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Kayode Adekeye

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Abubakar Muhammad

Haruna Sani B/k

Dr. Saifullahi Sani Ibrahim

Federal University, Dutsin-Ma,

Coventry University (coventry.ac.uk)

VICTOR CHUKWUNWEIKE EHIEDU PhD

DELTA STATE UNIVERSITY, ABRAKA, DELTA STATE, NIGERIA

European Scientific Journal ESJ

European Scientific Institute, ESI

Abubakar Muhammad

Nenubari J O H N Ikue

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Papers by Kayode Adekeye

On Pooled OLS and Panel Regression Models for Assessing the Contributions of Electronic Payment System on Commercial Banks Profitability

Journal of statistics : advances in theory and applications, Jul 10, 2021

This study examined the impact of electronic payment system on the profitability of commercial ba... more This study examined the impact of electronic payment system on the profitability of commercial banks in Nigeria. Pooled OLS and Panel regression models were fitted on the data extracted from the banks' annual reports, Nigerian interbank settlement scheme, and central bank of Nigeria website. The assessment of the contribution of the various electronic payment systems considered were measured using Breusch and Pagan Lagrangian Multiplier (LM) Test, the Hausman Test, Stationarity Test, The Schwarz Criterion, and the Akaike Information Criterion. Results obtained showed that the random effect model was more appropriate than the fixed effect model for all the electronic payment systems considered in this study. Furthermore, it was discovered that there exists a positive relationship between the electronic payment systems and profitability of the commercial banks in Nigeria.

A Review of Change Point Estimation Methods for Process Monitoring

Applied and computational mathematics, 2021

When one or more observations fall outside the control limits, the chart signals the existence of... more When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.

Modified Simple Robust Control Chart Based on Median Absolute Deviation

International Journal of Statistics and Probability, Jul 30, 2012

The control limits derived for the Median Absolute Deviation (MAD) based Standard deviation (S) c... more The control limits derived for the Median Absolute Deviation (MAD) based Standard deviation (S) control chart proposed by Abu-Shawiesh was for monitoring quality characteristics when a standard value of sigma (σ) is known or given by the management/ engineers. When sigma (σ) is unknown and we are interested in monitoring past/nonnormal data, then there is the need to modify the simple robust control limits. In this paper, the control limits for the ShewhartX and S control chart based on median absolute deviation were modified using the concept of three sigma (3σ) limits. An evaluation performance tool was also developed to evaluate the efficiency of the modified control chart. An algorithm implemented on S-Plus programming language was developed to compute the two evaluation parameters used in this study. The results show that the control limits interval and the average run length for the modified control charts is smaller than that of the existing control charts. Therefore, the modified control limits is more efficient than the existing control limits. It is recommended that the modified control limits be used when monitoring past/non-normal data or when there is no standard value of sigma specify by the process engineer/ management.

Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium

Journal of Mathematics, 2016

An investigation has been carried out to study entropy generation in a viscous, incompressible, a... more An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.

On the Comparison of Run Orders of Unreplicated 2 k–p Designs in the Presence of a Time Trend

Metrika, Feb 16, 2006

The response from a factorial experiment carried out in a time sequence may be affected by uncont... more The response from a factorial experiment carried out in a time sequence may be affected by uncontrollable variables that are highly correlated with the time in which they occur. In such a situation, one possibility is to randomize the run order of the experiment. Another possibility is to use a systematic run order that is robust against time-trends. Since randomized run orders make the time trend part of the error, it can be hoped that systematic run orders will be more effective to identify truly active factors. In this paper, a simulation study is used to compare the performances of the randomized and the systematic run orders. The response from an experiment where we have observed a strong time-trend is used to demonstrate the influence of a realistic time trend on the run orders under consideration. The performance of the run orders is then measured by taking the probabilities of false rejection and the probabilities of detection of active contrasts. Our results show that the randomized run order managed to keep the nominal level, while the systematic did not. Additionally, when there were active factors, then the systematic run orders did not achieve more power than did the randomized run order.

