A Comparative Study of Different Methodologies for Fault Diagnosis in Multivariate Quality Control

Different methodologies for fault diagnosis in multivariate quality control have been proposed in recent years. These methods work in the space of the original measured variables and have performed reasonably well when there is a reduced number of mildly correlated quality and/or process variables with a well-conditioned covariance matrix. These approaches have been introduced by emphasizing their positive or negative virtues, generally on an individual basis, so it is not clear for the practitioner the best method to be used. This paper provides a comprehensive study of the performance of diverse methodological approaches when tested on a large number of distinct simulated scenarios. Our primary aim is to highlight key weaknesses and strengths in these methods as well as clarifying their relationships and the requirements for their implementation in practice.Vidal Puig, S.; Ferrer, A. (2014). A Comparative Study of Different Methodologies for Fault Diagnosis in Multivariate Quality Control. Communications in Statistics - Simulation and Computation. 43(5):986-1005. doi:10.1080/03610918.2012.720745S9861005435Arteaga, F., & Ferrer, A. (2010). How to simulate normal data sets with the desired correlation structure. Chemometrics and Intelligent Laboratory Systems, 101(1), 38-42. doi:10.1016/j.chemolab.2009.12.003Doganaksoy, N., Faltin, F. W., & Tucker, W. T. (1991). Identification of out of control quality characteristics in a multivariate manufacturing environment. Communications in Statistics - Theory and Methods, 20(9), 2775-2790. doi:10.1080/03610929108830667Fuchs, C., & Benjamini, Y. (1994). Multivariate Profile Charts for Statistical Process Control. Technometrics, 36(2), 182-195. doi:10.1080/00401706.1994.10485765Hawkins, D. M. (1991). Multivariate Quality Control Based on Regression-Adiusted Variables. Technometrics, 33(1), 61-75. doi:10.1080/00401706.1991.10484770Editorial Board. (2007). Computational Statistics & Data Analysis, 51(8), iii-v. doi:10.1016/s0167-9473(07)00125-9Hayter, A. J., & Tsui, K.-L. (1994). Identification and Quantification in Multivariate Quality Control Problems. Journal of Quality Technology, 26(3), 197-208. doi:10.1080/00224065.1994.11979526HOCHBERG, Y. (1988). A sharper Bonferroni procedure for multiple tests of significance. Biometrika, 75(4), 800-802. doi:10.1093/biomet/75.4.800HOMMEL, G. (1988). A stagewise rejective multiple test procedure based on a modified Bonferroni test. Biometrika, 75(2), 383-386. doi:10.1093/biomet/75.2.383Kourti, T., & MacGregor, J. F. (1996). Multivariate SPC Methods for Process and Product Monitoring. Journal of Quality Technology, 28(4), 409-428. doi:10.1080/00224065.1996.11979699Li, J., Jin, J., & Shi, J. (2008). Causation-BasedT2Decomposition for Multivariate Process Monitoring and Diagnosis. Journal of Quality Technology, 40(1), 46-58. doi:10.1080/00224065.2008.11917712Mason, R. L., Tracy, N. D., & Young, J. C. (1995). Decomposition ofT2 for Multivariate Control Chart Interpretation. Journal of Quality Technology, 27(2), 99-108. doi:10.1080/00224065.1995.11979573Mason, R. L., Tracy, N. D., & Young, J. C. (1997). A Practical Approach for Interpreting Multivariate T2 Control Chart Signals. Journal of Quality Technology, 29(4), 396-406. doi:10.1080/00224065.1997.11979791Murphy, B. J. (1987). Selecting Out of Control Variables With the T 2 Multivariate Quality Control Procedure. The Statistician, 36(5), 571. doi:10.2307/2348668Rencher, A. C. (1993). The Contribution of Individual Variables to Hotelling’s T 2 , Wilks’ Λ, and R 2. Biometrics, 49(2), 479. doi:10.2307/2532560Roy, J. (1958). Step-Down Procedure in Multivariate Analysis. The Annals of Mathematical Statistics, 29(4), 1177-1187. doi:10.1214/aoms/1177706449Runger, G. C., Alt, F. B., & Montgomery, D. C. (1996). Contributors to a multivariate statistical process control chart signal. Communications in Statistics - Theory and Methods, 25(10), 2203-2213. doi:10.1080/03610929608831832Sankoh, A. J., Huque, M. F., & Dubey, S. D. (1997). Some comments on frequently used multiple endpoint adjustment methods in clinical trials. Statistics in Medicine, 16(22), 2529-2542. doi:10.1002/(sici)1097-0258(19971130)16:223.0.co;2-jTukey, J. W., Ciminera, J. L., & Heyse, J. F. (1985). Testing the Statistical Certainty of a Response to Increasing Doses of a Drug. Biometrics, 41(1), 295. doi:10.2307/253066

