Hassen A. Muttlak

Quality Control Chart for the Mean using Double Ranked Set Sampling

In this paper, an attempt is made to develop Quality Control Charts for monitoring the process mean based on Double Ranked Set Sampling (DRSS) rather than the traditional Simple Random Sampling (SRS). Considering a normal population and several shift values, the performance of the Average Run Length (ARL) of these new charts was compared with the control charts based on Ranked Set Sampling (RSS) and SRS with the same number of observations. It is shown that the new charts do a better job of detecting changes in process mean compared with SRS and RSS.

Statistical quality control based on ranked set sampling

Different quality control charts for the sample mean are developed using ranked set sampling (RSS), and two of its modifications, namely median ranked set sampling (MRSS) and extreme ranked set sampling (ERSS). These new charts are compared to the usual control charts based on simple random sampling (SRS) data. The charts based on RSS or one of its modifications are shown to have smaller average run length (ARL) than the classical chart when there is a sustained shift in the process mean. The MRSS and ERSS methods are compared with RSS and SRS data, it turns out that MRSS dominates all other methods in terms of the out-of-control ARL performance. Real data are collected using the RSS, MRSS, and ERSS in cases of perfect and imperfect ranking. These data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart. Throughout this study we are assuming that the underlying distribution is normal. A check of the normality for our example data set indicated that the normality assumption is reasonable.

Some estimators of a finite population mean using auxiliary information

In sample surveys, it is usual to make use of auxiliary information to increase the precision of estimators. Two classes of estimators are suggested to estimate the population mean for the variable of interest using two auxiliary variables. Some special cases of these two classes of estimators are considered and compared using real data set and computer simulation. It turns out that the newly suggested estimators dominate all other well-known estimators in terms of mean square error and bias. Finally we showed how to extend the two classes of estimators if more than two auxiliary variables are available.

Investigating the use of quartile ranked set samples for estimating the population mean

The ranked sampling method (ranked set sampling, RSS) as suggested by McIntyre [Australian Journal of Agricultural Research 3 (1952) 385] may be modified to come up with new sampling method called quartile ranked set sampling (QRSS) method. The newly suggested sampling method QRSS is compare to the simple random sampling (SRS), RSS and median ranked set sampling (MRSS) methods. It turns out that QRSS is more efficient than its counterpart SRS method for the distributions considered in this study. Also, it is more efficient than the RSS method for most of the probability distributions considered in this study. Finally it is more efficient than the MRSS method for some of the asymmetric probability distributions considered in this paper.

Median ranked set sampling with concomitant variables and a comparison with ranked set sampling and regression estimators

Ranked set sampling (RSS), as suggested by McIntyre (1952), assumes perfect ranking, i.e. without errors in ranking, but for most practical applications it is not easy to rank the units without errors in ranking. As pointed out by Dell and Clutter (1972) there will be a loss in precision due to the errors in ranking the units. To reduce the errors in ranking, Muttlak (1997) suggested using the median ranked set sampling (MRSS). In this study, the MRSS is used to estimate the population mean of a variable of interest when ranking is based on a concomitant variable. The regression estimator uses an auxiliary variable to estimate the population mean of the variable of interest. When one compares the performance of the MRSS estimator to RSS and regression estimators, it turns out that the use of MRSS is more efficient, i.e. gives results with smaller variance than RSS, for all the cases considered. Also the use of MRSS gives much better results in terms of the relative precision compared to the regression estimator for most cases considered in this study unless the correlation between the variable of interest and the auxiliary is more than 90 per cent.

Paired ranked set sampling : A more efficient procedure

The usual ranked set sampling (RSS) scheme is modified and a paired ranked set sampling (PRSS) method is suggested. Estimators for population mean and standard deviation using the PRSS method are obtained. The estimator of population mean based on the PRSS is compared with simple random sampling (SRS) mean, the RSS estimator of population mean and also with the minimum variance linear unbiased estimator (MVLUE) of population mean based on RSS. The estimator of standard deviation based on the PRSS is also compared with the MVLUE of population standard deviation. The estimators of population mean and standard deviation based on PRSS are found to be more efficient than their respective counterparts for six probability distributions considered. The estimators of population mean and standard deviation based on PRSS are compared with those based on the SRS and the RSS for normal distribution where errors in ranking are present. The estimators using the PRSS method are found to be more efficient than their respective counterparts for normal distribution, even in presence of errors in ranking. Copyright

Regression estimators in extreme and median ranked set samples

The ranked set sampling (RSS) method as suggested by McIntyre (1952) may be modified to come up with new sampling methods that can be made more efficient than the usual RSS method. Two such modifications, namely extreme and median ranked set sampling methods, are considered in this study. These two methods are generally easier to use in the field and less prone to problems resulting from errors in ranking. Two regression-type estimators based on extreme ranked set sampling (ERSS) and median ranked set sampling (MRSS) for estimating the population mean of the variable of interest are considered in this study and compared with the regression-type estimators based on RSS suggested by Yu & Lam (1997). It turned out that when the variable of interest and the concomitant variable jointly followed a bivariate normal distribution, the regression-type estimator of the population mean based on ERSS dominates all other estimators considered.

MVLUE of population parameters based on ranked set sampling

The minimum variance linear unbiased estimators (MVLUEs) of population parameters based on ranked set sampling are discussed for some distributions. Also values of the coefficients required for obtaining MVLUEs of the location and scale parameters are presented. For the same distributions, MVLUEs of the population mean are also obtained and the required coefficients are supplied. The MVLUEs of the population mean are compared with the other popular simple random sample (SRS) and ranked set sample (RSS) estimators of the population mean. The MVLUEs of the population mean are found to be more precise than the usual SRS or RSS estimators of the population mean for all cases considered.

Testing some hypotheses about the normal distribution using ranked set sample: a more powerful test

Abstract Ranked set sample (RSS) was introduced by McIntyre (1952) and by Takahasi and Wakimoto (1968) as a method of selecting data if the sampling units can be easily ranked without any cost, but it is very difficult or expensive to measure them. They proposed to use the RSS mean as an estimator for the population mean instead of the usual estimator which is the mean of the simple random sample (SRS). In this paper we consider testing some hypotheses about μ and σ2 of the normal distribution using RSS. It appears that the use of RSS gives much better results in terms of the power function compared to the SRS.

Estimating P(Y < X) using Ranked Set Sampling in Case of the Exponential Distribution

The problem of making statistical inference about θ =P(X > Y) has been under great investigation in the literature using simple random sampling (SRS) data. This problem arises naturally in the area of reliability for a system with strength X and stress Y. In this study, we will consider making statistical inference about θ using ranked set sampling (RSS) data. Several estimators are proposed to estimate θ using RSS. The properties of these estimators are investigated and compared with known estimators based on simple random sample (SRS) data. The proposed estimators based on RSS dominate those based on SRS. A motivated example using real data set is given to illustrate the computation of the newly suggested estimators.