Presence Of Gauge Measurement Errors Research Articles

A note on statistical analysis of C pk for autocorrelated data in the presence of random measurement errors

Process capability indices (PCIs) have been widely used for process performance assessment. It provides a quantitative measure of performance of an industrial production process. Several PCIs have been proposed in the literature. C p k is one of the most useful capability index. Statistical properties of the estimator of C p k have been discussed by many researches under the assumption of identically and independently normal distribution. Some statistical properties of the estimator of C p k for autocorrelated data in presence of gauge measurement errors have studied by Scagliarini (2010). However, we found some critical error in the expression of expectation and variance of the estimator when process is autocorrelated as well as measurement error is present. Through this article, we present a corrected version of expectation and variance of the estimator.

Performance comparison of generalized confidence interval and modified sampling distribution approaches for assessing one-sided capability indices with gauge measurement errors

This study compares the performances of the generalized confidence interval (GCI) and the modified sampling distribution (MSD) approaches in evaluating the capability of processes with one-sided tolerance under the presence of gauge measurement errors (GME). The performance of both approaches are measured through a series of simulation. In terms of coverage rates (CRs), GCI and MSD approaches appear to work satisfactorily in the presence of GME since the CRs of the lower confidence bound with considering GME were all close to the nominal value. Furthermore, some of the coverage rates with considering the GME of GCI approach were smaller than those of MSD approach. GCI approach has better ability to assess process capability in the presence of GME. Based on numerical results, both approaches can be recommended to practitioners who assess process performances for cases with one-sided tolerance when GME is actually inevitable.

Performance evaluation of processes with asymmetric tolerances in the presence of gauge measurement errors

ABSTRACTIn this study, the generalized confidence interval method is applied to evaluate the performances of processes with asymmetric tolerances taking into account the gauge measurement errors (GME). To examine the performance of the proposed method, a series of simulations is conducted. Moreover, a sensitivity study is carried out to analyze the effects of ignoring GME. The proposed method performs very well and can be recommended for assessing the performances of processes with asymmetric tolerances in the presence of GME.

Process Yield Analysis for Nonlinear Profiles in the Presence of Gauge Measurement Errors

Process yield plays an important role in many manufacturing industries for measuring process performance. However, gauge measurement errors have significant effect on process capability analysis. In this study, we present a method based on the yield index to evaluate the process yield of nonlinear profiles in the presence of gauge measurement errors. The results indicate that the presence of gauge measurement errors in the data leads to different behaviors of the yield index estimator according to the existence of the gauge variability. Our proposed test procedure can be easily used to determine whether or not manufacturing processes meet the quality requirements when gauge measurement errors are considered. A real example from a manufacturing process is used to demonstrate the applications of the proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

A precision-to-tolerance ratio model for the assessment of measurements uncertainty

Estimates of process capability indices are distorted by the presence of gauge measurement errors, a matter which results in two quality measures i.e., the actual and observed process capability indices (ACp and OCp). Gauge errors (Gauge uncertainty) add distrust to the measure data, as a result, one has to assure the accuracy of the gauge by conducting a gauge repeatability and reproducibility (GR&R) study. In this paper, we present novel relationships between the ACp and OCp using the precision-to-tolerance ratio (PTR) to assess the gauge as well as the process capability, simultaneously. Particularly, we will find the chances that an estimated process capability is measured by an erroneous or a perfect gauge. In addition, instead of using the strict threshold values of the PTR to judge the measurement gauge, a novel γ–δ significance characteristic curve will be introduced. The values of γ and δ will describe the accuracy of the measurement system while the critical process capability values/ratios will be computed in the so called χ2 and Cp domains. The introduced γ–δ curve symbolizes the PTR paradigm, here, the complications associated with the strict PTR thresholds used in the literature to judge the gauge capability will be avoided. The chances of having a measurement under the assumption of ACp distribution while it is the observed and vice versa will be established as type I and type II errors.To assess the descriptive merits of the proposed model and guidelines, two case studies from the literature of normally distributed data were addressed. The analysis showed that trustable gauge measurements cannot be proclaimed by just setting strict PTR values.

Process Capability Assessment for Asymmetric Tolerances with Consideration of Gauge Measurement Errors

In recent years, the issue of process capability assessment in the presence of gauge measurement errors (GME) for cases with symmetric tolerances was investigated enthusiastically. However, even processes with symmetric tolerances are very common in practical situations, cases of asymmetric tolerances also occur in manufacturing industries. In this article, a novel approach, called the generalized confidence interval (GCI) approach, is applied to assess the capabilities of processes with asymmetric tolerances in the presence of the GME. To examine the performance of the proposed approach, an exhaustive simulation was conducted. The conclusion is that the proposed approach appears quite satisfactorily for assessing process performance with asymmetric tolerances in the presence of GME in terms of the coverage rate (CR) and the average value of the generalized lower confidence limits.

