Department of Statistics
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Item 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 7202Statistical 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.Item 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 SanaullahIn 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 literatureItem Statistical Identification of Factors Responsible for Rice Yield: Regression Analysis Approach(Library Information Services, COMSATS University Islamabad, Lahore Campus., 2020-04-01) Muhammad Faheem Javaid; CIIT/FA19-BST-009/LHR; Dr. Aamir Sanaullah; LHR TP 9944The importance of agriculture in our economy is underscored by the fact that it provides essential food supplies to meet the needs of our growing population. In Pakistan, agriculture is a vital contributor to our economic growth, Accounting for 22.7% of the GDP and employing approximately 37.4% of the Labor force. The rice ranked at 3rd place with 5.03 billion metric tons production worldwide. Pakistan came at 9th place all over the world in producing milled rice with a production of 9.32 million metric tons, rice contributes 2.4% to the value addition and 0.5% to the GDP. In this study we have collected data of Rice yield from Agriculture Department with various factors that contribute in the yield of rice. Then we use regression approach to identify the factors that are contributing in the rice yield significantly and the factors that contributing insignificantly. From the multiple linear regression, we got the R2 = 58.1% and Adjusted R Squared = .553. And then we see that, some predictor variables were found to be statistically significant while others were not as they are important for the rice yield. We suspected multicollinearity and applied factor analysis to address it. Factor analysis is applied to the independent variables, generating factors that were then used in a multiple regression analysis. The results of this analysis showed an improvement over the previous model, by making factors from all the independent variables show that all the factors are now contributing significantly in the model and the R2 has also improved from 58.1% to 68.7%.Item Estimation of Population Mean Using Estimator Based on Auxiliary Variable in Simple Random Sampling(2020-04-01) Umme Habiba; CIIT/FA19-BST-007/LHR; Dr. Aamir Sanaullah; LHR TP 9951Survey sampling is a well-established methodology employed to choose a sample of individuals from a larger population. The primary objective of this study is to estimate the population mean efficiently, by employing a comprehensive approach. To achieve this, we proposed a generalized estimator up to first degree of approximation by use of one auxiliary variable under simple random sampling framework. By deriving expressions for both bias and mean square error (MSE) of the proposed generalized estimator, we are able to ascertain its effectiveness. Remarkably, our analysis reveals that the proposed generalized estimator outperforms. Furthermore, we obtained the minimum MSE of the proposed estimator, and empirical studies demonstrated that our estimator outperform than the existing estimator found in the literature in terms of efficiency. Finally it is shown that the proposed generalized estimator efficiently work.