Comparison of Capability Analysis of Cumulative Cardiac Thoracic Ratio (CTR) Outputs

Global Journal of Research In Engineering, Jun 30, 2014

This study investigated the Capability Process Analysis of cumulative Cardiac Thoracic Ratio (CTR... more This study investigated the Capability Process Analysis of cumulative Cardiac Thoracic Ratio (CTR) during Radiological Chest Examination using MX.4 Radiological Diagnostic Machine (DRM) at the Fate Medical Foundation Radiological Department, Auchi. The data for the study are classified as raw and simulated CTR values. Statistical process control was investigated to address process stability and capability analysis was performed for the two processes. The pattern of the means of the raw and simulated values was investigated using normal probability plots and empirical CDF functions. The raw computed CTR values and simulated CTR values confirmed that the system is operating under 1.0-1.3 sigma level for the raw CTR values. Around 28-39% of the raw CTR values obtained fall outside the specification limits. In addition, for all the cumulative raw CTR values suggested that the process is off centered and is towards the lower specification limit. Further study should be conducted on large repeated experimental CTR sample to ascertain the reliability of this study. Fellow up study of patients should be undertaken by the cardiologist to reduce the possible health risk associated with high CTR.

Evaluation of Global and Local Indicator of Spatial Autocorrelations of Kenaf in Experimental Plots in South Western Nigeria

Journal of Agricultural Research, 2010

A study was conducted to assess spatial variations in experimental plots through the global and l... more A study was conducted to assess spatial variations in experimental plots through the global and local indicator of spatial autocorrelation of kenaf. Field data obtained from experiment conducted at both Ilora and Ikenne outstations of the Institute of Agricultural Research and Training, Ibadan, Nigeria in 2006 were used to investigate spatial variability in experimental plots. The descriptive statistics showed that sample mean (μ) from different tessellated plots of the experimental sites were biased estimators which might have been probably caused by spatial variations in the experimental sites. Also, the global Moran I and Moran I scatter plots showed that these can be used as a measure of variation between the plots. Generally, the selected spatial autocorrelation indicators were found to be consistent with some other spatial statistical analytical tools.

Process Capability Indices Based on Median Absolute Deviation

Process capability is the performance of a process under normal and in-control conditions. Its in... more Process capability is the performance of a process under normal and in-control conditions. Its indices are to measure the inherent variability of a process and thus to reflect its performance. To calculate the capability indices for key characteristics, most industries normally assume that the distribution of their process output is normal. However, in practice, most key quality characteristics do fails the normality test and thus the accuracy of normal based process capability indices becomes doubtful and hence they cannot really reflect the performance of a process. This paper proposes the determination of the common process capability indices based on the median absolute deviation. The median absolute deviation is a robust estimate of variability when the sample data are non-normal or are skewed. Real process data and simulated process data from heavily skewed distributions are presented to demonstrate the application of the proposed indices and the results were compared with the existing indices for non-normal and skewed process data.

Thermal analysis for a gravity-driven liquid film along an inclined porous substrate

Journal of The Taiwan Institute of Chemical Engineers, May 1, 2021

Abstract This paper investigates the entropy generation in a thin film fluid flow along a heated ... more Abstract This paper investigates the entropy generation in a thin film fluid flow along a heated inclined substrate. The free end of the thin film is assumed to be exposed to adiabatic condition. The mathematical formulation for the fluid and heat flow leads to a dimensionless Boundary Value Problem (BVP) together with a partial differential equation (PDE). The exact solution of the BVP problem was obtained and the analytical solution for the PDE was obtained with the use of separation of variables. These solutions were used to profile the entropy generation in the thin film flow. The result earlier obtained in the absence of porous permeability was validated as a special case of the work and our contributions to knowledge were highlighted in the porous substrate case.

Bootstrap-T Technique for Minimax Multivariate Control Chart

Open Journal of Statistics, 2012

Bootstrap methods are considered in the application of statistical process control because they c... more Bootstrap methods are considered in the application of statistical process control because they can deal with unknown distributions and are easy to calculate using a personal computer. In this study we propose the use of bootstrap-t multivariate control technique on the minimax control chart. The technique takes care of correlated variables as well as the requirement of the distributional assumptions needed for the operation of the minimax control chart. The bootstrap-t technique provides the mean ˆB  of all the bootstrap estimators 1 i BB i B      where ˆi  is the estimate using the bootstrap sample and B is the number of bootstraps. The computation of the proposed bootstrap-t minimax statistic was performed on the values obtained from the bootstrap estimation. This method was used to determine the position of the four control limits of the minimax control chart. The bootstrap-t approach introduced to minimax multivariate control chart helps to detect shifts in the mean vector of a multivariate process and it overcomes the computational complexity of obtaining the distribution of multivariate data.

