Detecting and estimating the time of a step-change in multivariate Poisson processes

Knowing when a process has changed would simplify the search for and identification of the special cause. Consequently, having an estimate of the process change point following a control chart signal would be useful to process engineers. Much of the literature on change point models and techniques for statistical process control applications consider processes well modelled by the normal distribution. However, the Poisson distribution is commonly used in industrial quality control applications for modelling attribute-based process quality characteristics (e.g., counts of non-conformities). Some commonly used control charts for monitoring Poisson distributed data are the Poisson cumulative sum (CUSUM) and exponentially weighted moving average (EWMA) control charts. In this paper, we study the effect of changes in the design of the control chart on the performances of the change point estimators offered by these procedures. In particular, we compare root mean square error performances of the change point estimators offered by the Poisson CUSUM and EWMA control charts relative to that achieved by a maximum likelihood estimator for the process change point. Results indicate that the relative performance achieved by each change point estimator is a function of the corresponding control chart design. Relative mean index plots are provided to enable users of these control charts to choose a control chart design and change point estimator combination that will yield robust change point estimation performance across a range of potential change magnitudes.

Since the product quality of many industrial processes depends upon more than one dependent variable or attribute, they are either multivariate or multi-attribute in nature. Although multivariate statistical process control is receiving increased attention in the literature, little work has been done to deal with multi-attribute processes. In this article, we develop a new methodology to monitor multi-attribute processes. To do this, first we transform multi-attribute data in a way that their marginal probability distributions have almost zero skewness. Then, we estimate the transformed covariance matrix and apply the well-known T 2 control chart. In order to illustrate the proposed method and evaluate its performance, we use two simulation experiments and compare the results with the ones from both MNP chart and the χ2 control chart.

Precise identification of the time when a clinical process has changed, a control chart's signal, enables clinicians to search for a potential special cause more effectively. In this article, we develop a change point estimation method for Bernoulli processes in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point model and Markov Chain Monte Carlo to obtain posterior distributions of the change point parameters. The performance of the Bayesian estimator is investigated through applications on clinical data. We monitor outcomes of cardiac surgery and angioplasty procedures using Bernoulli exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts. We then identify the time of changes in prior signals obtained from charts. Study of the known potential causes of changes in the outcomes reveals that estimated change points and shifts in the known causes are coincident.

T 2 control charts are used to primarily monitor the mean vector of quality characteristics of a process. Recent studies have shown that using variable sample size (VSS) schemes results in charts with more statistical power for detecting small to moderate shifts in the process mean vector. In this study, we have presented a multiple-objective economic statistical design of VSS T2 control chart with the adjusted average time to signal (AATS) as the statistical objective and the expected cost per hour as the economic objective. Then, a multi-objective genetic algorithm for economic statistical design is proposed for identifying the Pareto optimal solutions of control chart design. Through an illustrative example, the advantages of the proposed approach are shown by providing a list of viable optimal solutions and graphical representations, which indicate the advantage of flexibility and adaptability of our approach.

6579 Background: Collecting electronic patient reported outcomes (ePROs) reduces the burden of cancer and prevents acute care hospitalizations. However, broad implementation in the routine care setting remains challenging, partly because the optimal implementation strategies – actions that are most likely to encourage adoption and use – are not known. Since 2019, the SIMPRO Consortium has deployed an ePRO-based symptom management program (eSyM) across 6 community-based cancer centers. Methods: We used statistical process control (SPC) charts to identify variation due to special versus common causes (random variation) for one key performance indicator (KPI) – the weekly ePROs response rate. All 6 SIMPRO sites contributed data for this analysis: 3 for chemotherapy patients and 3 for surgery patients. Sites had to have at least 18 months of KPI data; information from the first 4 months after eSyM rollout were excluded to account for program ramp-up. The KPI was calculated as the number of patients who submitted an ePRO questionnaire divided by the number eligible to submit a questionnaire each week. The upper and lower confidence limits were set at +/- 2 sigma to allow for 95% of observations to fall within the limits. Three rules were applied to identify special cause variation: 1) astronomical points (outside sigma limits), 2) shifts (8 or more points above or below a center line), and 3) trends (6 or more points consecutively ascending or descending). Implementation strategies that mapped to special cause variations were selected as those most likely to impact the KPI. Results: Across the 6 sites that deployed eSyM, the mean KPI performance ranged from 19.7%-35.7%. SPC charts detected multiple special cause variations in the KPI at all 6 sites, though the patterns varied by site. All sites demonstrated positive and negative astronomical variations as well as positive and negative shifts. Three sites demonstrated negative trends; no sites demonstrated positive trends. Direct patient outreach was the implementation strategy most frequently associated with special cause variation, followed by changes in promoting the ePRO program to clinical staff. Positive changes were associated with strategy initiation; negative changes were associated with strategy discontinuation. Conclusions: Applying SPC charts to a KPI from the eSyM deployment highlighted the effect of personal communication with patients and providers, suggesting that these implementation strategies could offer value to other sites deploying eSyM. The absence of positive trends early in eSyM program deployment underscores the need to identify better implementation strategies and allocate more resources to foster program adoption and sustainability. Applying SPCs to other KPIs, such as symptom severity and healthcare utilization, could improve eSyM deployment and impact.

