M.Phil / MS

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This collection archives the complete set of theses produced by students of the COMSATS University Islamabad, Lahore Campus.

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    Control Charts for new Reflected Pareto Distribution
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Huma Khalid; FA19-RST-007; Dr. Riffat Jabeen; LHR TP 7203
    Pareto distribution has vast application in different fields of medical and engineering sciences. In this thesis, we have proposed a new Reflected Pareto Distribution (RPD) using Cohen (1973) to reflect the parameter of distribution. We derive different mathematical properties such as mean, variance, rth moment. Reliability measures are also discussed including Survival Function, Hazard function and reversed hazard function. The method of Maximum Likelihood Estimator and Modified maximum likelihood estimator is used to estimate the model parameters. We used three different data sets to show the performance of Reflected Pareto distribution over already existing probability distributions. We also construct the control charts to monitor the shape parameter for reliability processes using Shewhart control chart and Exponentially weighted moving averages control chart. We compare the performance of maximum likelihood estimator and modified maximum likelihood estimator for the shape parameter of Reflected Pareto distribution.
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    An extended Marshall-Olkin simulated Pareto-exponential distribution: development, properties and application
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Fazia Shahid; FA19-RST-002; Dr. Muhammad Mohsin; LHR TP 7204
    Marshal-Olkin simulated Pareto-exponential distribution (MOSPED) is a new distribution developed from simulated Pareto-Exponential distribution (SPED) by using Marshal-Olkin technique. SPED is a special distribution which emerges out as a marginal distribution of Bivariate Affine-Linear Exponential (BALE) distribution by Mohsin et al. (2014) without adopting any procedure. Some mathematical properties of the proposed distribution including moments, mean variance, incomplete moments are discussed along with its characterization. The reliability analysis of MOSPED comprising survival function, hazard function, reversed hazard function along with different types of entropies such as Renyi entropy, β-entropy and γ-entropy are presented. We also develop and discuss the distributions of series as well as parallel systems for the proposed distribution to observe the performance of each component in the product. Moreover, we estimate the unknown parameters of our model, parallel system and series system by using the method of maximum likelihood estimation for each distribution. A simulation study is performed to observe the stability and consistency of the model parameters. The application of the MOSPED is presented by using three real life data sets and its comparison with some baseline distributions is given on the basis of log-likelihood, AIC and BIC.
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    Generalized Ratio Type Exponential Estimators for the Population Mean Using Ranked Set Sampling
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Amjad Ali; SP16-RST-002; LHR TP 4837; Dr. Muhammad Ismail
    The dominance of using ranked set sampling, for estimating the mean of a population, as compare to simple random sampling is well reputable. This technique is useful when visual ordering of a small set of size “m” can be made simply and precisely, since exact measurement of a value is most of the times very hard to obtain. In this dissertation, exponential ratio type estimators are proposed for evaluating the population mean by using ranked set sampling. We found through numerical results that the results of proposed ratio type estimators which is estimated under ranked set sampling is more reliable and competent than the simple random sampling (SRS) and some other already existed estimators under SRS are suggested by Cochran (1977), Parsad 1989, Bahl and Tuteja (1991). The comparison is also made with estimators under ranked set sampling by Samawi and Muttalak (1996), Rabail (2014) and Gajendra , Zeeshan and Carlos (2017).
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    Development of Estimators for Population Mean of Sensitive Variable in Survey Sampling
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2017) Muhammad Kamran ASLAM; SP16-RST-005; LHR TP 4833; Dr. Riffat Jabeen
    In Chapter 1, introduction about Survey sampling, use of auxiliary in formation in context stratified random sampling has been deliberated. Further in Chapter 1, Different methods dealing randomized response have been deliberated by different authors but Hansen-Hurwitz sub sampling has been consider in more detail. In Chapter 2, the literature regarding the use of classical sampling de sign has been deliberated. The literature about some existing estimators for calibration estimator under stratified random sampling has been ex press. Various work of randomized response has also been specified in Chapter 2. Some well-known existing randomized response model, scrambling vari able under auxiliary and study variable, with randomized response or complete response have been reproduced in Chapter3. The major con tribution of this study starts from next Chapter. In Chapter 4, new estimators using auxiliary information have been proposed for calibration estimator in randomized response under strat ified random sampling scheme. The mean square error each estimator has been derived along. In Chapter 5 conclusion has been drawn about the generalized class of estimators proposed in this study. Finally it is shown that the propose estimator II is more efficient than proposed estimator I.
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    On Extended Exponential Weighted Moving Average Control Charts for Monitoring Mean of a Process
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Aqsa Hussain; SP19-RST-001; LHR TP 6535; Dr. Aamir Sanaullah
    In chapter 1, the introduction about statistical process control, control charts and use of auxiliary information in control charts has been explained. Further in chapter 1, objectives of control charts also described. Objectives of the proposed study explained in chapter 1. In chapter 2, literature about some existing EWMA-type control charts has been provided. Various works of EWMA-type control charts using auxiliary information have also been specified in chapter 2. In chapter 3, an extended-EWMA control chart by Naveed et al. (2018) has been discussed. Further a EWMA control chart based on the auxiliary variable due to Abbas et al. (2014) for mean has been deliberated. In chapter 4, we are working on EEWMA control chart by using an auxiliary information for improving the efficiency of an extended-EWMA control chart due to Naveed et al. (2018), and then comparison of the proposed EEWMA with the existing EEWMA and EWMA control charts is presented. In chapter 5, we propose EEWMA sub-group mean control charts for mean with or without using auxiliary information to detect smaller shifts earlier. Comparison with the previous control charts is also done in this chapter. Finally it is shown that the proposed EEWMA control charts are more efficient as compare to the existing control charts of literature
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    Estimation of Population Mean of a Sensitive Variable under Systematic Sampling
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Kamran Khan; FA16-RST-002; LHR TP 5310
    In this research study, we consider the problem of mean estimation of a sensitive variable under systematic sampling. The estimator based on one auxiliary variable is proposed for the sensitive variable under systematic sampling. Further, estimators are studied in the presence of non-response. The mean square error (MSE) expressions are derived and efficiency of proposed estimator is proved by conducting simulations.