Median and Interquartile Range Control Charts Based on Quantiles of Marshall-Olkin Inverse Log-logistic Distribution

International Journal of Industrial and Systems Engineering, 2022

Conjugation of Generalized Gamma Prior with Poisson and Generalized Poisson Likelihoods for Disease Mapping

This article focused on the use of generalized Gamma distribution as conjugate prior with Poisson... more This article focused on the use of generalized Gamma distribution as conjugate prior with Poisson and generalized Poisson likelihoods to handle dispersion in small samples. Based on this conjugacy, Poisson-Generalized Gamma model (PGG) and Generalized Poisson-Generalized Gamma model (GPGG) are developed for Bayesian disease mapping and compared with the existing Poisson-Gamma model. The efficiency of these models was investigated using both simulated and real data applications. The deviance information criterion (DIC), dispersion test (DT), Monte Carlo error (MCE) and relative efficiency (reff) were used for comparison. All indicated that GPGG model provided the best precision and model efficiency to handle dispersion and relative risk estimation for disease mapping in small and large samples under uncontaminated and contaminated data. Thus, GPGG and PGG models served as alternative models in providing reliable mapping of diseas

Integration of Bayesian Model and Adaptive Clustered Sampling Into Contact Tracing to Curb the Spread of Covid -19 Cases

Fudma Journal of Sciences, Jun 25, 2021

On Estimation of Sparse Factor Loadings Using Distribution-free Approach

Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing s... more Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing simpler pattern of factor loadings by constraining insignicant loadings to be zero. However, existing SFA approaches require the assumption of normality of data since sparse factor loadings are obtained through a likelihood function with additional constraint or penalty function. This work proposes a method for obtaining sparse factor loadings without requiring any distributional assumption. In this method, the orthogonal sparse eigenvectors were computed based on Procrustes reformulation, and thereafter, an iterative procedure was provided to nd sparse factor loadings corresponding to the orthogonal sparse eigenvectors. In the end, the proposed method was compared with penalized likelihood factor analysis via nonconvex penalties using simulated data. Results show that sparse factor loadings from both methods provide simpler structure of factor loadings than the structure obtained from standard Exploratory Factor Analysis. In addition, the new method out-performs the penalized likelihood factor analysis via nonconvex penalties as it provides smaller values of MSE even when the two methods have the same level of sparsity.

Robust Scale Estimator-Based Control Charts for Marshall-Olkin InverseLog-Logistic Distribution

The combination of Shewhart X and S-control charts developed to control the process variability b... more The combination of Shewhart X and S-control charts developed to control the process variability based on the assumption that the underlying distribution of the quality characteristic is normal. The normality assumption is often violated when the underlying distribution of the characteristic under consideration is skewed; therefore, the use of the Shewhart X and S control charts on real-life data might lead to inaccurate estimation of control limits. The robust methods of estimation of control chart statistics can be used in such situations. In this paper, the robust scale estimator was used to estimate the mean, variance and median based on Marshall-Olkin Inverse log-logistic distribution. Monte Carlo simulation study was conducted using Marshall-Olkin Inverse log-logistic distribution to determine the performance of the proposed method in comparison with the Shewhart S and MAD methods. The proposed control limits showed an improvement over the Shewhart and stocktickerMAD control charts for non-normal process.

X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

African journal of pure and applied science, Nov 24, 2020

that the data are normally distributed and spread randomly about the mean. Process data are not a... more that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

Modeling the Response Rate of Apache Web Server Using Extreme Value Theory

On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

Journal of Probability and Statistics, Feb 25, 2020

In this paper, two methods of control chart were proposed to monitor the process based on the two... more In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. e proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. e coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X charts.

Performance of median absolute deviation and some alternatives to median absolute deviation control charts for skewed and heavily tailed process

Quality and Reliability Engineering International, May 25, 2021

In this paper, charts based on robust scale estimators (known as and estimators) are proposed, an... more In this paper, charts based on robust scale estimators (known as and estimators) are proposed, and the performance of control charts based on median absolute deviation (MAD) is compared with those based on some alternatives to MAD, which do not need any location estimate, for normal, skewed, and heavily tailed distributions. MAD is often used as a substitute for standard deviation in constructing control charts due to its robustness. Three alternatives to MAD namely the Sn, Qn, and Downton (D) are considered in this paper as location‐free estimators. A simulation study was carried out to appraise the performance of the control charts based on the MAD, , , and D estimators. The average run length (ARL), median run length (MRL), standard deviation run length (SDRL), and control limits interval (CLI) were used to assess the performance of the four control charts. The results showed that MAD, , and D are suitable estimators for standard deviation for mean charts while and are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.

Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Quality and Reliability Engineering International, Oct 27, 2015

Control charts are important tools in statistical process control used to monitor shift in proces... more Control charts are important tools in statistical process control used to monitor shift in process mean and variance. This paper proposes a control chart for monitoring the process mean using the Downton estimator and provides table of constant factors for computing the control limits for sample size (n ≤ 10). The derived control limits for process mean were compared with control limits based on range statistic. The performance of the proposed control charts was evaluated using the average run length for normal and non-normal process situations. The obtained results showed that the X D control chart, using the Downton statistic, performed better than Shewhart X chart using range statistic for detection of small shift in the process mean when the process is non-normal and compares favourably well with Shewhart X chart that is normally distributed.

On Pooled OLS and Panel Regression Models for Assessing the Contributions of Electronic Payment System on Commercial Banks Profitability

Journal of statistics : advances in theory and applications, Jul 10, 2021

This study examined the impact of electronic payment system on the profitability of commercial ba... more This study examined the impact of electronic payment system on the profitability of commercial banks in Nigeria. Pooled OLS and Panel regression models were fitted on the data extracted from the banks' annual reports, Nigerian interbank settlement scheme, and central bank of Nigeria website. The assessment of the contribution of the various electronic payment systems considered were measured using Breusch and Pagan Lagrangian Multiplier (LM) Test, the Hausman Test, Stationarity Test, The Schwarz Criterion, and the Akaike Information Criterion. Results obtained showed that the random effect model was more appropriate than the fixed effect model for all the electronic payment systems considered in this study. Furthermore, it was discovered that there exists a positive relationship between the electronic payment systems and profitability of the commercial banks in Nigeria.

A Review of Change Point Estimation Methods for Process Monitoring

Applied and computational mathematics, 2021

When one or more observations fall outside the control limits, the chart signals the existence of... more When one or more observations fall outside the control limits, the chart signals the existence of a change in the process. Change point detection is helpful in modelling and prediction of time series and is found in broader areas of applications including process monitoring. Three approaches were proposed for estimating change point in process for the different types of changes in the literature. they are: Maximum Likelihood Estimator (MLE), the Cumulative Sum (CUSUM), and the Exponentially Weighted Moving Average (EWMA) approaches. This paper gives a synopsis of change point estimation, specifies, categorizes, and evaluates many of the methods that have been recommended for detecting change points in process monitoring. The change points articles in the literature were categorized broadly under five categories, namely: types of process, types of data, types of change, types of phase and methods of estimation. Aside the five broad categories, we also included the parameter involved. Furthermore, the use of control charts and other monitoring tools used to detect abrupt changes in processes were reviewed and the gaps for process monitoring/controlling were examined. A combination of different methods of estimation will be a valuable approach to finding the best estimates of change point models. Further research studies would include assessing the sensitivity of the various change point estimators to deviations in the underlying distributional assumptions.

Modified Simple Robust Control Chart Based on Median Absolute Deviation

International Journal of Statistics and Probability, Jul 30, 2012

The control limits derived for the Median Absolute Deviation (MAD) based Standard deviation (S) c... more The control limits derived for the Median Absolute Deviation (MAD) based Standard deviation (S) control chart proposed by Abu-Shawiesh was for monitoring quality characteristics when a standard value of sigma (σ) is known or given by the management/ engineers. When sigma (σ) is unknown and we are interested in monitoring past/nonnormal data, then there is the need to modify the simple robust control limits. In this paper, the control limits for the ShewhartX and S control chart based on median absolute deviation were modified using the concept of three sigma (3σ) limits. An evaluation performance tool was also developed to evaluate the efficiency of the modified control chart. An algorithm implemented on S-Plus programming language was developed to compute the two evaluation parameters used in this study. The results show that the control limits interval and the average run length for the modified control charts is smaller than that of the existing control charts. Therefore, the modified control limits is more efficient than the existing control limits. It is recommended that the modified control limits be used when monitoring past/non-normal data or when there is no standard value of sigma specify by the process engineer/ management.

Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium

Journal of Mathematics, 2016

An investigation has been carried out to study entropy generation in a viscous, incompressible, a... more An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.

On the Comparison of Run Orders of Unreplicated 2 k–p Designs in the Presence of a Time Trend

Metrika, Feb 16, 2006

The response from a factorial experiment carried out in a time sequence may be affected by uncont... more The response from a factorial experiment carried out in a time sequence may be affected by uncontrollable variables that are highly correlated with the time in which they occur. In such a situation, one possibility is to randomize the run order of the experiment. Another possibility is to use a systematic run order that is robust against time-trends. Since randomized run orders make the time trend part of the error, it can be hoped that systematic run orders will be more effective to identify truly active factors. In this paper, a simulation study is used to compare the performances of the randomized and the systematic run orders. The response from an experiment where we have observed a strong time-trend is used to demonstrate the influence of a realistic time trend on the run orders under consideration. The performance of the run orders is then measured by taking the probabilities of false rejection and the probabilities of detection of active contrasts. Our results show that the randomized run order managed to keep the nominal level, while the systematic did not. Additionally, when there were active factors, then the systematic run orders did not achieve more power than did the randomized run order.

Comparison of Capability Analysis of Cumulative Cardiac Thoracic Ratio (CTR) Outputs

Global Journal of Research In Engineering, Jun 30, 2014

This study investigated the Capability Process Analysis of cumulative Cardiac Thoracic Ratio (CTR... more This study investigated the Capability Process Analysis of cumulative Cardiac Thoracic Ratio (CTR) during Radiological Chest Examination using MX.4 Radiological Diagnostic Machine (DRM) at the Fate Medical Foundation Radiological Department, Auchi. The data for the study are classified as raw and simulated CTR values. Statistical process control was investigated to address process stability and capability analysis was performed for the two processes. The pattern of the means of the raw and simulated values was investigated using normal probability plots and empirical CDF functions. The raw computed CTR values and simulated CTR values confirmed that the system is operating under 1.0-1.3 sigma level for the raw CTR values. Around 28-39% of the raw CTR values obtained fall outside the specification limits. In addition, for all the cumulative raw CTR values suggested that the process is off centered and is towards the lower specification limit. Further study should be conducted on large repeated experimental CTR sample to ascertain the reliability of this study. Fellow up study of patients should be undertaken by the cardiologist to reduce the possible health risk associated with high CTR.

Evaluation of Global and Local Indicator of Spatial Autocorrelations of Kenaf in Experimental Plots in South Western Nigeria

Journal of Agricultural Research, 2010

A study was conducted to assess spatial variations in experimental plots through the global and l... more A study was conducted to assess spatial variations in experimental plots through the global and local indicator of spatial autocorrelation of kenaf. Field data obtained from experiment conducted at both Ilora and Ikenne outstations of the Institute of Agricultural Research and Training, Ibadan, Nigeria in 2006 were used to investigate spatial variability in experimental plots. The descriptive statistics showed that sample mean (μ) from different tessellated plots of the experimental sites were biased estimators which might have been probably caused by spatial variations in the experimental sites. Also, the global Moran I and Moran I scatter plots showed that these can be used as a measure of variation between the plots. Generally, the selected spatial autocorrelation indicators were found to be consistent with some other spatial statistical analytical tools.

Process Capability Indices Based on Median Absolute Deviation

Process capability is the performance of a process under normal and in-control conditions. Its in... more Process capability is the performance of a process under normal and in-control conditions. Its indices are to measure the inherent variability of a process and thus to reflect its performance. To calculate the capability indices for key characteristics, most industries normally assume that the distribution of their process output is normal. However, in practice, most key quality characteristics do fails the normality test and thus the accuracy of normal based process capability indices becomes doubtful and hence they cannot really reflect the performance of a process. This paper proposes the determination of the common process capability indices based on the median absolute deviation. The median absolute deviation is a robust estimate of variability when the sample data are non-normal or are skewed. Real process data and simulated process data from heavily skewed distributions are presented to demonstrate the application of the proposed indices and the results were compared with the existing indices for non-normal and skewed process data.

