtain its lower confidence bound. This index provides an exact measure of the process yield for nonlinear profiles. A simulation study is conducted to assess the performance of the proposed method. The simulation results confirm that the estimated S_pkA value is close to the target value and has the smallest standard deviation. One real example is used to demonstrate the application of the proposed approach. Copyright © 2013 John Wiley & Sons, Ltd.     

Process Yield Analysis for Linear Within‐Profile Autocorrelation

In many industrial applications, the quality of a process or product can be characterized by a function or profile. Owing to spatial autocorrelation or time collapse, the assumption of the observations within each profile that are uncorrelated is violated. This paper aims at evaluating the process yield for linear within‐profile autocorrelation. We present an approximate lower confidence bound for S_pkA when the observations within each profile follow a first‐order autoregressive AR(1) model. A simulation study is conducted to assess the performance of the proposed method. The simulation results confirm that the proposed method performs well for the bias, the standard deviation, and the coverage rate. One real example is used to demonstrate the applications of the proposed approach. Copyright © 2014 John Wiley & Sons, Ltd.     

Yield‐Related Process Capability Indices for Processes of Multiple Quality Characteristics

Process capability indices (PCIs) have been widely used in industries for assessing the capability of manufacturing processes. Castagliola and Castellanos (Quality Technology and Quantitative Management 2005, 2(2):201–220), viewing that there were no clear links between the definition of the existing multivariate PCIs and theoretical proportion of nonconforming product items, defined a bivariate C_pk and C_p (denoted by BC_pk and BC_p, respectively) based on the proportions of nonconforming product items over four convex polygons for bivariate normal processes with a rectangular specification region. In this paper, we extend their definitions to MC_pk and MC_p for multivariate normal processes with flexible specification regions. To link the index to the yield, we establish a ‘reachable’ lower bound for the process yield as a function of MC_pk. An algorithm suitable for such processes is developed to compute the natural estimate of MC_pk from process data. Furthermore, we construct via the bootstrap approach the lower confidence bound of MC_pk, a measure often used by producers for quality assurance to consumers. As for BC_p, we first modify the original definition with a simple preprocessing step to make BC_p scale‐invariant. A very efficient algorithm is developed for computing a natural estimator of BC_p. This new approach of BC_p can be easily extended to MC_p for multivariate processes. For BC_p, we further derive an approximate normal distribution for , which enables us to construct procedures for making statistical inferences about process capability based on data, including the hypothesis testing, confidence interval, and lower confidence bound. Finally, the proposed procedures are demonstrated with three real data sets. Copyright © 2012 John Wiley & Sons, Ltd.     

Lower confidence bounds with sample size information for Cpm applied to production yield assurance

The process capability index C _pm , sometimes called the Taguchi index, has been proposed to the manufacturing industry as providing numerical measures on process performance. A lower confidence bound estimates the minimum process capability, conveying critical information regarding product quality, which is essential to quality assurance. The sample size determination is directly related to the cost of the data collection plan. The purpose of this paper is to provide explicit formulas with efficient algorithms to obtain the lower confidence bounds and sample sizes required for specified precision of the estimation on C _pm using the maximum likelihood estimator (MLE) of C _pm . We also provide tables for the engineers/practitioners to use for their in-plant applications. A real-world example taken from a microelectronics manufacturing process is investigated to illustrate the applicability of the proposed approach. The implementation of existing statistical theory for capability assessment bridges the gap between the theoretical development and factory applications.     

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.     

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.     

Assessing the actual Gamma process quality – a curve-fitting approach for modifying the non-normal flexible index

Process capability indices (PCIs) have been widely adopted for quality assurance activities. By analysing PCIs, a production department can trace and improve a poor process to enhance product quality level and satisfy customer requirements. Among these indices, C_pk remains the most prevalent for facilitating managerial decisions because it can provide bounds on the process yield for normally distributed processes. However, processes are often non-normal in practice, and C_pk may quite likely misrepresent the actual product quality. Hence, the flexible index C_jkp, which considers possible differences in the variability above and below the target value, has been developed for practical use. However, C_jkp continues to suffer from serious bias in assessing actual capability, especially when the process distribution is highly skewed. In this paper, we modify C_jkp for assessing the actual process quality of a Gamma process. A correction factor is obtained by the curve-fitting method. The results show that our proposed method can significantly reduce the bias for calculation of actual nonconformities. Moreover, we introduce a sample estimator for our modified index. The ratio of this estimator’s average value and the modified index is approximately 1. This implies that our proposed estimator can provide an appropriate estimation for assessing the actual Gamma process quality.     

