Angular Control Charts: A New Perspective for Monitoring Reliability of Multi-State Systems

Control charts, as had been used traditionally for quality monitoring, were applied alternatively to monitor systems' reliability. In other words, they can be applied to detect changes in the failure behavior of systems. Such purpose imposed modifying traditional control charts in addition to developing charts that are more compatible with reliability monitoring. The latter developed category is known as probability limits control charts. The existing reliability monitoring control charts were only dedicated to binary-state systems, and they can't be used to monitor several states simultaneously. Therefore, this paper develops a design of control charts that accommodates multi-state systems, called here as the Angular Control Chart, which represents a new version of the probability limits control charts. This design is able to monitor state transitions simultaneously and individually in addition. Illustrative system examples are implemented to explore the monitoring procedure of the new design and to demonstrate its efficiency, effectiveness, and limitations.Comment: 18 pages; 13 figure

Risk-adjusted CUSUM control charts for shared frailty survival models with application to hip replacement outcomes: a study using the NJR dataset

Background:  Continuous monitoring of surgical outcomes after joint replacement is needed to detect which brands’ components have a higher than expected failure rate and are therefore no longer recommended to be used in surgical practice. We developed a monitoring method based on cumulative sum (CUSUM) chart specifically for this application.  Methods:  Our method entails the use of the competing risks model with the Weibull and the Gompertz hazard functions adjusted for observed covariates to approximate the baseline time-to-revision and time-to-death distributions, respectively. The correlated shared frailty terms for competing risks, corresponding to the operating unit, are also included in the model. A bootstrap-based boundary adjustment is then required for risk-adjusted CUSUM charts to guarantee a given probability of the false alarm rates. We propose a method to evaluate the CUSUM scores and the adjusted boundary for a survival model with the shared frailty terms. We also introduce a unit performance quality score based on the posterior frailty distribution. This method is illustrated using the 2003-2012 hip replacement data from the UK National Joint Registry (NJR). Results:  We found that the best model included the shared frailty for revision but not for death. This means that the competing risks of revision and death are independent in NJR data. Our method was superior to the standard NJR methodology. For one of the two monitored components, it produced alarms four years before the increased failure rate came to the attention of the UK regulatory authorities. The hazard ratios of revision across the units varied from 0.38 to 2.28. Conclusions:  An earlier detection of failure signal by our method in comparison to the standard method used by the NJR may be explained by proper risk-adjustment and the ability to accommodate time-dependent hazards. The continuous monitoring of hip replacement outcomes should include risk adjustment at both the individual and unit level

Relative Survival Methods – Theory, Applications and Extensions to Monitoring

In cancer research, one is often interested in the part of the hazard which corresponds to the disease. If the cause of death is unknown as in cancer registry data, the standard methods in survival analysis do not distinguish between the mortality due to disease and other causes. This issue becomes the main motivation for the development of relative survival methods. First, the main concepts in relative survival are presented. Both non-parametric estimators and models of the excess hazard are studied and discussed. Simulation studies show that even if the Pohar-Perme method is an unbiased estimator of the so-called net survival, the traditional Ederer 2 estimator might still be preferable in certain situations due to its lower variance. When informative censoring is present, the degree of bias looks to be the same on average for both estimators. When it comes to modelling of the excess hazard, we cover two different types of models. The first group corresponds to parametric models where the baseline excess hazard is a piecewise constant function. For real-life data, this is usually not the case and a more flexible and semi-parametric model based on the EM-algorithm is therefore considered. By simulation, the piecewise constant models still perform decent if the gradient of the baseline excess hazard is not large and there are enough data such that a finer splitting of the follow-up interval can be used in the estimation procedure. In some situations, one might also want to monitor the excess hazard over time in order to detect a change. An approach based on methods from relative survival and statistical process control is proposed for this intention. Different simulation setups are used in order to illustrate the purpose of the method. Finally, most of the methods presented are applied to colon and rectum cancer data from the Norwegian Cancer Registry. Interesting results are obtained from the analysis. For instance, the effect of tumour location seems to vary between age groups. Similar arguments are observed related to cancer stage as well. The CUSUM charts show a clear improvement in the excess hazard over time, which agree with the results from non-parametric methods when stratified by diagnosis year period