Thermal analysis for a gravity-driven liquid film along an inclined porous substrate

Journal of The Taiwan Institute of Chemical Engineers, May 1, 2021

Abstract This paper investigates the entropy generation in a thin film fluid flow along a heated ... more Abstract This paper investigates the entropy generation in a thin film fluid flow along a heated inclined substrate. The free end of the thin film is assumed to be exposed to adiabatic condition. The mathematical formulation for the fluid and heat flow leads to a dimensionless Boundary Value Problem (BVP) together with a partial differential equation (PDE). The exact solution of the BVP problem was obtained and the analytical solution for the PDE was obtained with the use of separation of variables. These solutions were used to profile the entropy generation in the thin film flow. The result earlier obtained in the absence of porous permeability was validated as a special case of the work and our contributions to knowledge were highlighted in the porous substrate case.

Bootstrap-T Technique for Minimax Multivariate Control Chart

Open Journal of Statistics, 2012

Bootstrap methods are considered in the application of statistical process control because they c... more Bootstrap methods are considered in the application of statistical process control because they can deal with unknown distributions and are easy to calculate using a personal computer. In this study we propose the use of bootstrap-t multivariate control technique on the minimax control chart. The technique takes care of correlated variables as well as the requirement of the distributional assumptions needed for the operation of the minimax control chart. The bootstrap-t technique provides the mean ˆB  of all the bootstrap estimators 1 i BB i B      where ˆi  is the estimate using the bootstrap sample and B is the number of bootstraps. The computation of the proposed bootstrap-t minimax statistic was performed on the values obtained from the bootstrap estimation. This method was used to determine the position of the four control limits of the minimax control chart. The bootstrap-t approach introduced to minimax multivariate control chart helps to detect shifts in the mean vector of a multivariate process and it overcomes the computational complexity of obtaining the distribution of multivariate data.

Median and Interquartile Range Control Charts Based on Quantiles of Marshall-Olkin Inverse Log-logistic Distribution

International Journal of Industrial and Systems Engineering, 2022

Conjugation of Generalized Gamma Prior with Poisson and Generalized Poisson Likelihoods for Disease Mapping

This article focused on the use of generalized Gamma distribution as conjugate prior with Poisson... more This article focused on the use of generalized Gamma distribution as conjugate prior with Poisson and generalized Poisson likelihoods to handle dispersion in small samples. Based on this conjugacy, Poisson-Generalized Gamma model (PGG) and Generalized Poisson-Generalized Gamma model (GPGG) are developed for Bayesian disease mapping and compared with the existing Poisson-Gamma model. The efficiency of these models was investigated using both simulated and real data applications. The deviance information criterion (DIC), dispersion test (DT), Monte Carlo error (MCE) and relative efficiency (reff) were used for comparison. All indicated that GPGG model provided the best precision and model efficiency to handle dispersion and relative risk estimation for disease mapping in small and large samples under uncontaminated and contaminated data. Thus, GPGG and PGG models served as alternative models in providing reliable mapping of diseas

Integration of Bayesian Model and Adaptive Clustered Sampling Into Contact Tracing to Curb the Spread of Covid -19 Cases

Fudma Journal of Sciences, Jun 25, 2021

On Estimation of Sparse Factor Loadings Using Distribution-free Approach

Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing s... more Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing simpler pattern of factor loadings by constraining insignicant loadings to be zero. However, existing SFA approaches require the assumption of normality of data since sparse factor loadings are obtained through a likelihood function with additional constraint or penalty function. This work proposes a method for obtaining sparse factor loadings without requiring any distributional assumption. In this method, the orthogonal sparse eigenvectors were computed based on Procrustes reformulation, and thereafter, an iterative procedure was provided to nd sparse factor loadings corresponding to the orthogonal sparse eigenvectors. In the end, the proposed method was compared with penalized likelihood factor analysis via nonconvex penalties using simulated data. Results show that sparse factor loadings from both methods provide simpler structure of factor loadings than the structure obtained from standard Exploratory Factor Analysis. In addition, the new method out-performs the penalized likelihood factor analysis via nonconvex penalties as it provides smaller values of MSE even when the two methods have the same level of sparsity.