One‐sided Process Capability Assessment in the Presence of Measurement Errors

In the manufacturing industry, many product characteristics are of one‐sided specifications. The well‐known process capability indices C_PU and C_PL are often used to measure process performance. Most capability research works have assumed no measurement errors. Unfortunately, such an assumption is not realistic even if the measurement is conducted using highly sophisticated advanced measuring instruments. Therefore, conclusions drawn regarding process capability are not reliable. In this paper, we consider the estimation and testing of C_PU and C_PL with the presence of measurement errors, to obtain adjusted lower confidence bounds and critical values for true process capability, which can be used to determine whether the factory processes meet the capability requirement when the measurement errors are unavoidable. Copyright © 2005 John Wiley & Sons, Ltd.     

Monitoring manufacturing quality for multiple Li-BPIC processes based on capability index C pmk

The multi-process performance analysis chart (MPPAC) based on process capability indices has been developed to analyse the manufacturing performance for multiple processes, which conveys critical information regarding the departure of the process mean from the target value, process variability, capability levels, which provides a guideline of directions for capability improvement. Existing MPPAC researches have plotted the sample estimates of the process indices on the chart. Conclusions were then made on whether processes meet the capability requirement and directions need to be taken for further quality improvement. Such an approach is highly unreliable since the sample point estimate is a random variable with no assessment of the sampling errors. Further, existing MPPAC researches only considered one single sample. Current quality control practice is to estimate process capability using multiple groups of control chart samples rather than one single sample. In this paper, we propose the C _pmk MPPAC combining the accuracy index C _a to access the performance of multiple manufacturing processes. Distributions of the estimated C _pmk and C _a are derived based on multiple control chart samples, and accurate lower confidence bounds are calculated. The lower confidence bounds of the estimated C _pmk and C _a are then employed to the MPPAC to provide reliable capability grouping for those multiple processes. A real-world example is presented to illustrate the applicability of the proposed MPPAC.     

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.     

Lower confidence bounds for C PU and C PL based on multiple samples with application to production yield assurance

For stably normal processes with one-sided specification limits, capability indices C _PU and C _PL have been used to provide numerical measures on production yield assurance. Statistical properties of the estimators of C _PU and C _PL have been investigated extensively for cases with a single sample. It is shown that for multiple samples, the uniformly minimum-variance unbiased estimators of C _PU and C _PL are consistent and asymptotically efficient. Based on the uniformly minimum-variance unbiased estimators, an algorithm is developed with an efficient program using a direct search method to compute the lower confidence bounds for C _PU and C _PL. The lower confidence bounds convey critical information to the minimum capability of a process, providing a necessary yield assurance of production. The lower confidence bounds are tabulated for some commonly used capability requirement so that engineers/practitioners can use them for their in-plant applications. An example of a high-speed buffer amplifier is presented to illustrate the practicality of the approach to data collected from the factories for production yield assurance.     

Measuring production yield for processes with multiple quality characteristics

Process yield is an important criterion used in the manufacturing industry for measuring process performance. Methods for measuring yield for processes with single characteristic have been investigated extensively. However, methods for measuring yield for processes with multiple characteristics have been comparatively neglected. In this paper, we develop a generalized yield index, called TS _pk,PC , based on the index S_pk introduced by Boyles (Journal of Quality Technology, 23, 17–26, 1991 Boyles, RA. 1991. The Taguchi capability index. J. Qual. Technol., 23: 17–26. [Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]) using the principal component analysis (PCA) technique. We obtained a lower confidence bound (LCB) for the true process yield. The proposed method can be used to determine whether a process meets the preset yield requirement, and make reliable decisions. Examples are provided to demonstrate the proposed methodology.     

