Amer Ibrahim Al-Omari

Improved quality control charts for monitoring the process mean, using double-ranked set sampling methods

Statistical control charts are widely used in the manufacturing industry. The Shewhart-type control charts are developed to improve the monitoring process mean by using the double quartile-ranked set sampling, quartile double-ranked set sampling, and double extreme-ranked set sampling methods. In terms of the average run length, the performance of the proposed control charts are compared with the existing control charts based on simple random sampling, ranked set sampling and extreme-ranked set sampling methods. An application of real data is also considered to investigate the performance of the suggested process mean control charts. The findings of the study revealed that the newly suggested control charts are superior to the existing counterparts.

Estimation of mean based on modified robust extreme ranked set sampling

In this paper, double robust extreme ranked set sampling (DRERSS) and its properties for estimating the population mean are considered. It turns out that, when the underlying distribution is symmetric, DRERSS gives unbiased estimators of the population mean. Also, it is found that DRERSS is more efficient than the simple random sampling (SRS), ranked set sampling (RSS), and extreme ranked set sampling (ERSS) methods. For asymmetric distributions considered in this study, the DRERSS has a small bias and it is more efficient than SRS, RSS, and ERSS. A real data set is used to illustrate the DRERSS method.

Acceptance sampling plan based on truncated life tests for exponentiated fréchet distribution

Abstract In this paper, exponentiated Fréchet distribution is considered as a model for a life time random variable when the life test is truncated at a pre-assigned time. The operating characteristic functions values of the suggested sampling plans and the corresponding producers risk are obtained.

Improved Exponentially Weighted Moving Average Control Charts for Monitoring Process Mean and Dispersion

Exponentially weighted moving average (EWMA) control charts are mostly used to monitor the manufacturing processes. In this paper, we propose some improved EWMA control charts for detecting the random shifts in the process mean and process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered ranked set sampling (ORSS) and ordered imperfect ranked set sampling (OIRSS), named EWMA-ORSS and EWMA-OIRSS charts, respectively. Monte Carlo simulations are used to estimate the average run length, median run length and standard deviation of run length of the proposed EWMA control charts. It is observed that the EWMA-ORSS mean control chart is able to detect the random shifts in the process mean substantially quicker than the Shewhart-cumulative sum and the Shewhart-EWMA control charts based on the RSS scheme. Both EWMA-ORSS and EWMA-OIRSS location charts perform better than the classical EWMA, hybrid EWMA, Shewhart-EWMA and fast initial response-EWMA charts. The EWMA-ORSS dispersion control chart performs better than the simple random sampling based CS-EWMA and other EWMA control charts in efficient detection of the random shifts that occur in the process variability. An application to real data is also given to explain the implementation of the proposed EWMA control charts. Copyright

Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes

Control charts are a powerful statistical process monitoring tool often used to monitor the stability of manufacturing processes. In quality control applications, measurement errors adversely affect the performance of control charts. In this paper, we study the effect of measurement error on the detection abilities of the exponentially weighted moving average (EWMA) control charts for monitoring process mean based on ranked set sampling (RSS), median RSS (MRSS), imperfect RSS (IRSS) and imperfect MRSS (IMRSS) schemes. We also study the effect of multiple measurements and non-constant error variance on the performances of the EWMA control charts. The EWMA control chart based on simple random sampling is compared with the EWMA control charts based on RSS, MRSS, IRSS and IMRSS schemes. The performances of the EWMA control charts are evaluated in terms of out-of-control average run length and standard deviation of run lengths. It turns out that the EWMA control charts based on MRSS and IMRSS schemes are better than their counterparts for all measurement error cases considered here.

Estimation of entropy using random sampling

In this paper, three new entropy estimators of continuous random variables are proposed using simple random sampling (SRS), ranked set sampling (RSS) and double ranked set sampling (DRSS) techniques. The new estimators are obtained by modifying the estimators suggested by Noughabi and Arghami (2010) and Ebrahim et al. (1994). In terms of the root mean square error (RMSEs) and bias values, a numerical comparison is considered to compare the suggested estimators with Vasiceks (1976) estimator. Our results reveal that the suggested estimators have smaller mean squared error than Vasiceks estimator. Also, the suggested estimators under double ranked set sampling are more efficient than other suggested estimators based on SRS and RSS.

Modified BLUEs and BLIEs of the location and scale parameters and the population mean using ranked set sampling

Ranked set sampling (RSS) is a sampling procedure that can be used to improve the cost efficiency of selecting sample units of an experiment or a study. In this paper, RSS is considered for estimating the location and scale parameters a and b>0, as well as the population mean from the family F((x−a)/b). Modified best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) are considered. Numerical computations with different location-scale distributions and different sample sizes are conducted to assess the efficiency of the suggested estimators. It is found that the modified BLIEs are uniformly higher than that of BLUEs for all distributions considered in this study. The modified BLUE and BLIE are more efficient when the underlying distribution is symmetric.

Estimation of the population mean and median using truncation-based ranked set samples

In this paper, a new sampling method is suggested, namely truncation-based ranked set samples (TBRSS) for estimating the population mean and median. The suggested method is compared with the simple random sampling (SRS), ranked set sampling (RSS), extreme ranked set sampling (ERSS) and median-ranked set sampling (MRSS) methods. It is shown that for estimating the population mean when the underlying distribution is symmetric, TBRSS estimator is unbiased and it is more efficient than the SRS estimator based on the same number of measured units. For asymmetric distributions considered in this study, TBRSS estimator is more efficient than the SRS for all considered distributions except for exponential distribution when the selection coefficient gets large. When compared with ERSS and MRSS methods, TBRSS performs well with respect to ERSS for all considered distributions except for U(0, 1) distribution, while TBRSS efficiency is higher than that of MRSS for U(0, 1) distribution. For estimating the population median, the TBRSS estimators have higher efficiencies when compared with SRS and ERSS. A real data set is used to illustrate the suggested method.

Statistical Quality Control Limits for the Sample Mean Chart Using Robust Extreme Ranked Set Sampling

Abstract In this paper, new quality control charts for the mean are considered using robust extreme ranked set sampling (RERSS) method. The new charts are compared with the classical control charts using simple random sampling (SRS) and ranked set sampling methods (RSS). It is found that the RERSS charts perform better than all other charts based on SRS and RSS methods in terms of their average run length (ARL).

Mixed ranked set sampling design

The main focus of agricultural, ecological and environmental studies is to develop well designed, cost-effective and efficient sampling designs. Ranked set sampling (RSS) is one method that leads to accomplish such objectives by incorporating expert knowledge to its advantage. In this paper, we propose an efficient sampling scheme, named mixed RSS (MxRSS), for estimation of the population mean and median. The MxRSS scheme is a suitable mixture of both simple random sampling (SRS) and RSS schemes. The MxRSS scheme provides an unbiased estimator of the population mean, and its variance is always less than the variance of sample mean based on SRS. For both symmetric and asymmetric populations, the mean and median estimators based on SRS, partial RSS (PRSS) and MxRSS schemes are compared. It turns out that the mean and median estimates under MxRSS scheme are more precise than those based on SRS scheme. Moreover, when estimating the mean of symmetric and some asymmetric populations, the mean estimates under MxRSS scheme are found to be more efficient than the mean estimates with PRSS scheme. An application to real data is also provided to illustrate the implementation of the proposed sampling scheme.