A Quantile Dependency Model for Predicting Optimal Centrifugal Pump Operating Strategies

Used in many industrial applications, centrifugal pumps have optimal operating criteria specified at design. These criteria may not be precisely adhered to during operation which will ultimately reduce the life of the asset. Operators would therefore benefit from anticipating how often the design point is deviated from and hence how much asset degradation results. For centrifugal pumps, a novel set of covariates were proposed in this paper which formally partition observed operating zones with an Empirical Bivariate Quantile Partitioned distribution. This captured the dependency relation between operating parameters across plant configurations to predict the component wear that results from particular settings. The effectiveness of this was demonstrated through an operational case study in civil nuclear generation feedwater pumps where corroboration with bearing movements provides an indicator of plant wear. Such a technique is envisaged to inform operators of optimal plant configuration from multiple possibilities in advance of undertaking them.

Efficient estimation of the risk of a disease by quantile-categories of a key predictor variable using generalized additive models

Suppose that one wishes to make inference to the risk of a disease by the population quartile-categories of a key continuous predictor variable. When one collects data on a prospective cohort, the standard method is simply to categorize the key predictor variable by the empirical quartiles. One may then include indicator variables for these empirical quartile-categories as predictors, along with other covariates, in a generalized linear model (GLM), with the observed health status of each subject as the response. The standard GLM method, however, is relatively inefficient, because it treats all observations that fall in the same quartile-category of the predictor variable identically, regardless of whether they lie in the centre or near the boundaries of that category. Alternatively, one may include the key predictor variable, along with other covariates, in a generalized additive model (GAM), again with the observed health status of each subject as the response. The alternative GAM method non-parametrically estimates the functional relationship between the key predictor variable and the response. One may then compute statistics of interest, such as proportions and odds ratios, from the fitted GAM equation using the empirical quartile-categories. Simulations show that both the GLM and GAM methods are nearly unbiased, but the latter method produces smaller variances and narrower bootstrap confidence intervals. An example from nutritional epidemiology illustrates the use of these methods.

Using lowess to remove systematic trends over time in predictor variables prior to logistic regression with quantile categories

In case-control studies one may employ logistic regression to model the relationship between binary responses and continuous predictor variables that have been categorized by the empirical quartiles of the controls. Sometimes, however, systematic trends over time (or drifts) contaminate the laboratory measurements of predictor variables. In this paper we consider the use of locally weighted robust regression (lowess) to estimate and remove these systematic trends when the trends for the cases and controls have a common shape. One can then use the lowess adjusted data in the desired logistic regression model. We illustrate these methods with a case-control study that was designed to assess the risk of oesophageal cancer as a function of the quartile categories of sphinganine levels in the blood serum. Upon examination of the data, it was discovered that the sphinganine laboratory measurements were contaminated by a systematic trend, the magnitude of which depended only on the day of analysis. This trend needed to be removed before performing further analyses of the data. In addition, we present simulations to examine the use of lowess methods to estimate and remove various shapes of trends from contaminated predictor data before constructing logistic regression models with quartile categories. We found that using the trend-contaminated data tends to give attenuated parameter estimates and hence lower significance and power levels than using the uncontaminated data. Conversely, using appropriate lowess methods to adjust the data tends to give nearly unbiased parameter estimates, near nominal significance levels, and improved power.