Shuguang He

Multivariate measurement system analysis in multisite testing: An online technique using principal component analysis

Multisite testing improves manufacturing throughput and reduces costs by applying simultaneous testing to products with multiple measurement instruments in parallel. It is important to perform measurement system analysis (MSA) on a multisite testing system to assess its testing capability. Traditional MSA methods are designed to be either univariate or multivariate in a single-site system. They are not capable of analyzing a complex multisite testing system where there are multivariate measurements and multiple instruments in parallel. We propose an online multivariate MSA approach to detecting faulty test instruments in a multisite testing system. In order to pinpoint a faulty test instrument in a multisite testing system we compare the performance of each test instrument to the overall performance of all the parallel instruments in the system. A modified principal component analysis (PCA) method is proposed to transform multivariate measurement data with dependent variables into those with independent principal components. Assuming that all the instruments have the same measurement accuracy and precision we consider a faulty instrument as one whose principal component values are beyond the three sigma control limits of the principal component values of all instruments. We conduct an experiment to provide empirical evidence that the proposed approach is capable of identifying the faulty instruments in a multisite testing system. This approach can be implemented as an online monitoring technique so that production is not interrupted until a faulty instrument is identified.

CUSUM charts for monitoring a zero‐inflated poisson process

A zero-inflated Poisson (ZIP) process is different from a standard Poisson process in that it results in a greater number of zeros. It can be used to model defect counts in manufacturing processes with occasional occurrences of non-conforming products. ZIP models have been developed assuming that random shocks occur independently with probability p, and the number of non-conformities in a product subject to a random shock follows a Poisson distribution with parameter λ. In our paper, a control charting procedure using a combination of two cumulative sum (CUSUM) charts is proposed for monitoring increases in the two parameters of the ZIP process. Furthermore, we consider a single CUSUM chart for detecting simultaneous increases in the two parameters. Simulation results show that a ZIP-Shewhart chart is insensitive to shifts in p and smaller shifts in λ in terms of the average number of observations to signal. Comparisons between the combined CUSUM method and the single CUSUM chart show that the latters performance is worse when there are only increases in p, but better when there are only increases in λ or when both parameters increase. The combined CUSUM method, however, is much better than the single CUSUM chart when one parameter increases while the other decreases. Finally, we present a case study from the light-emitting diode packaging industry. Copyright

Warranty claims forecasting based on a general imperfect repair model considering usage rate

Because manufacturers of products sold with any type of warranty incur additional costs from servicing customer warranty claims, accurately forecasting the number of warranty claims has become increasingly important to manufacturers. Under the assumption of Weibull distributed time to failure, we propose two models based on a generalised renewal process that consider product usage rate to forecast the number of failures of products sold with a two-dimensional warranty policy. The accelerated failure time model is used to investigate the effects of the product usage rate on system reliability. The maximum likelihood estimation combined with a nonlinear constrained programming method is used to estimate the parameters of the proposed models. We conduct data experiments based on both simulation and real data collected from an excavator manufacturer in China to test the performance of the proposed models. The results indicate that the models incorporating a variable usage rate more accurately forecast the number of failures than those models based on a nominal usage rate.

CUSUM Control Charts for Multivariate Poisson Distribution

A cumulative sum control chart for multivariate Poisson distribution (MP-CUSUM) is proposed. The MP-CUSUM chart is constructed based on log-likelihood ratios with in-control parameters, Θ0, and shifts to be detected quickly, Θ1. The average run length (ARL) values are obtained using a Markov Chain-based method. Numerical experiments show that the MP-CUSUM chart is effective in detecting parameter shifts in terms of ARL. The MP-CUSUM chart with smaller Θ1 is more sensitive than that with greater Θ1 to smaller shifts, but more insensitive to greater shifts. A comparison shows that the proposed MP-CUSUM chart outperforms an existing MP chart.

Modified multivariate process capability index using principal component analysis

The existing research of process capability indices of multiple quality characteristics mainly focuses on nonconforming of process output, the concept development of univariate process capability indices, quality loss function and various comprehensive evaluation methods. The multivariate complexity increases the computation difficulty of multivariate process capability indices(MPCI), which makes them hard to be used in practice. In this paper, a new PCA-based MPCI approach is proposed to assess the production capability of the processes that involve multiple product quality characteristics. This approach first transforms the original quality variables into standardized normal variables. MPCI measures are then provided based on the Taam index. Moreover, the statistical properties of these MPCIs, such as confidence intervals and lower confidence bound, are given to let the practitioners understand the capability indices as random variables instead of deterministic variables. A real manufacturing data set and a synthetic data set are used to demonstrate the effectiveness of the proposed method. An implementation procedure is also provided for quality engineers to apply our MPCI approach in their manufacturing processes. The case studies demonstrate the effectiveness and feasibility of this new kind of MPCI, which is easier to be used in production practice. The proposed research provides a novel approach of MPCI calculation.