Product defect rate confidence bound with attribute and variable data

The upper confidence bound for a product defect rate is a very important index for evaluating the production process in industry. In this paper, we provide a bootstrap methodology to construct a (1?α)100% upper confidence bound for the overall defect rate of a product whose quality assessment involves multiple pass/fail binary data and multiple continuous data. When only the pass/fail data are included we propose using a bootstrap method which is consistent with the Clopper–Pearson one‐sided confidence interval. When only the continuous data are included the BC_a bootstrap method is recommended. These two methods are combined to provide an upper confidence bound for the overall defect rate of the product when multiple pass/fail binary data and multiple continuous data are present. All methods are clearly stated in algorithmic form, investigated through simulation and demonstrated using example data sets. In the simulation studies and examples the proposed algorithms show great advantages in both coverage probability and computational efficiency. Copyright © 2010 John Wiley & Sons, Ltd.     

Markov chain Monte Carlo in Bayesian models for testing gamma and lognormal S-type process qualities

The process capability index C_pu is widely used to measure S-type process quality. Many researchers have presented adaptive techniques for assessing the true C_pu assuming normality. However, the quality characteristic is often abnormal, and the derived techniques based on the normality assumption could mislead the manager into making uninformed decisions. Therefore, this study provides an alternative method for assessing C_pu of non-normal processes. The Markov chain Monte Carlo, an emerging popular statistical tool, is integrated into Bayesian models to seek the empirical posterior distributions of specific gamma and lognormal parameters. Afterwards, the lower credible interval bound of C_pu can be derived for testing the non-normal process quality. Simulations show that the proposed method is adaptive and has good performance in terms of coverage probability.     

Accuracy Analysis of the Estimated Process Yield Based on Spk

Process yield has been the most basic and common criterion used in the manufacturing industry as a base for measuring process performance. Boyles considered a measurement formula called S_pk, which establishes the relationship between the manufacturing specification and the actual process performance, providing an exact (rather than approximate) measure of process yield. Unfortunately, the sampling distribution and the associated statistical properties of S_pk are analytically intractable. In this paper, we consider the natural estimator of the measure S_pk. We investigate the accuracy of the natural estimator of S_pk computationally, using a simulation technique to find the relative bias and the relative mean square error for some commonly used quality requirements. Extensive simulation results are provided and analyzed, which are useful to the engineers for factory applications in measuring process performance. Copyright © 2004 John Wiley & Sons, Ltd.     

Integrating Customer Perception into Process Capability Measures

Process capability indices provide a measure of the output of an in‐control process that conforms to a set of specification limits. These measures, which assume that process output is approximately normally distributed, are intended for measuring process capability for manufacturing systems. When the performance of a system results in a product that fails to fall within a given specification range, however, the product is typically scrapped or reworked, and the actual distribution that the customer perceives after inspection is truncated. In this paper, the concept of a truncated measure for three types of quality characteristics is introduced as the key to linking customer perception to process capability. Subsequently, a set of customer‐perceived process capability indices is presented as an extension of traditional manufacturer‐based counterparts. Finally, data transformation‐based process capability indices are also discussed. A comparative study and numerical example reveal considerable differences among the traditional and proposed process capability indices. It is believed that the proposed process capability index for various quality characteristics may more aptly lead to process improvement by facilitating a better understanding of the integrated effects found in engineering design problems. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

An improved control chart structure for process location parameter

The article proposes a Shewhart‐type control chart, namely M_t chart, for an improved monitoring of the mean level of a quality characteristic of interest, say Y, in a process. The proposed control chart uses the information on a single auxiliary characteristic, say X, of the process and is based on product–difference‐type estimator, say M_t (in fact the spirit is to pool different styles of using information on auxiliary variable(s)). Assuming bivariate normality of the characteristic of interest Y and the auxiliary characteristic X, design structure of the proposed M_t chart is developed and its comparisons are made with those of some existing control charts used for the same purposes. The comparisons reveal an improved performance of the proposed M_t chart relative to its existing counterparts due to suggested merger of different approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

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.