Department of Statistics

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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.
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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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    INTERNSHIP AT AUR-LAB
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) FAZEEL UMAR; FA20-BST-002; Dr. Mian Muhammad Farooq
    AUR Lab is a cooperative venture between Predominant College, as of now positioned No. 1 private for influence among private colleges in Pakistan (QS Positioning), and We-Plan, an Australian plan firm working in Pakistan. In the span of 10 months of foundation, it has accomplished the achievement of one of its startup projects being shortlisted among top two out of roughly 100+ entries from Pakistan in the Endeavor Cup Global contest. Current undertakings are managing in various business ventures, including archeological the travel industry; Metaverse; NFT Commercial center; administration and casting a ballot; Style plan; healthcare; Shrewd Agrarian; environmental the travel industry; structural plan; AR-based promoting; energy effectiveness; street wellbeing; orientation equity; also, land income. Our group of specialists incorporates specialized staff as well as business improvement staff: Dr. Muhammad Ashraf Khan; Prof. Saleem Zubair; Ms. Qurratulain Sonia Kashmiri; Mr. Muhmmad Ahmad; Mr. Jawad Ahmad; also, Mr. Javaid Iqbal
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    INTERNSHIP REPORT AUR LAB
    (Library Information Services COMSATS University Islamabad Lahore Campus, 2024-04-02) Nouman Ali; Dr. Mian Muhammad Farooq
    LAB is a collaboration between Superior University, which is presently ranked first in Pakistan for effect among private universities (QS Ranking), and we Plan, an Australian design business based in Pakistan. Within 10 months of its inception, one of its startup initiatives was selected as one of the top two out of about 100+ proposals from Pakistan in the Venture Cup International competition. Current projects include archaeological tourism, Metaverse, NFT Marketplace, governance and voting, fashion design, healthcare, Smart Agriculture, ecological tourism, architectural design, AR-based advertising, energy efficiency, road safety, gender equality, and land revenue. Dr. Muhammad Ashraf Khan, Prof. Saleem Zubair, Ms. Qurratulain Sonia Kashmiri, Mr. Muhmmad Ahmad, Mr. Jawad Ahmad, and Mr. Javaid Iqbal are among our technical and business development professionals.