Department of Mathematical Sciences

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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).
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.
Combined Control Scheme for Monitoring Quality Characteristics
(2014) Adekeye, Kayode
ABSTRACT: In the literature, the Exponentially Weighted Moving Average (EWMA) and Exponentially Weighted Moving Variance (EMWV) control schemes have been used separately to monitor the process average and process variability respectively. Here the two are combined and applied on simulated process with different level of variation. The control limit interval (CLI) and the average run length (ARL) were evaluated for the combined chart. The combined chart performed better than the two independently. Furthermore, an algorithm was developed for the two control charts and implemented on visual basic VB6.0. The obtained results show that the combined EWMA and EWMV control chart is very sensitive in detecting shifts in production process and every shift in the process mean is always preceded by the shift in the process variability.
Comparison of Capability Analysis of Cumulative Cardiac Thoracic Ratio (CTR) Outputs
(2014) Adekeye, Kayode
Abstract- 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.
Comparison of Capability Analysis of Cumulative Cardiac Thoracic Ratio (CTR) Outputs
(Global Journals Inc. (USA), 2014) Adekeye, Kayode
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 â€“ 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 a 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
Conjugation of Generalized Gamma Prior With Poisson and Generalized Poisson Likelihoods for Disease Mapping
(2021) Adekeye, Kayode
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 disease.
Control Chart Limits for Monitoring Process Mean Based on Downton’s Estimator
(John Wiley & Sons, Ltd., 2015) Adekeye, Kayode
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 XD 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.
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.
Evaluating Process Capability Indices for some Quality Characteristics of a Manufacturing Process
(2013) Adekeye, Kayode
The effectiveness of a manufacturing product produced depends on whether the specified standards by the management / production engineers are met or not. It is possible that a process will be stable but will not meet the specification set by the production engineer or management. In order to determine whether a process meets the specification of the process engineer or management, process capability indices (PCIs) are often used. This study is aimed at evaluating the capability and the percentage of nonconforming unit of a manufacturing process. Data on two quality characteristics were extracted from the records of Evans Medical PLC, Agbara, Nigeria. The process capability indices were used to determine the capability of the process and the percent non-conforming was used to check the amount of the process that does not meet the required standard. The obtained results reflect the amount of the products produced during the period of study that do not conform to specification and the gain of testing for the normality assumption as reflected in the parts per million defects for the process data. The confidence interval derived for the process indices can be used to improve the capability of the process.
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.
A Generalized Regression Estimation of the Item Sum Technique in Sensitive Surveys
(2019) Adekeye, Kayode
Survey researchers often nd it di cult to collect reliable data of human populations, yet the validity of any research depends mainly on the accuracy of self-reported behavior especially when the respondents are to re ect about sensitive issues or highly personal matter. It is therefore important to develop methods of improving interviewees responses in any survey. The Item Sum Technique (IST) is the most recent indirect questioning method and it is a variant of the Item Count Technique (ICT) which can be used only for qualitative responses. The aim of this study is to estimate the sensitive characteristic when using the IST especially if two or more sensitive questions are investigated. It also focuses on the theoretical framework which includes the introduction of a classical method called the Generalized Regression model (GREG) using the IST. The e ciency of the GREG method was ascertained in comparison to the Calibration estimator by an extensive simulation study. Results from the statistical analysis indicates that the GREG estimator competes well with the calibration method and can further be used for a small sample size or data that is not normally distributed.
Mathematical analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium
(2016) Adekeye, Kayode
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.
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.
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.
On Estimation of Sparse Factor Loadings using Distribution-free Approach
(2020) Adekeye, Kayode
Sparse Factor Analysis (SFA) is often used for the analysis of high dimensional data, providing simpler pattern of factor loadings by constraining insigni cant 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.
On Performance of Two-Parameter Gompertz-Based X-bar Control Charts
(Hindawi, 2020) Adekeye, Kayode
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 charts.
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.
Performance of Median Absolute Deviation and some Alternatives to Median Absolute Deviation Control Charts for Skewed and Heavily Tailed Process
(John Wiley & Sons, Ltd., 2020) Adekeye, Kayode
In this paper, ̄X charts based on robust scale estimators (known as 𝑆𝑛 and 𝑄𝑛 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, 𝑆𝑛, 𝑄𝑛, 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, 𝑆𝑛, and D are suitable estimators for standard deviation for mean charts while 𝑆𝑛 and 𝑄𝑛 are suitable estimators for standard deviation for dispersion charts for skewed and heavily tailed distributions.

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