Traditional multivariate control charts such as Hotelling’s χ2 and T2 control charts are designed to monitor vectors of variable quality characteristics. However, in certain situations, data are expressed in linguistic terms and, under these circumstances, variable or attribute multivariate control charts are not suitable choices for monitoring purposes. Fuzzy multivariate control charts such as fuzzy Hotelling’s T2 could be considered as efficient tools to overcome the problems of linguistic observations. The purpose of this paper is to develop a fuzzy multivariate exponentially weighted moving average (F-MEWMA) control chart. In this paper, multivariate statistical quality control and fuzzy set theory are combined to develop the proposed method. Fuzzy sets and fuzzy logic are powerful mathematical tools for modeling uncertain systems in industry, nature, and humanity. Through a numerical example, the performance of the proposed control chart was compared to the fuzzy Hotelling’s T2 control chart. Results indicate uniformly superior performance of the F-MEWMA control chart over Hotelling’s T2 control chart.

The magnificent seven statistical process control (SPC) tools are commonly used to monitor the variation in the process. Control charts are the most efficient and real‐time monitoring tool from the SPC toolkit. A control chart visually differentiates the effect of special or inherent cause variations and indicates the process as out‐of‐control when such a special cause exists. For single occasion problems, simple random sampling (SRS) is used as a sampling design. When the quality of a product is assessed at regular intervals, then modified successive sampling (MSS) is chosen as the preferred sampling mechanism. Hence, this paper intends to propose EWMA‐MSS(S) and CUSUM‐MSS(S) charts under MSS schemes to monitor moderate to small shifts in the location parameter of a process. We presented the performance evaluation of EWMA‐MSS(S) and CUSUM‐MSS(S) charts in terms of run length metrics and compared them with the Shewhart‐MSS(S) control chart. The outcomes show that the EWMA‐MSS(S) perform amazingly well as compared to the Shewhart‐MSS(S) and CUSUM‐MSS(S) control charts. Further, illustration of the proposed charts on the QSAR aquatic toxicity dataset is also used to demonstrate the application of the proposed charts.

A hybrid fuzzy-statistical clustering approach for estimating the time of changes in fixed and variable sampling control charts

Control charts are intended to aid quality practitioners in monitoring whether a change has occurred in a process. When a control chart indicates an out-of-control signal, it means that the process has changed. However, control chart signals do not indicate the real time of process changes; so estimators are applied to indicate the time when a change in the process takes place, which is referred to as the change point. This paper provides a maximum likelihood estimator to identify the real time of a step change in phase II monitoring of binary profiles, in which the quality of a process is characterized by a logistic regression between the response and predictor variables. Simulation studies are provided to evaluate the effectiveness of the change point estimator.

Co-organized by the Intermountain, Long Island, Silicon Valley and Upper Midwest Chapters and the Students & Young Professionals Committee Technical Presentations: 1. Professor Ron Lasky, PhD, PE, Dartmouth College and Senior Technologist, Indium Corporation Title: Statistical Process Control 101 Abstract:. The presentation will cover statistical process control (SPC). SPC is an important tool in controlling SMT assembly processes, especially stencil printing. It will start with a discussion of the 6 Ms of variation and then delineate common cause and special cause variation. The difference between precision and accuracy will then be clarified. After discussing the precision tolerance ratio, the technique to perform a Gage R&R (Repeatability and Reproducibility) analysis will be presented. Process control charts, and their development will then be discussed including the Shewhart Rules. Several sets of SPC Xbar-R and C Chart data will then be plotted and analyzed with commercial statistical software. The webinar will conclude with a discussion and application of the process capability indices Cp and Cpx. SPC 101 Topics Covered Include: The 6 Ms of variation Special Cause and Common Variation Measuring as a Process Precision and Accuracy Precision/Tolerance Ratio Gage R&R (Repeatability & Reproducibility) Analysis Control Charts- Shewhart Rules Xbar R Charts Stencil Printing Example C Charts Pareto Charts Cp and Cpk with Examples Commercial statistical software will be used throughout 2. Chrys Shea, President, Shea Engineering Services Title: The Use of SPC in Relation to Stencil Printing Abstract: The presentation will review the typical variables monitored under SPC on typical SMT assembly lines, with special focus on the solder paste printing process. The print process is arguably the most important to monitor because it is the most easily affected by both Special and Common causes of variation. The presentation will review a fishbone diagram of print process factors as well as a discussion of troubleshooting print problems and specific defect modes. Biographies: Ron Lasky Ron Lasky is currently an Instructional Professor at Dartmouth College, a Senior Technologist at Indium Corporation and a Consultant with ITM. Prior to this, he had over thirty years experience in electronic and optoelectronic packaging and assembly at IBM, Universal Instruments and Cookson Electronics. He has authored or edited 7 books on science, electronics, and optoelectronics and numerous technical papers and authored articles for Scientific American. He holds a number of patent disclosures and is the developer of several new concepts in SMT processing software relating to cost estimating, line balancing and process optimization. He is the co-creator of engineering certification exams in electronic assembly and the Director of Dartmouth"™s Lean Six Sigma Program. He was awarded the SMTA Founder's Award in 2003 and Member of Technical Distinction Award in 2021. He has four degrees, including a Ph.D. from Cornell University in Materials Science. Ron is a New York State licensed professional engineer and a Lean Six Sigma Master Black Belt. Chrys Shea is the President of Shea Engineering Services, a consulting firm that produces technical studies and communications tools for the electronics manufacturing industry. Chrys is an SMTA "Member of Technical Distinction," an SMTA "Distinguished Speaker" and four-time winner of the SMTAI "Rich Freiberger Best of Conference" award for her research on solder paste printing. She earned a Bachelor's Degree in Mechanical Engineering and a Master's Degree in Manufacturing Engineering. Chrys' background is in SMT process engineering. She is a member of the SMTA International Technical Committee and the IPC 7526A Stencil Cleaning Handbook Committee. She held various production engineering, new product introduction, research and management positions before launching her own business in 2008. Chrys Shea Files Available to Download: Recorded Presentation (On-Demand) Presentation Slides Part 1 (PDF) Presentation Slides Part 2 (PDF) Additional Resources (PDF)

