PhD

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Mixed Extended Exponentially Weighted Moving Average–Cumulative Sum Charts for Process Mean Monitoring
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2021) Memoona; FA19-RST-006; Dr. Aamir Sanaullah; LHR TP 7202
Statistical quality control (SPC) is common main technique used for examining the process’s output during production. One of its tools which is extensively used worldwide is Control charts. It helps to point out the variations in production process such as common cause and assignable cause and differentiate between them to take further action. Assignable cause occurs in the form of shifts which are the values of parameter process(s). Small, moderate and high shifts are the three categories of shifts. Two different type of charts work for different shifts. Memory-less control charts are available for large shifts monitoring whereas Memory-based control charts are useful small-moderate type shifts. However, some great researchers have formed some mixed control charts which have all types of shift detection ability by one chart such as Mixed Shewhart-CUSUM control chart. Meanwhile many studies have shown an improvement in ability of monitoring the shift in a process parameter when control charts of EWMA and CUSUM are mixed-up. Therefore, this study is finding a space to mix-up EEWMA by CUSUM control chart in order to get more efficient control chart to monitor the process mean than EEWMA control chart and CUSUM control chart. Furthermore, this study finds a space to make the practice of auxiliary variable to make the mixed-EEWMA-CUSUM control chart more competent to monitor the shift in the mean of process. Thus, in this study, a mixed chart based on classical CUSUM and EEWMA named as EEWMA-CUSUM is proposed. Evaluation is conducted through average run length (ARL) criterion. The solo purpose of this research is to make the chart more sensitive to smaller shifts than existing charts. The comparisons of proposed chart are done with different literature control chart naming CUSUM, EWMA, EEWMA. The comparison purpose is to show how the proposed Mixed EEWMA CUSUM surpasses other charts in the form of small to moderate shifts in the value of process mean. Eventually, to prove the superiority of proposed chart numerically and practically, simulation study is used. Furthermore, as auxiliary information gives more power to detection ability of control chart. So, Mixed EEWMA-CUSUM using auxiliary information is proposed as well to check if its results outcast the Mixed proposed EEWMA-CUSUM control chart’s performance. ARLs method is adopted to evaluate this chart.
Generating New Class of Distributions
(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2020) Ahtasham Gul; FA13-PSTAT-001; Muhammad Mohsin; LHR TP 7741
Probability distributions analyze the variability in real life problems systematically by providing appropriate models. These models are capable of handling the complex situations and draw useful inferences. In spite of immense work on probability distributions in literature, the development of new models and modifications of the existing models are made out continuously even today. In the similar vein, truncated distributions have their own importance in modeling the real life data in these days due to limited resources, time and expenses. Generally, the probability distributions apply to infinite domain i.e. 0 to ∞ but there have been certain situations when we need the reduced or finite domains. The infinite domain of a probability distribution is reduced to finite domain by truncation and the resulting distribution is called the truncated distribution. Truncated distributions are constantly utilized in various fields like astronomy, medicine, epidemiology, biometry, engineering, hydrology and economy. This thesis is categorized into six chapters. Chapter 1 is introductory in nature and provides genesis of the probability distributions. A brief survey of the literature on existing truncated distributions and their applications are given. In Chapter 2, a new methodology is proposed for generating a new family of truncated distributions and its general mathematical properties are derived. Some families of generalized truncated distributions for different XT distributions are tabulated. In Chapter 3, Gumbel-Truncated exponential distribution is developed by using the proposed methodology. The structural and statistical properties including moments, moment generating function, entropy, hazard function and order statistics are derived. The parameters are estimated by using maximum likelihood estimation technique. The simulation study is carried out to examine the performance of the proposed distribution. The proposed truncated model is fitted on real-life data sets to highlight its compatibility. In Chapter 4, another life time model i.e. Half logistic-Truncated exponential distribution (HL-TEXPD) is developed by using the proposed methodology and its various statistical properties have been studied. The parameters are again estimated by using maximum likelihood estimation technique. HL-TEXPD is fitted on real-life data sets to check its applicability. In Chapter5, the recurrence relations for HL-TEXPD are established for the single and product moments of order statistics for various values of scale parameter θ. These recurrence relations are used to calculate the first k moments of all order statistics in a simple xi and efficient manner and tabulate means, variances and co-variances, percentage points of the extremes and modes of all order statistics for samples of size n=1(1)10 for different values ofscale parameter. In Chapter 6, the thesis is summarized and some new directions for future research are highlighted

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