Properties of multivariate process capability in the presence of gauge measurement errors and dependency measure of process variables

Nowadays process capability has been extensively studied as a mean of summarizing process performance relative to a set of specification limits. Most of the research papers related to process capability indices have assumed that there are no gauge measurement errors. Unfortunately, such an assumption does not reflect real situations accurately even with highly sophisticated advanced measuring instruments. In this paper, we study the behavior of multivariate process capability index ( M C p ) in the presence of gauge measurement errors. In addition, the effect of correlation coefficient and measurement capability on the statistical properties of the estimated M C p are also studied. The results indicate that correlation coefficients of process variables will notability change the statistical behavior of the multivariate process capability in the presence of gauge measurement errors. With the adjusted confidence intervals and suitable estimation method the more accurate testing procedure for M C p by considering different values of correlation coefficient is obtained.

Inference on C pk for autocorrelated data in the presence of random measurement errors

The present paper examines the properties of the C pk estimator when observations are autocorrelated and affected by measurement errors. The underlying reason for this choice of subject matter is that in industrial applications, process data are often autocorrelated, especially when sampling frequency is not particularly low, and even with the most advanced measuring instruments, gauge imprecision needs to be taken into consideration. In the case of a first-order stationary autoregressive process, we compare the statistical properties of the estimator in the error case with those of the estimator in the error-free case. Results indicate that the presence of gauge measurement errors leads the estimator to behave differently depending on the entity of error variability.

Estimating and Testing Process Precision with Presence of Gauge Measurement Errors

Process capability indices have been widely used in the manufacturing industry. Those capability indices, quantifying process potential and performance, are important for any successful quality improvement activities and quality program implementation. Because of the simplicity and easy of understanding, the precision index Cp has gained its popularity for measuring process consistency. However, the quality of data on the process characteristics relies very much on the gauge measurement. Conclusions about capability of the process just only based on the single numerical value of the index are not reliable. In this paper, we not only conduct the performance of the index Cp with gauge measurement errors, but also present adjusted confidence interval bounds and critical values for capability testing purpose of Cp with unavoidable measurement errors. Our research would help practitioners to determine whether the factory processes meet the capability requirement, and make more reliable decisions.

Measuring process capability based on Cpmk with gauge measurement errors

AbstractDue to their effectiveness and simplicity of use, the process capability indices $C_{p}$, $C_{pk}$, and $C_{pm}$ 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, $C_{pmk}$, 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 $C_{pmk}$ 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 $C_{pmk}$ in the presence of gauge measurement errors. We consider the use of capability testing of $C_{pmk}$ 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.

Testing process capability based on Cpm in the presence of random measurement errors

Process capability indices have been widely used in the manufacturing industry providing numerical measures on process performance. The index Cp provides measures on process precision (or product consistency). The index Cpm, sometimes called the Taguchi index, meditates on process centring ability and process loss. Most research work related to Cp and Cpm assumes no gauge measurement errors. This assumption insufficiently reflects real situations even with highly advanced measuring instruments. Conclusions drawn from process capability analysis are therefore unreliable and misleading. In this paper, we conduct sensitivity investigation on process capability Cp and Cpm in the presence of gauge measurement errors. Due to the randomness of variations in the data, we consider capability testing for Cp and Cpm to obtain lower confidence bounds and critical values for true process capability when gauge measurement errors are unavoidable. The results show that the estimator with sample data contaminated by the measurement errors severely underestimates the true capability, resulting in imperceptible smaller test power. To obtain the true process capability, adjusted confidence bounds and critical values are presented to practitioners for their factory applications.

Measuring process capability based on CPK with gauge measurement errors

The well-known process capability index C PK has been popularly used in the manufacturing industry for measuring process reproduction capability. Existing research papers related to C PK have assumed with no gauge measurement errors. Unfortunately, such assumption does not reflect real situations accurately even with highly sophisticated advanced measuring instruments. Conclusions drawn from process capability analysis are hence unreliable. In this paper, we consider estimating and testing C PK with presence of gauge measurement errors. The results show that the estimator using the sample data contaminated by the measurement errors severely underestimates the capability, resulting imperceptible power of capability testing. To obtain the true process capability, modified confidence bounds and critical values are presented to practitioners for their factory applications.