A study of properties and applications of control charts for high yield processes

Ph.DDOCTOR OF PHILOSOPH

A study of modelling and monitoring time-between-events with control charts

Ph.DDOCTOR OF PHILOSOPH

A study of advanced control charts for complex time-between-events data

Ph.DDOCTOR OF PHILOSOPH

ISBIS 2016: Meeting on Statistics in Business and Industry

This Book includes the abstracts of the talks presented at the 2016 International Symposium on Business and Industrial Statistics, held at Barcelona, June 8-10, 2016, hosted at the Universitat Politècnica de Catalunya - Barcelona TECH, by the Department of Statistics and Operations Research. The location of the meeting was at ETSEIB Building (Escola Tecnica Superior d'Enginyeria Industrial) at Avda Diagonal 647. The meeting organizers celebrated the continued success of ISBIS and ENBIS society, and the meeting draw together the international community of statisticians, both academics and industry professionals, who share the goal of making statistics the foundation for decision making in business and related applications. The Scientific Program Committee was constituted by: David Banks, Duke University Amílcar Oliveira, DCeT - Universidade Aberta and CEAUL Teresa A. Oliveira, DCeT - Universidade Aberta and CEAUL Nalini Ravishankar, University of Connecticut Xavier Tort Martorell, Universitat Politécnica de Catalunya, Barcelona TECH Martina Vandebroek, KU Leuven Vincenzo Esposito Vinzi, ESSEC Business Schoo

Modeling and designing control chart for monitoring time-between events data

Ph.DDOCTOR OF PHILOSOPH

Change Point Estimation in Monitoring Survival Time

Precise identification of the time when a change in a hospital outcome has occurred enables clinical experts to search for a potential special cause more effectively. In this paper, we develop change point estimation methods for survival time of a clinical procedure in the presence of patient mix in a Bayesian framework. We apply Bayesian hierarchical models to formulate the change point where there exists a step change in the mean survival time of patients who underwent cardiac surgery. The data are right censored since the monitoring is conducted over a limited follow-up period. We capture the effect of risk factors prior to the surgery using a Weibull accelerated failure time regression model. Markov Chain Monte Carlo is used to obtain posterior distributions of the change point parameters including location and magnitude of changes and also corresponding probabilistic intervals and inferences. The performance of the Bayesian estimator is investigated through simulations and the result shows that precise estimates can be obtained when they are used in conjunction with the risk-adjusted survival time CUSUM control charts for different magnitude scenarios. The proposed estimator shows a better performance where a longer follow-up period, censoring time, is applied. In comparison with the alternative built-in CUSUM estimator, more accurate and precise estimates are obtained by the Bayesian estimator. These superiorities are enhanced when probability quantification, flexibility and generalizability of the Bayesian change point detection model are also considered

A semi-empirical Bayesian chart to monitor Weibull percentiles

This paper develops a Bayesian control chart for the percentiles of the Weibull distribution, when both its in-control and out-of-control parameters are unknown. The Bayesian approach enhances parameter estimates for small sample sizes that occur when monitoring rare events as in high-reliability applications or genetic mutations. The chart monitors the parameters of the Weibull distribution directly, instead of transforming the data as most Weibull-based charts do in order to comply with their normality assumption. The chart uses the whole accumulated knowledge resulting from the likelihood of the current sample combined with the information given by both the initial prior knowledge and all the past samples. The chart is adapting since its control limits change (e.g. narrow) during the Phase I. An example is presented and good Average Run Length properties are demonstrated. In addition, the paper gives insights into the nature of monitoring Weibull processes by highlighting the relationship between distribution and process parameters.Comment: 21 pages, 3 figures, 5 table