Department of Mathematical Sciences

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On the Comparison of Run Orders of Unreplicated 2 k–p Designs in the Presence of a Time-Trend
(2006) Adekeye, Kayode
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.
Evaluating the Impact of Internet on Research in Nigeria
(Oriental Journal of Computer Science & Technology, 2008) Okewole, Dorcas Modupe
The benefits accrued from the advent of the Internet especially in developing countries can not be overemphasized. At the click of a button on a desktop, Internet users can have access to vast information that covers almost all areas of human endeavors. This has made Internet the greatest achievement of the century. Research in the past for all levels of Nigerian researchers used to be tedious and done under stress. Most times, there used to be inadequate information that is required to produce qualitative and timely output. This could result in substandard research output. Additionally, oftentimes research persons failed to meet up with set deadlines. These days, researchers have experienced tremendous improvement in access to vast amount of data and information required to produce competitive research result. There is the need to evaluate the depth of the impact of Internet on research, hence a kind of research like this. The research was carried out with the use of questionnaires administered to some higher institutions in Nigeria and the views of various levels of researchers were analyzed based on a number of factors. From the study, confirmation was made of the positive impact of Internet on research and recommendations were made based on the factors identified to be hindering the maximal utilization of the Internet for research in the Nigerian situation
Steady State Solution of Optimal Production Control of a Dynamic Four-Product Manufacturing System with Setup Costs and Setup Time
(International Journal of Numerical Methods and Applications, 2009-09-01) Onanaye, Adeniyi Samson
The steady state solution of optimal control of a one-machine four-product manufacturing system with setup changes, operating in a continuous time dynamic environment is considered here. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The aim is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels).
Evaluation of Global and Local Indicator of Spatial Autocorrelations of Kenaf in Experimental Plots in South Western Nigeria
(2010) Adekeye, Kayode
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.
Analyses of Spatial Variations of Kenaf in Experimental Field
(2010) Adekeye, Kayode
Preliminary investigations of experimental field usually involve collection of soil samples at widely spaced locations which are patchily or globally at variant spatially. This study was carried out to evaluate spatial variations in experimental fields using a split plot experiment distributed in a completely randomized design at Ikenne and Ilora between June and September 2006 (test crop was kenaf). The preliminary descriptive statistics suggested the dependency of the stem girth and height on the spatial positions. The variance - covariance analyses matrices of the plots showed that stem girth and plant height were independently distributed and exhibited a non stationarity principle. The results also revealed that spatial autocorrelation exists in patches in the experimental fields while the entire plots showed random distributions because the autocorrelatons were neither dominated by negative nor positive correlation and more than 50% of these values fall within the range of ± 2√n. From this study, a regionalized spatial variation is imminent in 625 m2 experimental plot despite the difference in the treatments. Spatial variations study was found necessary in any plot not more than an acre (250 m2) of land otherwise such variations should be treated as block or environmental effect(s).
Minimax Multivariate Control Chart Using a Polynomial Function
(2011) Adekeye, Kayode
Minimax control chart uses the joint probability distribution of the maximum and minimum standardized sample means to obtain the control limits for monitoring purpose. However, the derivation of the joint probability distribution needed to obtain the minimax control limits is complex. In this paper the multivariate normal distribution is integrated numerically using Simpson’s one third rule to obtain a non-linear polynomial (NLP) function. This NLP function is then substituted and solved numerically using Newton Raphson method to obtain the control limits for the minimax control chart. The approach helps to overcome the problem of obtaining the joint probability distribution needed for estimating the control limits of both the maximum and the minimum statistic for monitoring multivariate process.
A Comparative Study of the Classical and Bayesian Methods of Estimating a Just-Identified Simultaneous Equations Econometric Model
(Asian Social Science, 2011-05) Okewole, Dorcas Modupe
A just identified two-equation econometric model is simulated using both Classical and Bayesian procedures. The estimates of the parameters for both methods were compared under a wide range of scenarios; sample size, residual variance and variance of the data on the predetermined variable. The Monte Carlo experiment was performed using E-veiws and WinBUGS computer softwares. The median, being a robust estimator of average in terms of validity, was used as the posterior estimate. As indicated in similar research in the past where the posterior mode was used as estimate, the Bayesian procedure performed better in most cases, while some scenarios showed similar behavior for the two procedures.
