Incapability Index Research Articles

Fuzzy Testing Method of Process Incapability Index

The process capability index is a tool for quality measurement and analysis widely used in the industry. It is also a good tool for the sales department to communicate with customers. Although the value of the process capability index can be affected by the accuracy and precision of the process, the index itself cannot be differentiated. Therefore, the process incapability index is directly divided into two items, accuracy and precision, based on the expected value of the Taguchi process loss function. In fact, accuracy and precision are two important reference items for improving the manufacturing process. Thus, the process incapability index is good for evaluating process quality. The process incapability index contains two unknown parameters, so it needs to be estimated with sample data. Since point estimates are subject to misjudgment incurred by the inaccuracy of sampling, and since modern businesses are in the era of rapid response, the size of sampling usually tends to be small. A number of studies have suggested that a fuzzy testing method built on the confidence interval be adopted at this time because it integrates experts and the experience accumulated in the past. In addition to a decrease in the possibility of misjudgment resulting from sampling error, this method can improve the test accuracy. Therefore, based on the confidence interval of the process incapability index, we proposed the fuzzy testing method to assess whether the process capability can attain a necessary level of quality. If the quality level fails to meet the requirement, then an improvement must be made. If the quality level exceeds the requirement, then it is equivalent to excess quality, and a resource transfer must be considered to reduce costs.

Process incapability index for autocorrelated data in the presence of measurement errors

Process incapability index is a useful tool for measuring the performance of a process to maintain the quality of products. In this article, we discuss some statistical properties of the estimator of process incapability index when process observations are autocorrelated and contaminated by measurement errors. In many industry, it has been proven that observed quality characteristics for consecutive items are autocorrelated. Moreover, some amount of measurement errors is always present in the observed data. Therefore, it is important to analyze the statistical properties of the estimator under the combined effect of autocorrelation and measurement error for commenting approximately on the ability of a manufacturing process.

A new incapability index for simple linear profile with asymmetric tolerances

Simple linear profiles (SLPs) are modeled by linear functional relationship between a response variable and an explanatory variable. A number of process capability indices (PCIs) for SLPs with symmetric tolerances have been proposed. However, PCIs for SLPs with asymmetric tolerances have received little attention. This article proposes a new functional incapability index for dealing with asymmetric tolerances. To demonstrate the improved performance of the new index, numerical examples and simulation studies are used to compare it to existing functional PCIs. Bootstrap confidence intervals for the proposed index are also obtained. Two examples illustrate the applicability of the proposed index.

The PO bootstrap approach for comparing process incapability applied to non-normal process selection

ABSTRACT Process selection has been a focal task in operation management. This research focuses on finding alternatives to the current process that have to be at least as capable as the current process. Having multiple alternative processes available enables the manufacturers to have better resource utilization and scheduling flexibility. However, selecting the right process under non-normal data remains a challenge. Quality loss is a popular criterion because of its direct relationship with cost objectives. In this research, we propose the Cpp -based PO bootstrap approach to evaluate candidate processes based on quality loss by utilizing the incapability index. The Cpp index represents Taguchi’s Loss function k(x – T)2, which is suitable for the nominal-the-best type of quality characteristic. It measures production loss caused by process inaccuracy and imprecision. The experiments show that the proposed method can loosen up the reliance on normal assumption by controlling type I error and providing higher power compared to the extended method from the literature. The application to amplifier circuits manufacturing showed that the proposed method is effective to identify the inferior processes despite the severe departure of data from normal, while the opposed method built under normality assumption fails to do so.

Multivariate incapability index for high technology manufacturing processes in presence of the measurement errors: A case study in electronic industry

Process capability indices play a vital role in evaluating the conformity of the process properties to the required specifications. Process incapability indices are created by transformation in the process capability indices, leading to the separation of information related to the process accuracy and precision. This separation of information can be very beneficial to specify whether the process is capable or not and to detect deviations in the production processes that produce high-tech products, such as the electronics industry. The main goal of this study is to propose a process incapability index by considering the measurement error for processes with multivariate quality characteristics. The efficiency of this index is then examined by a numerical example using Monte Carlo simulation method. Moreover, the performance of proposed approach is compared with the case where there is no measurement error. In addition, as a practical example, this index is compared with a number of recently proposed indices in the literature, and sensitivity analysis is conducted, as well. The simulation results showed that the measurement error has a significant effect on process capability and incapability indices. Therefore, we strongly suggest that the measurement error has to be considered in the process analysis.

Multivariate Process Incapability Index Considering Measurement Error in Fuzzy Environment

Process Capability Indices (PCI) show that the process conforms to the specification limits; when the product quality depends on more than one characteristic, Multivariate Process Capability Indices (MCPI) are used. By modifying in the process capability indices, the process incapability indices are created; these indices then provide information about the accuracy and precision of the process separately. In the real world, in most cases, the parameters cannot be specified precisely; therefore, the use of fuzzy sets can solve this problem in statistical quality control. The purpose of this paper is to present, for the first time, a Multivariate Process Incapability Index by considering the measurement error in a fuzzy environment. The presented index is shown for practical examples solved by considering Triangular Fuzzy Numbers; then the capability of the model is compared to the time when fuzzy logic is not used. The obtained results emphasize that ignoring the measurement error also leads to the incorrect calculation of process capability, causing a lot of damage to manufacturing industries, especially high-tech ones.