Multivariate process monitoring and fault identification using multiple decision tree classifiers

Machine learning based algorithms, such as a decision tree (DT) classifier, have been applied to automated process monitoring and fault identification in manufacturing processes, however the current DT-based process control models employ a single DT classifier for both mean shift detection and fault identification. As many manufacturing processes use automated data collection for multiple process parameters, a DT classifier would have to handle a large number of classes. Previous research shows that a large number of classes can degrade the accuracy of a DT multiclass classifier. In this study we propose a new process monitoring model using multiple DT classifiers with each handling a small number of classes. Moreover, we not only detect mean shifts but also identify process variability levels that may cause out-of-control signals. Experimental results show that our proposed model achieves satisfactory performance in process monitoring and fault identification with various parameter settings. It achieves better ARL performance compared with the baseline method based on a single DT classifier.

Two-dimensional base warranty design based on a new demand function considering heterogeneous usage rate

Abstract Warranties are prevalent in the market. The manufacturer of products sold with warranties often faces a problem of balancing a trade-off between warranty cost and boosted demand by warranties when designing the warranties. For a two-dimensional base warranty with both age limit and usage limit, the heterogeneous usage rate of customers not only has an effect on warranty cost but also differentiates customers’ perceptions on warranty period. For example, the high-usage customers are more concerned about the usage limit of the warranty period, while the low-usage customers are more preferred to a longer age limit. This paper defines an attractiveness index based on the available warranty region to describe the extent of attractiveness of a two-dimensional warranty period to customers with heterogeneous usage rate. Moreover, a demand function based on the attractiveness index is proposed to describe the boosted demand of extending the warranty period. From the perspective of the manufacturer, the optimal two-dimensional base warranty period is designed by maximising the expected profit considering the trade-off. Both numerical examples and a case study are presented to illustrate the application of the proposed method.

Field reliability modeling based on two-dimensional warranty data with censoring times

ABSTRACT Warranty data can be used for estimating product reliability, identifying causes of failure and designing warranty policy. Based on two-dimensional warranty data, we utilize an accelerated failure time model to investigate the effect of usage rate on product degradation. The stochastic expectation-maximization algorithm is proposed to estimate parameters of the reliability model considering both censored data and field data. Extensive simulation studies are used to validate the proposed method and to compare it with the maximum likelihood method. The utilities of the results have been demonstrated through real warranty data collected from an automobile manufacturer in China.

A Combination of CUSUM Charts for Monitoring a Zero-Inflated Poisson Process

The Zero-inflated Poisson distribution (ZIP) is used to model the defects in processes with a large number of zeros. We propose a control charting procedure using a combination of two cumulative sum (CUSUM) charts to detect increases in the parameters of ZIP process, one is a conforming run length (CRL) CUSUM chart and another is a zero truncated Poisson (ZTP) CUSUM chart. The control limits of the control charts are obtained using both Markov chain-based methods and simulations. Simulation experiments show that the proposed method outperforms an existing method. Finally, a real example is presented.

CUSUM Charts for Monitoring Bivariate Zero-Inflated Poisson Processes With an Application in the LED Packaging Industry

The zero-inflated Poisson (ZIP) model is an extension of the standard Poisson distribution. It is often used to describe a near zero-defect process with occasional occurrences of non-conforming products. In the past, research on the control charts for ZIP process has concentrated on univariate ZIP process where there is only one type of defect. However, it is common in some high quality processes that there are several types of defects to be considered and the count variables are correlated. It is not appropriate to monitor the process using independent univariate ZIP based control charts. In this paper, a control charting procedure using a combination of two cumulative sum charts is proposed for monitoring shifts in a bivariate ZIP (BZIP) process, which is a special case of the multivariate ZIP model. We use simulations to obtain the upper control limit of the control charts based on a specified in-control average number of observations to signal. We also use simulations to evaluate the control charting procedure in three situations: shifts only in the p-set parameters; shifts only in the λ-set parameters; and shifts in all the parameters. The simulation results show that the proposed control charts are effective in detecting shifts in the parameters of a BZIP process. Finally, we present an application of our proposed method in the light emitting diode packaging industry.