Degradation of Phenols, Dyes and Selected Pharmaceutically Active Compounds Using Horseradish Peroxidase Immobilized Onto Composites of Gelatin

Abstract

An efficient estimate of the population mean using ranked set samples instead of simple random samples plays an important role in the field of sample surveys, especially when the measurement of the variable of interest is costly and/or time-consuming. The main focus of this dissertation is to enhance the mean estimation and to improve the joint monitoring of the process mean and process standard deviation using exponentially weighted moving average (EWMA) control chart with generalized likelihood ratio (GLR) test for Pair ranked set sampling (PRSS) and Double ranked set sampling (DRSS) schemes. In Chapter 1, the discussion about the classical ranked set sampling (RSS) scheme, RSS scheme with auxiliary variable and control charts like EWMA control chart, EWMA control chart for joint monitoring process mean and process standard deviation and EWMA control chart with measurement error has been given. In Chapter 2, the literature review on classical and existing RSS schemes along with control charts under different RSS schemes, joint monitoring control charts with and without measurement error is discussed. The complete procedures of some existing RSS schemes and mean estimators with their variance expressions are given in Chapter 3. Following the previous chapters, the major contribution of this dissertation starts from Chapter 4. A joint monitoring EWMA control chart for process mean and variance under PRSS procedure using GLR test statistic is present in this chapter. Using the PRSS will cut down the number of units to be sampled from the population to half of what is need in RSS competitors. The structure of the likelihood ratio-based EWMA (ELR) chart using PRSS scheme is incorporated. A simulation study is conducted using real data set for evaluating the performance of the proposed method and the application by using real data set is presented. In Chapter 5, an attempt is made to develop a new chart that integrates the EWMA procedure with GLR test statistic for joint monitoring the process mean and the process dispersion under DRSS. Monte Carlo simulations study is conducted to estimate the average run length (ARL) and standard deviation of run length (SDRL) of the proposed control chart. We compared the performances of the proposed chart with PRSS chart when detecting shifts in the process mean, variance or both. An application to real data is also provided to illustrate the implementations of the proposed and existing control charts.xi Measurement error is known to result in reduced power to detect a given change in the mean or variance of a quality characteristic and badly affect the capability of control charts in detecting out-of-control (OOC) situations. Chapter 6 analyzed the effect of measurement error and multiple measurements using the GLR test statistic under the setting of EWMA control chart. For this purpose, different OOC scenarios including mean shifts, variance shifts, and simultaneous shifts in both using RSS and PRSS procedures are considered. The performance of the suggested control chart with measurement error is evaluated in terms of ARLs and SDRLs. The EWMA control chart is utilized as an improved alternative to the Shewhart mean control chart for detecting small/moderate shifts in the process because a small shift can be led to a significant financial loss. In Chapter 7, we analyzed the effect of measurement error (for the covariate model and using multiple measurements) for EWMA control chart using the GLR test statistic for the process mean and variance. The effect of measurement error on the detection abilities of the (ELR) control chart for monitoring process mean and process variability based on DRSS scheme is explored. A simulation study is conducted in detecting the performance of the proposed approach and comparison of the proposed chart has been made with RSS and PRSS in detecting a wide range of shifts even in the presence of measurement error. An example is provided to illustrate the use of ELR-DRSS and MELR-DRSS control charts with measurement error. In last chapter, another RSS-type scheme, namely modified extreme RSS (MERSS) is introduced for parametric estimation. In order to compare the performance of the proposed sampling scheme (MERSS) with SRS and RSS type schemes, a simulation study is considered to estimate the population mean for some symmetrical and non-symmetrical distributions.