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Browsing by Author "Abdel-Salam, Abdel-Salam Gomaa"

Now showing 1 - 7 of 7
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    Access Control Design on Highway Interchanges
    Rakha, Hesham A.; Flintsch, Alejandra Medina; Arafeh, Mazen; Abdel-Salam, Abdel-Salam Gomaa; Dua, Dhruv; Abbas, Montasir M. (Virginia Center for Transportation Innovation and Research, 2008-01-01)
    The adequate spacing and design of access to crossroads in the vicinity of freeway ramps are critical to the safety and traffic operations of both the freeway and the crossroad. The research presented in this report develops a methodology to evaluate the safety impact of different access road spacing standards. The results clearly demonstrate the shortcomings of the AASHTO standards and the benefits of enhancing them. The models developed as part of this research were used to compute the crash rate associated with alternative section spacing. The study demonstrates that the models satisfied the statistical requirements and provide reasonable crash estimates. The results demonstrate an eight-fold decrease in the crash rate when the access road spacing increases from 0 to 300 m. An increase in the minimum spacing from 90 m (300 ft) to 180 m (600 ft) results in a 50 percent reduction in the crash rate. The models were used to develop lookup tables that quantify the impact of access road spacing on the expected number of crashes per unit distance. The tables demonstrate a decrease in the crash rate as the access road spacing increases. An attempt was made to quantify the safety cost of alternative access road spacing using a weighted average crash cost. The weighted average crash cost was computed considering that 0.6, 34.8, and 64.6 percent of the crashes were fatal, injury, and property damage crashes, respectively. These proportions were generated from the field observed data. The cost of each of these crashes was provided by VDOT as $3,760,000, $48,200, and $6,500 for fatal, injury, and property damage crashes, respectively. This provided an average weighted crash cost of $43,533. This average cost was multiplied by the number of crashes per mile to compute the cost associated with different access spacing scenarios. These costs can assist policy makers in quantifying the trade-offs of different access management regulations.
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    Linear Regression Crash Prediction Models : Issues and Proposed Solutions
    Rakha, Hesham A.; Arafeh, Mohamadreza; Abdel-Salam, Abdel-Salam Gomaa; Guo, Feng; Flintsch, Alejandra Medina (Virginia Tech. Virginia Tech Transportation Institute, 2010-05)
    The paper develops a linear regression model approach that can be applied to crash data to predict vehicle crashes. The proposed approach involves novice data aggregation to satisfy linear regression assumptions namely error structure normality and homoscedasticity. The proposed approach is tested and validated using data from 186 access road sections in the state of Virginia. The approach is demonstrated to produce crash predictions consistent with traditional negative binomial and zero inflated negative binomial general linear models. It should be noted however that further testing of the approach on other crash datasets is required to further validate the approach.
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    Model robust profile monitoring for the generalized linear mixed model for Phase I analysis
    Bandara, Keerthi; Abdel-Salam, Abdel-Salam Gomaa; Birch, Jeffrey B. (2020-11-02)
    The generalized linear mixed model (GLMM) becomes very popular in profile monitoring, especially when the production processes follow nonnormal distribution. In most of the real-life applications in industry, medicine, biology horizontal ellipsis and so on researchers assume that the response variable follows a Bernoulli or Binomial distribution. The majority of previous studies in profile monitoring focused on parametric modeling using the logistic regression model, with both fixed or random effects, under the assumption of correct model specification. This research considers those cases where the parametric logistic regression model for the family of profiles is unknown or at least uncertain. Consequently, we propose two mixed model methods to monitor profiles from the exponential family: a nonparametric (NP) regression method based on the penalized spline regression technique and a semiparametric method (model robust profile monitoring for the generalized linear mixed model) which combines the advantages of both the parametric and NP methods. Several Hotelling T2 charts that have been studied for a binary response variable with replicates for Phase I profile monitoring. The performance of the proposed method is evaluated by using mean squares of errors and probability of signals criteria. The results showed satisfactory performance of the proposed control charts.
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    Nonparametric and Semiparametric Linear Mixed Models
    Waterman, Megan J.; Birch, Jeffrey B.; Abdel-Salam, Abdel-Salam Gomaa (Virginia Tech, 2012)
    Mixed models are powerful tools for the analysis of clustered data and many extensions of the classical linear mixed model with normally distributed response have been established. As with all parametric models, correctness of the assumed model is critical for the validity of the ensuing inference. An incorrectly specified parametric means model may be improved by using a local, or nonparametric, model. Two local models are proposed by a pointwise weighting of the marginal and conditional variance-covariance matrices. However, nonparametric models tend to fit to irregularities in the data and may provide fits with high variance. Model robust regression techniques estimate mean response as a convex combination of a parametric and a nonparametric model fit to the data. It is a semiparametric method by which incomplete or incorrectly specified parametric models can be improved by adding an appropriate amount of the nonparametric fit. We compare the approximate integrated mean square error of the parametric, nonparametric, and mixed model robust methods via a simulation study and apply these methods to two real data sets: the monthly wind speed data from counties in Ireland and the engine speed data.