Robust Scale Estimator-Based Control Charts for Marshall-Olkin InverseLog-Logistic Distribution

The combination of Shewhart X and S-control charts developed to control the process variability b... more The combination of Shewhart X and S-control charts developed to control the process variability based on the assumption that the underlying distribution of the quality characteristic is normal. The normality assumption is often violated when the underlying distribution of the characteristic under consideration is skewed; therefore, the use of the Shewhart X and S control charts on real-life data might lead to inaccurate estimation of control limits. The robust methods of estimation of control chart statistics can be used in such situations. In this paper, the robust scale estimator was used to estimate the mean, variance and median based on Marshall-Olkin Inverse log-logistic distribution. Monte Carlo simulation study was conducted using Marshall-Olkin Inverse log-logistic distribution to determine the performance of the proposed method in comparison with the Shewhart S and MAD methods. The proposed control limits showed an improvement over the Shewhart and stocktickerMAD control charts for non-normal process.

X̅ and R control charts based on marshall-olkin inverse log-logistic distribution for positive skewed data

African journal of pure and applied science, Nov 24, 2020

that the data are normally distributed and spread randomly about the mean. Process data are not a... more that the data are normally distributed and spread randomly about the mean. Process data are not always normally distributed, hence there is need to set up appropriate control charts that gives accurate control limits to monitor processes that are skewed. In this study Shewhart-type control charts for monitoring positively skewed data that are assumed to be from Marshall-Olkin Inverse Loglogistic Distribution (MOILLD) was developed. Average Run Length (ARL) and Control Limits Interval (CLI) were adopted to assess the stability and performance of compared with Classical Shewhart (CS) and Skewness Correction (SC) control charts using the ARL and CLI. It was discovered that the control charts based on MOILLD performed better and are more stable compare to CS and SC control charts. It is therefore recommended that for positively skewed data, a Marshall-Olkin Inverse Loglogistic Distribution based control chart will be more appropriate.

Modeling the Response Rate of Apache Web Server Using Extreme Value Theory

On Performance of Two-Parameter Gompertz-Based X¯ Control Charts

Journal of Probability and Statistics, Feb 25, 2020

In this paper, two methods of control chart were proposed to monitor the process based on the two... more In this paper, two methods of control chart were proposed to monitor the process based on the two-parameter Gompertz distribution. e proposed methods are the Gompertz Shewhart approach and Gompertz skewness correction method. A simulation study was conducted to compare the performance of the proposed chart with that of the skewness correction approach for various sample sizes. Furthermore, real-life data on thickness of paint on refrigerators which are nonnormal data that have attributes of a Gompertz distribution were used to illustrate the proposed control chart. e coverage probability (CP), control limit interval (CLI), and average run length (ARL) were used to measure the performance of the two methods. It was found that the Gompertz exact method where the control limits are calculated through the percentiles of the underline distribution has the highest coverage probability, while the Gompertz Shewhart approach and Gompertz skewness correction method have the least CLI and ARL. Hence, the two-parameter Gompertz-based methods would detect out-of-control faster for Gompertz-based X charts.

Performance of median absolute deviation and some alternatives to median absolute deviation control charts for skewed and heavily tailed process

Quality and Reliability Engineering International, May 25, 2021

In this paper, charts based on robust scale estimators (known as and estimators) are proposed, an... more In this paper, charts based on robust scale estimators (known as and estimators) are proposed, and the performance of control charts based on median absolute deviation (MAD) is compared with those based on some alternatives to MAD, which do not need any location estimate, for normal, skewed, and heavily tailed distributions. MAD is often used as a substitute for standard deviation in constructing control charts due to its robustness. Three alternatives to MAD namely the Sn, Qn, and Downton (D) are considered in this paper as location‐free estimators. A simulation study was carried out to appraise the performance of the control charts based on the MAD, , , and D estimators. The average run length (ARL), median run length (MRL), standard deviation run length (SDRL), and control limits interval (CLI) were used to assess the performance of the four control charts. The results showed that MAD, , and D are suitable estimators for standard deviation for mean charts while and are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.

Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Quality and Reliability Engineering International, Oct 27, 2015

Control charts are important tools in statistical process control used to monitor shift in proces... more Control charts are important tools in statistical process control used to monitor shift in process mean and variance. This paper proposes a control chart for monitoring the process mean using the Downton estimator and provides table of constant factors for computing the control limits for sample size (n ≤ 10). The derived control limits for process mean were compared with control limits based on range statistic. The performance of the proposed control charts was evaluated using the average run length for normal and non-normal process situations. The obtained results showed that the X D control chart, using the Downton statistic, performed better than Shewhart X chart using range statistic for detection of small shift in the process mean when the process is non-normal and compares favourably well with Shewhart X chart that is normally distributed.