Matthew J. Keefe

The Difficulty in Designing Shewhart X-bar and X Control Charts with Estimated Parameters

The performance of the Shewhart X̄ control chart with estimated in-control parameters has been discussed a number of times in the literature. Previous studies showed that at least 400/(n – 1) phase I samples, where n > 1 is the sample size, are required so that the chart performs on average as if the in-control process parameter values were known. This recommendation was based on the in-control expected average run length (ARL) performance. The reliance on the expected ARL metric, however, averages across the practitioner-to-practitioner variability. This variability occurs due to the different historical data sets practitioners use, which results in varying parameter estimates, control limits, and in-control ARL values. In our article, we show that taking this type of variability into consideration leads to far larger amounts of phase I data than what was previously recommended. This is to ensure low levels of variation in the in-control ARL values among practitioners. The standard deviation of the ARL (SDARL) metric is used to evaluate performance for various amounts of phase I data. We show that no realistic phase I sample size is sufficient to have confidence that the attained in-control ARL is close to the desired value. We additionally investigate the effect of different process standard deviation estimators on the X̄-chart performance, showing that it is best to use a biased estimator. We also study the design of the X-chart for the case n = 1, drawing similar conclusions regarding the amount of phase I data. An alternative approach to designing control charts is recommended.

The Conditional In-Control Performance of Self-Starting Control Charts

ABSTRACT The recommended size of the Phase I data set used to estimate the in-control parameters has been discussed many times in the process monitoring literature. Collecting baseline data, however, can be difficult or slow in some applications. Such issues have resulted in the development of self-starting control charts that allow charting early, near the start of data collection. In our article, we use the average of the in-control average run length (AARL) and the standard deviation of the in-control average run length (SDARL) to assess the in-control run length performance of self-starting charts conditioned on the preliminary data used. This approach accounts for practitioner-to-practitioner variability in the in-control average run length (ARL) of self-starting charts, which has not been considered previously. We found that there was a significant amount of variation in the in-control ARL values obtained by practitioners due to the sampling variation of the initial estimators of the in-control parameters. The amount of variation was surprisingly low, however, compared to that resulting from the use of standard Phase I sampling and estimation.

Adoption of Energy Star certifications: theory and evidence compared

ABSTRACT Energy Star, the largest voluntary housing eco-labelling programme in the US, conveys important signals to housing market actors about the energy efficiency of homes. With energy demand from housing being a significant energy consumer and contributor to climate change, gaining insight into the diffusion patterns of these certifications is an important analytical step. Informed by theories of new product adoption, research is used to identify the factors associated with the diffusion patterns of Energy Star certifications into US single-family housing from 2002 to 2013. The findings are generally congruent with recent studies of energy-efficiency adoption patterns in commercial property (real estate) and residential building construction. The key significant predictors of variation in the proportion of Energy Star-certified homes across US core-based statistical areas (CBSAs) are found to be public policy, climate, market attributes, industry characteristics and energy prices.

Modeling Patterns of Total Dissolved Solids Release from Central Appalachia, USA, Mine Spoils

Surface mining in the central Appalachian coalfields (USA) influences water quality because the interaction of infiltrated waters and O with freshly exposed mine spoils releases elevated levels of total dissolved solids (TDS) to streams. Modeling and predicting the short- and long-term TDS release potentials of mine spoils can aid in the management of current and future mining-influenced watersheds and landscapes. In this study, the specific conductance (SC, a proxy variable for TDS) patterns of 39 mine spoils during a sequence of 40 leaching events were modeled using a five-parameter nonlinear regression. Estimated parameter values were compared to six rapid spoil assessment techniques (RSATs) to assess predictive relationships between model parameters and RSATs. Spoil leachates reached maximum values, 1108 ± 161 μS cm on average, within the first three leaching events, then declined exponentially to a breakpoint at the 16th leaching event on average. After the breakpoint, SC release remained linear, with most spoil samples exhibiting declines in SC release with successive leaching events. The SC asymptote averaged 276 ± 25 μS cm. Only three samples had SCs >500 μS cm at the end of the 40 leaching events. Model parameters varied with mine spoil rock and weathering type, and RSATs were predictive of four model parameters. Unweathered samples released higher SCs throughout the leaching period relative to weathered samples, and rock type influenced the rate of SC release. The RSATs for SC, total S, and neutralization potential may best predict certain phases of mine spoil TDS release.

Monitoring foreclosure rates with a spatially risk-adjusted Bernoulli CUSUM chart for concurrent observations

ABSTRACT Frequently in process monitoring, situations arise in which the order that events occur cannot be distinguished, motivating the need to accommodate multiple observations occurring at the same time, or concurrent observations. The risk-adjusted Bernoulli cumulative sum (CUSUM) control chart can be used to monitor the rate of an adverse event by fitting a risk-adjustment model, followed by a likelihood ratio-based scoring method that produces a statistic that can be monitored. In our paper, we develop a risk-adjusted Bernoulli CUSUM control chart for concurrent observations. Furthermore, we adopt a novel approach that uses a combined mixture model and kernel density estimation approach in order to perform risk-adjustment with regard to spatial location. Our proposed method allows for monitoring binary outcomes through time with multiple observations at each time point, where the chart is spatially adjusted for each Bernoulli observations estimated probability of the adverse event. A simulation study is presented to assess the performance of the proposed monitoring scheme. We apply our method using data from Wayne County, Michigan between 2005 and 2014 to monitor the rate of foreclosure as a percentage of all housing transactions.

Improved implementation of the risk-adjusted Bernoulli CUSUM chart to monitor surgical outcome quality

Methodology issue The traditional implementation of the risk-adjusted Bernoulli cumulative sum (CUSUM) chart for monitoring surgical outcome quality requires waiting a pre-specified period of time after surgery before incorporating patient outcome information. Proposed solution We propose a simple but powerful implementation of the risk-adjusted Bernoulli CUSUM chart that incorporates outcome information as soon as it is available, rather than waiting a pre-specified period of time after surgery. Evaluation A simulation study is presented that compares the performance of the traditional implementation of the risk-adjusted Bernoulli CUSUM chart to our improved implementation. We show that incorporating patient outcome information as soon as it is available leads to quicker detection of process deterioration. Advice to practitioners Deterioration of surgical performance could be detected much sooner using our proposed implementation, which could lead to the earlier identification of problems.