Steady State Solution of Optimal Production Control of a Dynamic Five-Product Manufacturing System with Setup Costs and Setup Time
(International Journal of Numerical Methods and Applications, 2011-10-03) Onanaye, Adeniyi Samson
The steady state solution of optimal control of a one-machine five-product manufacturing system with setup changes, operating in a continuous time dynamic environment is considered here. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The aim is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels).
A Model for Technical and Economic Efficiency of Cement Production in Nigeria in the presence of Multicollinearity
(Brown Walker Press, 2011-10-30) Adesina, Olumide Sunday
The Cobb-Douglas model is widely used in research for forecast and organisational decision-making. In this study Technical and Economic Efficiency of cement production in Nigeria is determined by considering substitutability of factors of production; Labour, Capital and Material. Millions of Dollars has been invested on Research and Development to ensure massive cement production in Nigeria. However, Cobb-Douglas Production function is known to be associated with the problem of Multicollinearity, this is known as linear or near linear relationship among variables. The result is reliable and can be used for decision-making by cement Production Company in Nigeria.
Heat Transfer to Magnetohydrodynamic Non-Newtonian Couple Stress Pulsatile Flow between Two Parallel Porous Plates
(Verlag der Zeitschrift fur Naturforschung, Tubingen, 2012) Adesanya, Samuel
Derivation of the Limits for Control Chart Using the Median Absolute Deviation for Monitoring Non-Normal Process
(2012) Adekeye, Kayode
The Shewhart and S control charts, in the literature, were combined to evaluate the stability of a process. These charts were based on the fundamental assumption of normality of the quality characteristics under investigation. In practice, the normality assumption was often violated by real-life data, therefore, the use of the Shewhart X-bar and S control charts on real-life data might lead to misplacement of control limits. There were many alternatives in the literature to handle the nonnormality of quality characteristics. The Median Absolute Deviation (MAD) claimed in the literature to be the best estimate when the data under consideration is non-normal. Thus in this study, we derived the control limits for the control chart using the median absolute deviation for monitoring process stability when the quality characteristic under investigation was non-normal. Results: The derived control limits were compared with the control limits when the sample standard deviation was used as a measure of controlling the process variability using manufacturing process (real-life) data. Furthermore, a simulation study was carried out to evaluate the performance of the proposed MAD based control charts on both normal and non-normal processes. The obtained results show that the derived control limit is an improvement on the control limit of the Shewhart and that the MAD control charts performed better for the non-normal process than for the normal process.
Design of CUSUM Scheme for Monitoring Road Accident Fatalities
(2012) Adekeye, Kayode
In recent years, road accident fatalities in Nigeria have continued to be on the increase. Thus, urgent attention is needed to reduce or eliminate road accidents fatalities. To achieve this goal, the cumulative sum (Cusum) control chart scheme was designed for monitoring the road accident fatalities using the recorded occurrence of road accident fatalities in a state in the western part of Nigeria. The designed Cusum detects the period of the years when the highest occurrence of road accident fatalities occurred. These periods were observed to be festive periods such as Christmas, Easter, Eid-el-Kabir, and Eid-el-Moluod. Therefore, the festive periods of the year should be used as benchmark by road managers as periods where more attention or precaution measure should be put in place on the roads to drastically reduce or eliminate high occurrence of road accident fatalities. The designed Cusum control chart can be adapted for other states in the country and also for the larger society for detecting the periods when the rate of death as a result of road accidents was prevalent.
Modified Simple Robust Control Chart Based on Median Absolute Deviation
(2012) Adekeye, Kayode
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 Shewhart X 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.
Modified Simple Robust Control Chart Based on Median Absolute Deviation
(2012) Adekeye, Kayode
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 Shewhart ¯X and S control charts 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 the 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 are smaller than that of the existing control charts. Therefore, the modified control limits are 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 specified by the process engineer/ management.