This study considers the construction of control charts when outliers could occur in the data. Simply increasing the width of control limits will make it more difficult to detect an out-of-control signal. This study aims to determine weights for each observation by measuring their respective distances to the average. The study proposes a retrospective weighted average and weighted inter-quartile range (WIQR) control chart based on the normal distribution that accounts for the false alarm rate, special causes, outliers, and a combination of special causes and outliers that might exist within the process. In addition to validating the detection effectiveness of the proposed control charts, this study also compares various average-type and range-type control charts for detecting the outliers and special causes. The proposed control charts show superior detection effectiveness in four tested scenarios compared to other types of control charts. Finally, the study also illustrates the practical application of the control charts for measuring the tensile strength of a deformed bar in coil. [Received 10 February 2014; Revised 21 August 2015; Revised 3 November 2015; Accepted 14 December 2015]

Quality control charts have proven to be very effective in detecting out of control signals. It is very important to practitioners to determine at what point in the past the signal was initiated. If a control chart signals a change in the process parameter, identifying the time of the change will substantially help the signal diagnostics procedure since it simplifies the search for special causes. In this paper the researchers propose the observations following multivariate normal distribution. They have used multivariate exponentially weighted moving average (MEWMA) control chart to detect signals. This research provides two ways to detect the change point, first MLE, and then neural network is used to identify the time of the change in the parameters (mean) in the past. The researchers intended to assess the performance of two approaches and compare them through computer simulation experiments. The results show that neural network performs effectively and equally well for the whole process dimensions. Thus, the neural network provides process engineers with an accurate and useful estimate of the actual time of the change in the process mean.

When control charts are used to monitor processes to detect special causes, it is usually assumed that a special cause will produce a sustained shift in a process parameter that lasts until the shift is detected and the cause is removed. However, some special causes may produce a transient shift in a process parameter that lasts only for a short period of time. Control charts are usually based on samples of n ≥ 1 observations using a sampling interval of fixed length, say d. When n > 1, the usual practice, based on the so-called rational subgroups concept, is to take a concentrated sample at one time point at the end of the sampling interval d, but another option is to disperse the sample over the interval d. In this paper, we investigate the question of whether it is better to use n = 1, or to use n > 1 and either concentrated or dispersed samples. The objective of monitoring is assumed to be the detection of special causes that may produce either a sustained or transient shift in the process mean %mU and/or process standard deviation σ. It is assumed that the sampling rate in terms of the number of observations per unit time is fixed, so that the ratio n/d is fixed. The best sampling strategy depends on the type of control chart being used, so Shewhart and cumulative sum (CUSUM) charts are considered. For both types of control charts, a combination of two charts is investigated; one chart is designed to monitor μ, and the other is designed to monitor σ. The overall conclusion is that it is best to take samples of n = 1 and use a CUSUM chart combination. The Shewhart chart combination with the best overall performance is based on n > 1, but this combination has inferior statistical performance compared with the CUSUM chart combination.

The process personnel always seek the opportunity to improve the processes. One of the essential steps for the process improvement is to recognize the starting time or the change point of a process disturbance quickly. Different from the traditional normally distributed assumption for a process, this study considers a process that follows a gamma distribution. The proposed approach combines the commonly used control chart with the Bayesian estimation technique to estimate the change point. Two Bayes estimators corresponding to an informative and a noninformative prior along with maximum likelihood estimation (MLE) are considered. Their efficiency is compared through a series of simulations. The results show that the Bayes estimator with the informative prior is more accurate and more precise when the means of the process before and after the change point time are not too closed. Additionally, the efficiency of the Bayes estimator with the informative prior increases as either the sample size increases or the change point goes away from the origin.

Autoregressive coefficients based Hotelling’s T2 control chart for structural health monitoring