A Binary Control Chart to Detect Small Jumps

The classic N p chart gives a signal if the number of successes in a sequence of inde- pendent binary variables exceeds a control limit. Motivated by engineering applications in industrial image processing and, to some extent, financial statistics, we study a simple modification of this chart, which uses only the most recent observations. Our aim is to construct a control chart for detecting a shift of an unknown size, allowing for an unknown distribution of the error terms. Simulation studies indicate that the proposed chart is su- perior in terms of out-of-control average run length, when one is interest in the detection of very small shifts. We provide a (functional) central limit theorem under a change-point model with local alternatives which explains that unexpected and interesting behavior. Since real observations are often not independent, the question arises whether these re- sults still hold true for the dependent case. Indeed, our asymptotic results work under the fairly general condition that the observations form a martingale difference array. This enlarges the applicability of our results considerably, firstly, to a large class time series models, and, secondly, to locally dependent image data, as we demonstrate by an example

Multivariate control charts based on Bayesian state space models

This paper develops a new multivariate control charting method for vector autocorrelated and serially correlated processes. The main idea is to propose a Bayesian multivariate local level model, which is a generalization of the Shewhart-Deming model for autocorrelated processes, in order to provide the predictive error distribution of the process and then to apply a univariate modified EWMA control chart to the logarithm of the Bayes' factors of the predictive error density versus the target error density. The resulting chart is proposed as capable to deal with both the non-normality and the autocorrelation structure of the log Bayes' factors. The new control charting scheme is general in application and it has the advantage to control simultaneously not only the process mean vector and the dispersion covariance matrix, but also the entire target distribution of the process. Two examples of London metal exchange data and of production time series data illustrate the capabilities of the new control chart.Comment: 19 pages, 6 figure

Implementing evaluation of the measurement process in an automotive manufacturer: a case study

Reducing process variability is presently an area of much interest in manufacturing organizations. Programmes such as Six Sigma robustly link the financial performance of the organization to the degree of variability present in the processes and products of the organization. Data, and hence measurement processes, play an important part in driving such programmes and in making key manufacturing decisions. In many organizations, however, little thought is given to the quality of the data generated by such measurement processes. By using potentially flawed data in making fundamental manufacturing decisions, the quality of the decision-making process is undermined and, potentially, significant costs are incurred. Research in this area is sparse and has concentrated on the technicalities of the methodologies available to assess measurement process capability. Little work has been done on how to operationalize such activities to give maximum benefit. From the perspective of one automotive company, this paper briefly reviews the approaches presently available to assess the quality of data and develops a practical approach, which is based on an existing technical methodology and incorporates simple continuous improvement tools within a framework which facilitates appropriate improvement actions for each process assessed. A case study demonstrates the framework and shows it to be sound, generalizable and highly supportive of continuous improvement goals

Using Informatics to Improve Autism Screening in a Pediatric Primary Care Practice