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    Hybrid Exponentially Weighted Moving Average Control Chart Using Ranked Set Sampling
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Navara Shabbir; SP17-RST-001; LHR TP 5301; Dr. Muhammad Noor-ul-Amin
    In manufacturing process, the products are subjected to variations which directly impact the quality of a product e.g. in the process of filling juice bottles, the amount of juice filled may not exactly the same. Quality control combined with statistical techniques is called statistical process control (SPC). To achieve the level of perfection in a production procedure SPC play an important role, it generally contains tools for monitoring the dissimilarities caused during a production process. SPC has a direct impact in increasing the quality of a product by reducing the amount of variation and enabling it to attain desired satisfaction level.
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    Estimation of Population Mean by Using Robust Regression
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Salah ud din Asghar; SP16-RST-003; LHR TP 5250; Dr. Muhammad Noor-ul-amin
    In the linear regression problems, ordinary least square (OLS) estimates violate in the presence of outliers as according to the assumptions of the OLS model that there should not be outliers in the data. More specifically, since the classical procedures are not applicable to the case of outliers presence. So, for the purpose of estimation there is another approach which handles this situation of outliers that is robust regression. Robust regression is an important tool for investigating data that are tainted with outliers and provide efficient results. In robust regression, estimates completely reject the effect of outliers and provide good estimates of the population parameter. In this work we focus on the problem of outliers occur in the data which provides a bad estimate of the population mean. In this dissertation, redescending M-estimator and ratio estimator have been proposed to estimate finite population mean using the information from auxiliary variable. Discussions have been made about the robust estimation method based on M-estimation, outliers, ratio estimators and auxiliary variable in Chapter 1. The literature about the robust regression and ratio estimator is discussed in Chapter 2. This research work is based on the two main chapters. The 3rd and 4th Chapters are the most important chapters of the thesis. For the first strategy, in the 3rd Chapter a redescending M-estimator is proposed by reworking on the redescending M-estimator proposed by Insha-ullah et al. (2006) which assign a weight closer to zero to the extreme values and closer to one to the good observations. Most of the redescending M-estimators are solved by iteratively reweighted least square method. For the second strategy we adopt the ratio estimators proposed by Kadilar and Cingi (2004) in the 4th Chapter and replace OLS coefficient with our redescending M-estimator proposed in 3rd Chapter in these ratio estimators. In both parts numerical illustrations and simulation studies were used to analyze the results of the proposed estimators with the comparative estimators to achieve the main results of the research. The intention of this research is to analyze, introduce and improve robust estimation methodologies to solve real life problems such as outliers in data. And finally in 5th chapter conclusion is written based upon whole the results of research.
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    Some New Insights of Exponential Weighted Moving Average Control Chart with Fuzzy Control Lenses
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Muhammad Javed; SP16-RST-001; LHR TP 5249; Dr. Tajammal Hussain
    Statistical process control (SPC) is an approaching path that analyzes processes despite the fact whether they are under statistical control or out of control. So, Control charts are commonly employed for this purpose. Possibly, sample data may possess some uncertainties occurring owing to systems of measurement and conditions of the surrounding environment, for this purpose fuzzy numbers or language variables are usable to seize such form of uncertainties. Thereby, the well-known control charts, exponentially weighted moving average control chart (EWMA) to univariate data are formed up under the environment that is fuzzy one. The fuzzy EWMA control charts (FEWMA) are also usable in order to detect minute changes in the data presented by fuzzy numbers. FEWMA lessens various mistaken and unreliable decisions by catering further flexibleness upon the control limits. As far as the production process is monitored and controlled by dint of FEWMA control chart.
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    Estimation of Mean for a Finite Population Using Sub Sampling of Non-Responden
    (Library Information Services, COMSATS University Islamabad, Lahore Campus, 2018) Iqra Ehsan; SP16-RST-004; LHR TP 4834; Dr. Aamir Sanaullah
    In Chapter 1, introduction about Survey sampling, use of auxiliary information in context of single and two-phase sampling has been deliberated. Further in Chapter 1, the problem of non-response in two has been deliberated. Different methods dealing non-response have been deliberated by different authors but Hansen-Hurwitz sub-sampling has been deliberated in more detail. In Chapter 2, the literature regarding the use of classical sampling design has been deliberated. The literature about some existing estimators for single and two-phase sampling has been deliberated. Various work of non-response has also been specified in Chapter 2. Research methodology of proposed work has been given in chapter # 3. The major contribution of this study starts from Chapter 4 & 5. In chapter 4, we proposed some estimators using single auxiliary variables when population mean of auxiliary variable is available under simple random sampling in the occurrence of non- response. Further the properties of the proposed class of estimators have been deliberated in chapter 4. Also optimum conditions for which proposed class of estimators has minimum MSE’s has been deliberated with their empirical studies. In chapter 5, we proposed some estimators using single auxiliary variable when population mean of auxiliary variable is not available in prior under simple random sampling in the occurrence of non- response. Further the properties of the proposed class of estimators have been deliberated in chapter 5. Also optimal conditions for which proposed class of estimators attain minimum MSE’s has been deliberated with their empirical studies. In Chapter 6 conclusion has been drawn about the generalized class of estimators proposed in this study. Finally it is shown that the proposed estimators are more efficient as compare to the existing estimators of literature
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