What can fuzziness do for capability analysis based on fuzzy data

An advantage of process incapability index over the classical process capability index is that it provides uncontaminated separation between process accuracy and process precision. However, the value of the index is hard to be obtained accurately when process parameters cannot be determined precisely. In such case fuzzy set theory can be applied to get more flexible and more sensitive information. In this article a fuzzy process incapability index is proposed when the specification limits are assumed to be type-2 fuzzy. When the process mean and variance are unknown and when the data collected is fuzzy, three fuzzy estimators are considered. A simulation study is conducted based on a TFT-LCD fuzzy process. By employing the total integral value method to the membership function of a fuzzy index, the comparisons of quality among different processes become easier.

The effect of measurement error on the process incapability index

Process capability and incapability indices are numerical tools that evaluate the ability of a process in conformance with the required specifications. The process incapability index , introduced by Chen (1998), provides numerical measures on process precision, accuracy and performance. This paper considers the effect of measurement error, usually from measuring instruments, on and investigates the statistical properties of the estimated index. The results indicate that incapability index based on the measurement error has an important role in detecting process performance and ignoring it causes the process performance to be underestimated.

Reliable confidence intervals for assessing normal process incapability

ABSTRACTThis study aims to provide a reliable confidence interval for assessing the process incapability index [Cpp]. The concept of the generalized pivotal quantities is utilized for constructing the generalized confidence interval for [Cpp]. And, simulations are performed for demonstrating our proposed method and one existent method. The results show that the empirical confidences of these two methods are significantly affected by the degree of process departure. Therefore, we suggest the practitioners to select proper one for capability testing purpose based on the information of degree of process departure.

Developing Acceptance Sampling Plans based on Incapability Index Cpp

Most acceptancesampling plans focus on the percentage of defective products instead of considering the process loss, which doesn't distinguish among the products that fall within the specification limits. Therefore, it is essential to develop an acceptance sampling plan with process loss consideration. In this paper, a variable sa mpling plan based on incapability index Cpp is proposed to deal with lot sentencing. The required sample sizesn and the critical acce ptance value c with some combination of acceptance quality level are tabulated. One example is used to illustrate the proposed methodology. The proposed sampling plan provides a feasible policy, which can be applied to products requiring low process loss where classical sampling plans cannot be applied.

The process incapability index under fuzziness with an application for decision making

AbstractProcess capability indices (PCIs) provide numerical measures on whether a process confirms to the defined capability prerequisite. They have been used to measure the ability of process to decide how well the process meets the specification limits (SLs). The PCIs have been successfully applied by companies for evaluating the quality and productivity performance. In this paper, one of the most important PCIs, process incapability index (Cpp) that provides more process information than other PCIs is analyzed together with the indices inaccuracy (C ia) and imprecision (Cip) under uncertainty. When there are some uncertainties in process parameters, traditional PCIs have failed to summarize process performance. Therefore the fuzzy set theory (FST) can be employed to overcome this problem. In this paper, the index Cpp is analyzed by using the FST to obtain more sensitiveness and a deep and flexible analysis. The fuzzy estimations of the index Cpp are derived for both of triangular and trapezoidal fuzzy ...

Evaluating process performance based on the incapability index for measurements with uncertainty

Process capability indices are widely used in industry to measure the ability of firms or their suppliers to meet quality specifications. The index C PP , which is easy to use and analytically tractable, has been successfully developed and applied by competitive firms to dominate highly-profitable markets by improving quality and productivity. Hypothesis testing is very essential for practical decision-making. Generally, the underlying data are assumed to be precise numbers, but in general it is much more realistic to consider fuzzy values, which are imprecise numbers. In this case, the test statistic also yields an imprecise number, and decision rules based on the crisp-based approach are inappropriate. This study investigates the situation of uncertain or imprecise product quality measurements. A set of confidence intervals for sample mean and variance is used to produce triangular fuzzy numbers for estimating the C PP index. Based on the δ -cuts of the fuzzy estimators, a decision testing rule and procedure are developed to evaluate process performance based on critical values and fuzzy p-values. An efficient computer program is also designed for calculating fuzzy p-values. Finally, an example is examined for demonstrating the application of the proposed approach.

Development of a New Process Incapability Index with an Application to the Evaluation of Manufacturing Risk

Process capability indices have been widely used in industry today since they provide quantitative measures of process performance. Instead of using process capability index, the process incapability index C pp introduced by Greenwich and Jahr-Schaffrath (1995) has an advantage of separating the information of process accuracy and precision for a symmetric tolerance. Using C pp process incapability index, the process performance and its risk level can easily be understood by quality practitioners. Another process incapability index proposed by Chen (1998) is to measure the process performance for an asymmetric tolerance. However, it can't correctly reflect the true manufacturing risk. In order to accurately measure the process performance for both symmetric and asymmetric tolerances, a new process incapability index using desirability function is proposed in this article. The relationship between various new process incapability indices and their associated nonconforming rates has also been explored. Finally, two numerical examples show that our new process incapability index can be used in the evaluation of manufacturing risk.