Bootstrap-T Technique for Minimax Multivariate Control Chart
(2012) Adekeye, Kayode
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 multi- variate 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 of all the bootstrap estimators 1iB  where 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.
A Dummy Variable Regression on Students' Academic Performance
(Transnational Journal of Science and Technology, 2012-07) Okewole, Dorcas Modupe
A good formal education system is judged by the performance of the students involved. However, there are several factors also influencing this performance. Studies that have been carried out on this has identified Economic, environmental and social factors. Most of these researches focused on the public schools. This paper is a report on a survey carried out in a Nigerian private University (Redeemer’s University) having the undergraduates as the target Population. A dummy variable regression was carried out on the cumulative grade point average of the respondent. The factors considered were; the study hours, reading habit, mother’s level of education, monthly allowance and involvement in extra-curricular activities. Of all these factors, reading habit and mother’s level of education were significant at the 5% level. Specifically, reading on a daily basis was the significant category of the reading habit factor in the dummy variable regression while educated mother is the significant category in the mother’s education factor.
Steady State Solution of Optimal Production Control of a Dynamic Six-Product Manufacturing System with Setup Costs and Setup Time
(Journal of the Nigerian Association of Mathematical Physics, 2012-11-01) Onanaye, Adeniyi Samson
The steady state solution of optimal control of a one-machine six-product manufacturing system with setup changes, operating in a continuous time dynamic environment is considered here. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The aim is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels).
Bayesian Estimation of an Over-identified Multi-equation Model in the Presence of Multicollinearity
(Journal of the Nigerian Statistical Association, 2013) Okewole, Dorcas Modupe
Multi-equation systems have wide applications in modeling Economic issues. The Bayesian approach received very little attention in the past but is now gaining popularity with extensive application to areas hitherto handled by the classical method. The increasing interest is as a result of availability of numerical intensive software capable of solving intractable or complex numerical integration and other mathematical or computational difficulties. Violations of the assumptions underlying the models often arise in actual observed data. Multicollinearily is one of such violations which several researches have shown classical estimation approaches to he sensitive to. Studies on the performance of the Bayesian approach to such violations are however limited. This paper presents a Monte Carlo study of the Bayesian approach to multi-equation models estimation in the presence of multicollinearity. The mean, bias and MSE were used to compare the performance of the Bayesian approach to that of some classical approaches. A number of research scenarios were specified depicting presence and absence of multicollinearity. MSE from the scenario representing absence of multicollinearity was smaller than that from the scenario representing presence of multicollinearity. Results from the Bayesian approach in run 1 (representing presence of multicollinearity) showed that MSE for fir(one of the correlated exogenous variables) are 0.2825, 0.1128, 0.1079 and 0.0649 for sample sizes 20, 40, 60 and 100 respectively, whereas, they were 0.2503, 0.0642, 0.0406 and 0.0414 in the absence of multicollinearity represented by run 2. MSE for fl„from the classical approach were 0.4230, 0.1583, 0,1498 and 0.0897 for sample sizes 20, 40, 60 and 100 respectively, whereas, they were 0.3639, 0.0837, 0.0517 and 0.0540 in run 2. MSE from the Bayesian approach were smaller than those from the classical approach. The results showed that the Bayesian approach is less sensitive to multicollinearity in estimating the coefficients of exogenous variables of over-identified model.
Thermal Stability Analysis of Reactive Hydromagnetic Third-Grade Fluid through a Channel with Convective Co
(Journal of the Nigerian Mathematical Society, 2013) Adesanya, Samuel
This paper investigates the hydromagnetic flow of a reactive third grade fluid between two parallel plates with convective boundary conditions. Approximate solution of the strongly nonlinear boundary value problem is obtained using modified Adomian decomposition method (mADM). The rapidly convergent series solution is combined with the diagonal Pade approximants to determine the singularity inherent in the solution. Parametric study of the fluid flow are conducted and discussed including bifurcation conditions.
Process Capability Indices Based on Median Absolute Deviation
(2013) Adekeye, Kayode
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.

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