Department of Statistics
Permanent URI for this communityhttps://repository.cuilahore.edu.pk/handle/123456789/25
Browse
4 results
Search Results
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 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 7203Pareto 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.Item 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 7204Marshal-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.Item Spatial and Temporal Analysis of Drought(Library Information Services, COMSATS University Islamabad, Lahore Campus, 2023) Muhammad Furqan Ahmad; CIIT/FA19-BST-002/LHR; Dr. Mian Muhammad Farooq; LHR TP 9937In the recent years climate change is the hot topic of research. Climate change can have severe effect on the environment. The drought is an important factor of the climate. If a drought occur in some area it will affect the agriculture, water resources and other important factors of the country. In this study, the impact of drought in different districts of Punjab, Pakistan was studied using Standardized Precipitation Index (SPI) and Standardized Anomaly Index (SAI). The SPI is applied on the rain data and the SAI was applied on the temperature data. The data was collected from Pakistan Metrological Department. At first, we fit the data on Length Biased Exponential Distribution and then we applied Standardized Precipitation Index on the rain data received from Pakistan Meteorological Department from 1993 to 2022. We also computed SPI using 3-month, 6-month, and 12-month moving average of the original data. We conducted spatial and temporal analysis using SPI and for the visual representation we also plot maps of the past five years for better understanding of the drought. Standardized Anomaly Index (SAI) is a useful tool to measure and monitor deviations from normal conditions in terms of temperature or other relevant variables associated with drought. We used temperature to better explain the drought impact in Pakistan. After applying SAI, we find out that temperate of the data is above average which means there is drought impact in different districts of Pakistan. The results show the clear drought pattern in different districts of Pakistan. We ignore the 0 and negative values of rain data before fitting the Length Biased Exponential Distribution as it is undefined for these values and then we compute the results. The graphs show that after taking moving average the drought patterns decrease in districts and also few years does not show any drought pattern.