Background: According to the most recent report from the CDC (2018), autism spectrum disorder (ASD) affects approximately one in 59 children in the United States (U.S.). In 2007, the American Academy of Pediatrics (AAP) issued a strong recommendation for all primary care providers to screen children for autism, using a validated tool, at the 18 and 24-month well-child visits, in order to begin the referral process for more formal testing, and intervention, promptly. Despite the strong stance of the AAP and evidence supporting the importance of early intervention for children with ASD, not all primary care providers are screening for ASD or developmental delay. Purpose: To improve the percentage of eligible children, presenting for 18 and 24 month wellchild visits in a pediatric primary care office, who are screened for ASD, by integrating the Modified Checklist for Autism in Toddlers (M-CHAT) screening tool into the electronic medical record with tablets. The specific aims were to increase the percentage of children screened and improve the documentation of the screens performed. Methods: This quality improvement project utilized a before-after quantitative design to support the improvement. Reports were obtained for three months prior to the implementation of the tablets and process change, and again for three months following the implementation. Manual chart reviews were also performed to verify the data from the reports. The definition used for complete screening for this project included 1) presence of the completed screen in the medical record, 2) provider documentation of the result, interpretation, and plan if indicated, and 3) CPT code entry for charge capture completed in the electronic medical record. Results: The results of the project revealed improvements in overall percentages of eligible children screened for autism at D-H Nashua Pediatrics. The percentage of complete screening increased from 64.7% to 73.9% following the implementation of the project, a change which is statistically significant (t=31.6105, df=16,p=0.05). Each individual element was also tracked and those results showed that 1) the completeness of provider documentation related to the screening increased from 93.6% to 96% (t=41.3321, df=16, p=0.05) and 2) the M-CHAT screen was present in the electronic health record (EHR) 98.9% of the time, which was an increase from 84.6% (t=295.4084, df=16, p=0.05). The charge capture completion rate remained statistically unchanged at 76.5% (t=0.4664, df=16, p=0.05). Additionally, only one screening was noted to be missed altogether, out of 280 eligible children. Prior to the project, there were four missed screenings (out of 156 eligible children) captured by the chart reviews conducted over three months prior to the implementation of the project. Overall, the results show that the project resulted in an increase the percentage of M-CHAT screening, an increase in the presence of source documentation in the electronic health record (EHR), and more complete provider documentation related to the screening

The development of egg hatching and storage machines equipped with cooling and heating systems and iot

The development of egg hatching and storage machines equipped with cooling and heating systems and IoT was for helping chicken breeders to address the issue of chicken production shortages. To produce large numbers of poultry production, eggs hatching is one of the major step that needs to pay attention to. There are several reasons why egg hatching process fails, such as lack of care by hen, eaten by rooster, and unsuitable hatching environment and temperature. In addition, if the eggs are not incubated within 1 week, the eggs will be damaged having producing a hatching machine and egg storage can help the chicken breeders to produce a better amount of chicken production. Internet of Things (IoT) elements such as the Arduino and Blynk are also used to make this egg hatching and storage machine attractive and to meet the needs and requirements of users. The objectives of this study were to design, develop and evaluate the functionality of egg hatching and storage machines in combination with cooling and heating systems along with IoT. Methodology is a technique and method that incorporates methods and approaches used to achieve the objectives and objectives of the study. The model used is the ADDIE model which consists of 5 phases namely Analysis, Design, Development, Implementation, and Evaluation. This product has received expert confirmation in terms of design and functionality. The results show that the egg hatching and storage machine is well developed and can attract users when using this hatching and storage machine

Sequential control chart methodology

A modification of the V mask sequential control chart is proposed. In this modified scheme, a parabolic section is included in the mask to provide better performance when the process undergoes a large change in the mean from goal conditions. It is shown that the modified V mask can be implemented either in conventional graphic form, or in an algorithmic form suitable for a digital computer. Average run lengths are given for a typical range of circumstances. It also is shown that the conventional Shewhart chart is better than a sequential chart for the specific purpose of promptly detecting very large shifts of the mean from goal conditions