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    Nonparametric and Semiparametric Mixed Model Methods for Phase I Profile Monitoring
    Abdel-Salam, Abdel-Salam Gomaa; Birch, Jeffrey B.; Jensen, Willis A. (Virginia Tech, 2010)
    Profile monitoring is an approach in quality control best used where the process data follow a profile (or curve). The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random-effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or, at least uncertain. Consequently, we consider monitoring profiles via two methods, a nonparametric (NP) method and a semiparametric procedure that combines both parametric and NP profile fits. We refer to our semiparametric procedure as mixed model robust profile monitoring (MMRPM). Also, we incorporate a mixed model approach to both the parametric and NP model fits to account for the autocorrelation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we propose two Hotelling’s T² statistics for use in Phase I analysis to determine unusual profiles, one based on the estimated random effects and one based on the fitted values and obtain the corresponding control limits. Our simulation results show that our methods are robust to the common problem of model misspecification of the user’s proposed parametric model. We also found that both the NP and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency when compared to parametric methods commonly used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications. An example using our techniques is also presented.
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    Outlier Robust Nonlinear Mixed Model Estimation
    Williams, James D.; Birch, Jeffrey B.; Abdel-Salam, Abdel-Salam Gomaa (Virginia Tech, 2014)
    In standard analyses of data well-modeled by a nonlinear mixed model (NLMM), an aberrant observation, either within a cluster, or an entire cluster itself, can greatly distort parameter estimates and subsequent standard errors. Consequently, inferences about the parameters are misleading. This paper proposes an outlier robust method based on linearization to estimate fixed effects parameters and variance components in the NLMM. An example is given using the 4-parameter logistic model and bioassay data, comparing the robust parameter estimates to the nonrobust estimates given by SASR®.
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    Profile Monitoring with Fixed and Random Effects using Nonparametric and Semiparametric Methods
    Abdel-Salam, Abdel-Salam Gomaa (Virginia Tech, 2009-10-14)
    Profile monitoring is a relatively new approach in quality control best used where the process data follow a profile (or curve) at each time period. The essential idea for profile monitoring is to model the profile via some parametric, nonparametric, and semiparametric methods and then monitor the fitted profiles or the estimated random effects over time to determine if there have been changes in the profiles. The majority of previous studies in profile monitoring focused on the parametric modeling of either linear or nonlinear profiles, with both fixed and random effects, under the assumption of correct model specification. Our work considers those cases where the parametric model for the family of profiles is unknown or at least uncertain. Consequently, we consider monitoring profiles via two techniques, a nonparametric technique and a semiparametric procedure that combines both parametric and nonparametric profile fits, a procedure we refer to as model robust profile monitoring (MRPM). Also, we incorporate a mixed model approach to both the parametric and nonparametric model fits. For the mixed effects models, the MMRPM method is an extension of the MRPM method which incorporates a mixed model approach to both parametric and nonparametric model fits to account for the correlation within profiles and to deal with the collection of profiles as a random sample from a common population. For each case, we formulated two Hotelling's T 2 statistics, one based on the estimated random effects and one based on the fitted values, and obtained the corresponding control limits. In addition,we used two different formulas for the estimated variancecovariance matrix: one based on the pooled sample variance-covariance matrix estimator and a second one based on the estimated variance-covariance matrix based on successive differences. A Monte Carlo study was performed to compare the integrated mean square errors (IMSE) and the probability of signal of the parametric, nonparametric, and semiparametric approaches. Both correlated and uncorrelated errors structure scenarios were evaluated for varying amounts of model misspecification, number of profiles, number of observations per profile, shift location, and in- and out-of-control situations. The semiparametric (MMRPM) method for uncorrelated and correlated scenarios was competitive and, often, clearly superior with the parametric and nonparametric over all levels of misspecification. For a correctly specified model, the IMSE and the simulated probability of signal for the parametric and theMMRPM methods were identical (or nearly so). For the severe modelmisspecification case, the nonparametric andMMRPM methods were identical (or nearly so). For the mild model misspecification case, the MMRPM method was superior to the parametric and nonparametric methods. Therefore, this simulation supports the claim that the MMRPM method is robust to model misspecification. In addition, the MMRPM method performed better for data sets with correlated error structure. Also, the performances of the nonparametric and MMRPM methods improved as the number of observations per profile increases since more observations over the same range of X generally enables more knots to be used by the penalized spline method, resulting in greater flexibility and improved fits in the nonparametric curves and consequently, the semiparametric curves. The parametric, nonparametric and semiparametric approaches were utilized for fitting the relationship between torque produced by an engine and engine speed in the automotive industry. Then, we used a Hotelling's T 2 statistic based on the estimated random effects to conduct Phase I studies to determine the outlying profiles. The parametric, nonparametric and seminonparametric methods showed that the process was stable. Despite the fact that all three methods reach the same conclusion regarding the –in-control– status of each profile, the nonparametric and MMRPM results provide a better description of the actual behavior of each profile. Thus, the nonparametric and MMRPM methods give the user greater ability to properly interpret the true relationship between engine speed and torque for this type of engine and an increased likelihood of detecting unusual engines in future production. Finally, we conclude that the nonparametric and semiparametric approaches performed better than the parametric approach when the user's model is misspecified. The case study demonstrates that, the proposed nonparametric and semiparametric methods are shown to be more efficient, flexible and robust to model misspecification for Phase I profile monitoring in a practical application. Thus, our methods are robust to the common problem of model misspecification. We also found that both the nonparametric and the semiparametric methods result in charts with good abilities to detect changes in Phase I data, and in charts with easily calculated control limits. The proposed methods provide greater flexibility and efficiency than current parametric methods used in profile monitoring for Phase I that rely on correct model specification, an unrealistic situation in many practical problems in industrial applications.