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.     

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.     

A Bayesian procedure for process capability assessment

The usual practice of judging process capability by evaluating point estimates of some process capability indices has a flaw that there is no assessment on the error distributions of these estimates. However, the distributions of these estimates are usually so complicated that it is very difficult to obtain good interval estimates. In this paper we adopt a Bayesian approach to obtain an interval estimation, particularly for the index C_pm. The posterior probability p that the process under investigation is capable is derived; then the credible interval, a Bayesian analogue of the classical confidence interval, can be obtained. We claim that the process is capable if all the points in the credible interval are greater than the pre‐specified capability level ω, say 1.33. To make this Bayesian procedure very easy for practitioners to implement on manufacturing floors, we tabulate the minimum values of Ĉ_pm/ω, for which the posterior probability p reaches the desirable level, say 95%. For the special cases where the process mean equals the target value for C_pm and equals the midpoint of the two specification limits for C_pk, the procedure is even simpler; only chi‐square tables are needed. Copyright © 1999 John Wiley & Sons, Ltd.     

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.     

Optimal process capability analysis for process design

Conventional process capability analysis is used to measure and control the quality level of a production process in real exercises for on-line quality management. There has been a deficiency in this type of management; namely, the defects which occur in the production process are only passively detected and modified afterwards. Additionally, conventional process capability expression has difficulty distinguishing between alternatives for process selection among possible candidates before process realisation. There is, therefore, considerable motivation for developing a process capability expression which can be used to evaluate alternatives at the beginning of the process design, i.e., off-line application. The conventional C_pm expression is built up by measuring mean deviation and process variances for on-line application. However, if C_pm is used for the process capability analysis for process design, an erroneous C_pm value is found and an inappropriate process design is ended. Thus, the proposed process capability expression revised from the conventional C_pm in consideration of the balance between tolerance cost and quality loss has been developed. This development is the main contribution of this research and, with this development, the appropriate mean and tolerance values can be determined simultaneously prior to the real production process so as to maximise the proposed process capability value. The production is then processed with the pre-determined mean and tolerance values in a real production process. The expectation after process realisation is that the produced responses will be the best of all the alternatives in terms of quality and cost, and that the process capability value obtained after the real production process will be close to the proposed process capability value maximised prior to the real production process.     

Assessing non‐normally distributed processes by interval estimation of the incapability index Cpp

Process capability indices have been widely used in the manufacturing industry. While most studies consider estimation of capability indices for normal processes, comparatively little is known about their behavior in non‐normal settings. Greenwich and Jahr‐Schaffrath (Int. J. Qual. Reliab. Manage. 1995; 12:58–71) introduced the incapability index C_pp to evaluate processes. In this paper, we explore the interval estimation of the incapability index C_pp for non‐normally distributed processes by utilizing seven feasible methods. We further develop an efficient criterion, which is relative coverage, to evaluate the performance of the seven methods. Detailed discussion of simulation results for six non‐normally distributed processes is presented. The results display that the bootstrap pivotal method developed by Wasserman (All of Statistics: A Concise Course in Statistical Inference. Springer Science, Business Media, Inc., 2004) is the best feasible method to estimate C_pp. An example is also demonstrated to illustrate how the method may be used in practice. Copyright © 2008 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.     

Recursive parameter estimation for categorical process control

Statistical process adjustment (SPA) is utilised prevalently in novel manufacturing scenarios. When quality characteristics rather than internal process variables are inspected for the purpose of quality control, data with different resolutions may be collected. This paper proposes a Bayesian framework for parameter estimation when only categorical observations are available. The proposed method incorporates categorical information recursively and updates parameter estimates in real time. Simulation results show that the framework is effective in utilising low-resolution information in parameter estimation, model building and process control.     

A RFID-based recursive process mining system for quality assurance in the garment industry

With the increasing concern about product quality, attention has shifted to the monitoring of production processes to be assured of good quality. Achieving good quality is a challenging task in the garment industry due to the great complexity of garment products. This paper presents an intelligent system, using fuzzy association rule mining with a recursive process mining algorithm, to find the relationships between production process parameters and product quality. The goal is to derive a set of decision rules for fuzzy logic that will determine the quantitative values of the process parameters. Learnt process parameters used in production form new inputs of the initial step of the mining algorithm so that new sets of rules can be obtained recursively. Radio frequency identification technology is deployed to increase the efficiency of the system. With the recursive characteristics of the system, process parameters can be continually refined for the purpose of achieving quality assurance. A case study is described in which the system is applied in a garment manufacturing company. After a six-month pilot run of the system, the numbers of critical defects, major defects and minor defects were reduced by 7, 20 and 24%, respectively while production time and rework cost improved by 26 and 30%, respectively. Results demonstrate the practical viability of the system to provide decision support for garment manufacturers who may not be able to determine the appropriate process settings for achieving the desired product quality.     

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.     

Measuring process capability based on Cpmk with gauge measurement errors

Due to their effectiveness and simplicity of use, the process capability indices , , and have been popularly accepted in the manufacturing industry as management tools for evaluating and improving process quality. Combining the merits of those indices, a more advanced index, , is proposed that takes into account process variation, process centering, and the proximity to the target value, and has been shown to be a very useful index for manufacturing processes with two‐sided specification limits. Most research works related to assume no gauge measurement errors. However, such an assumption inadequately reflects real situations even when highly advanced measurement instruments are employed. Conclusions drawn regarding process capability are therefore unreliable and misleading. In this paper, we conduct a sensitivity investigation for the process capability index in the presence of gauge measurement errors. We consider the use of capability testing of as a method for obtaining lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that using the estimator with sample data contaminated by measurement errors severely underestimates the true capability, resulting in an imperceptibly smaller test power. To measure the true process capability, three methods for the adjusted confidence bounds are presented and their performances are compared using computer simulation. Copyright © 2006 John Wiley & Sons, Ltd.     

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.     

Optimal process adjustment by integrating production data and design of experiments

This paper proposes a method to improve the process model estimation based on limited experimental data by making use of abundant production data and to achieve the optimal process adjustment based on the improved process model. The proposed method is called an Estimation‐adjustment (EA) method. Furthermore, this paper proves three properties associated with the EA, which guarantee the feasibility and effectiveness of using EA for integrating production and experimental data for optimal process adjustment. Also, the paper develops a sequential hypothesis testing procedure for implementing the EA. The properties and implementation of the EA are demonstrated in a cotton spinning process. Copyright © 2010 John Wiley & Sons, Ltd.     

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.     

Using analytic hierarchy process to determine process economics in multivariate loss functions

Performance of a product usually depends on several responses (quality characteristics) which must meet all of the specifications simultaneously. This could be achieved by applying of (the) robust design methodology to problems with multiple characteristics. In the literature, several works have been published concerning multi-response optimization methods, which aim to achieve the best possible robustness. One of the approaches for multi-response optimization is Loss Function Approach which allows the practitioner to include variance–covariance structure of the responses, prediction quality and the economic importance of the responses relevant to the product or process. In this paper, we propose utilizing Analytic Hierarchy Process, a multi-criteria decision making tool, to determine the economic importance matrix in the multivariate loss function. An example of the suggested method is presented on a study conducted for a company producing water proof polymer roofing materials.     

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.