A research note on the estimated incapability index

Process incapability index, which provides an uncontaminated separation between information concerning the process accuracy and the process precision, has been proposed to the manufacturing industry for measuring process performance. Contributions concerning the estimated incapability index have focused on single normal process in existing quality and statistical literature. However, the contaminated model is more appropriate for real-world cases with multiple manufacturing processes where the raw material, or the equipment may not be identical for each manufacturing process. Investigations based on contaminated normal processes are considered. Sampling distributions and r-th moments of the estimated index are derived. The proposed model will facilitate quality engineers on process monitor and performance assessment.

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

AbstractProcess 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 Cpp to evaluate processes. In this paper, we explore the interval estimation of the incapability index Cpp 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 Cpp. An example is also demonstrated to illustrate how the method may be used in practice. Copyright © 2008 John Wiley & Sons, Ltd.

Comparing confidence limits for short-run process incapability index C pp

Process incapability index C pp has been proposed in the manufacturing industry to assess process incapability. In industries it is sometimes unable to get large samples, and, hence, the CAN (consistent and asymptotically normal) property of the unbiased estimator for C pp is missing. In this paper, six bootstrap methods are applied to construct upper confidence bounds (UCBs) of C pp for short-urn production processes where sample size is small; standard bootstrap (SB), Bayesian bootstrap (BB), bootstrap pivotal (BP), percentile bootstrap (PB), bias-corrected percentile bootstrap (BCPB), and bias-corrected and accelerated bootstrap (BCa). A numerical simulation study is conducted in order to demonstrate the performance of the six various estimation methods. We further investigate the accuracy of the six methods by calculating the relative coverage (defined as the ratio of coverage percentage to average length of UCB). Detailed discussions of simulation results for seven short-run processes are presented. Finally, one real example from Ford Company’s Windsor Casting Plant is used to illustrate the six interval estimation methods.

A Bayesian approach on monitoring process capability

The generalized process incapability index has been developed in the manufacturing industry to provide numerical measures on evaluating process performance. Contributions on the estimated incapability index in existing quality assurance and statistical literature are almost from the frequentist point of view. In this paper, a Bayesian approach is developed under a non-informative prior to obtain the interval estimation for the generalized process incapability index . Useful maximum values required to ensure the posterior probability reaching a certain desirable level based on are tabulated. A Bayesian procedure for judging whether the process satisfies the preset quality reliability requirement is proposed. A practical example is also presented to illustrate how the proposed procedure may be applied.

Multi-process capability plot and fuzzy inference evaluation

Process capability indices C p, C pk, C pm and C pp fitting for nominal-the-best type quality characteristics, are effective tools to assess process capability since these indices can reflect a centering process capability and process yield adequately. The index C pp introduced by Greenwith and Jahr-Schaffrath [Greenwith, M., Jahr-Schaffrath, B.L., 1995. A process incapability index. International Journal of Quality and Reliability Management 12, 58–71] provides additional and individual information concerning the process accuracy and the process precision. Although C pp is useful to evaluate process capability for a single product in common situation, C pp cannot be applied to evaluate the multi-process capability. Referring to Vännman and Deleryd's ( C dr, C dp)-plot, a fuzzy inference approach is proposed in our study to evaluate the multi-process capability based on distance values of a confidence box. This method takes the advantages of fuzzy systems such that a grade instead of sharp evaluation result can be obtained. An illustrated example of color STN display demonstrates that the presented method is effective for assessment of multi-process capability.

A Bayesian approach based on multiple samples for measuring process performance with incapability index

Process incapability index, which provides an uncontaminated separation between information concerning the process accuracy and the process precision, has been proposed to the manufacturing industry for measuring process performance. Investigations concerning the estimated incapability index have focused on single sample in existing quality and statistical literatures. However, contributions based on multiple samples have been comparatively neglected. In this paper, investigations based on multiple samples are considered for normally distributed processes. A Bayesian approach to obtain an upper bound for the incapability index is proposed. A computational program using Maple software is proposed to evaluate critical values required to ensure the posterior probability reaching a certain desirable level for the incapability index. A practical example is also provided to illustrate how the proposed reliable Bayesian procedure may be applied in process capability assessment.

A hypothesis testing procedure on assessing process performance

Process incapability index has been introduced to provide quantitative measures on process performance. Investigations of the estimated incapability index based on multiple samples have been proposed and arrested substantial research attention. In this paper, investigation based on multiple samples is considered for normally distributed processes. A reliable inferential procedure based on the Uniformly Minimum Variance Unbiased Estimator (UMVUE) of the incapability index is proposed. Useful critical values required to ensure the process reaching a certain desirable level of the time are also tabulated. A practical example is provided to demonstrate how the proposed procedure may be applied for judging whether the process runs under the desirable quality requirement.