Developments and Estimation in Ranked Set Sampling

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 monitoring of the process mean using the newly proposed ranked set sampling (RSS) schemes.

In Chapter 1, a comprehensive discussion about the classical RSS scheme and control charting mechanisms, like Shewhart mean control chart and exponentially weighted moving average (EWMA) control chart, has been given. In Chapter 2, the literature work on classical and existing RSS schemes along with control charts under different RSS schemes 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. Focusing on such situations when recognition or ranking cost of sampling units cannot be ignored, a costeffective and efficient scheme, named quartile pair RSS (QPRSS) for estimating the population mean is introduced in this chapter. The mathematical properties of newly suggested QPRSS mean estimator are studied and found unbiased estimator. In order to compare the performance of QPRSS mean estimator with its counterparts in simple random sampling (SRS), pair RSS (PRSS) and extreme pair RSS (EPRSS) schemes, an elucidatory simulation study is also presented in this chapter for several symmetrical and nonsymmetrical probability distributions.

In Chapter 5, a more efficient quartile paired double RSS (QPDRSS) scheme for estimating the population parameters is proposed. The mathematical results of QPDRSS mean estimator are discussed and found unbiased in case of symmetric distribution. A comparison of the performance of proposed mean estimator and its competitors in SRS, double RSS (DRSS), extreme paired double RSS (EPDRSS) and paired double RSS (PDRSS) schemes is presented using simulation study for several probability distributions. The QPDRSS scheme instead of DRSS can be applied with full confidence to estimate the mean when it is not easy to conduct DRSS due to shortage of sampling units and/or high measurement cost of experimental units.The sampling scheme plays an important role in the performance of control charts because quality practitioners keep in view its features like costeffective, efficient and time saving for improved monitoring of process mean. Chapter 6 leads to the development of new Shewhart-type mean control charts to monitor the process by employing advantageous PRSS- and PDRSS-type schemes. The control charts performance measures average run length (ARL) and standard deviation of run length (SDRL) are utilized in this chapter to investigate the performance of proposed Shewhart-type mean control charts by using Monte Carlo simulation study. The illustrative examples are also discussed in this chapter to explain the implementation and working of proposed charts.

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 small shift can be leaded to a significant financial loss. In Chapter 7, the new EWMA-type control charts are developed based on different PRSS- and PDRSS-type schemes for efficiently monitoring the process mean. The ARL and SDRL results of suggested charts are computed using simulation study. On comparing with that of existing charts, it is found that proposed EWMA-type control charts are more effective than SRS based EWMA control chart in detecting an out of control signal for given range of shifts in process mean.

In chapter 8, another RSS-type scheme, namely even order RSS (EORSS) is introduced for parametric estimation. The properties of newly proposed sampling scheme for mean estimator of population mean are given. It is proved that proposed estimator is an unbiased estimator of the population mean for symmetric distribution. In order to compare the performance of proposed sampling scheme (EORSS) with SRS and RSS type schemes, the theoretical and simulation study are considered to estimate the population mean for some symmetrical and non-symmetrical distributions. Finally, the conclusion and some recommendations are given in last chapter.