Nonparametric estimation of mean residual lifetime in ranked set sampling with a concomitant variable

ABSTRACTRecently, a hybrid ranked set sampling (HRSS) scheme has been proposed in the literature. The HRSS scheme encompasses several existing ranked set sampling (RSS) schemes, and it is a cost-effective alternative to the classical RSS and double RSS schemes. In this paper, we propose an improved estimator for estimating the cumulative distribution function (CDF) using HRSS. It is shown, both theoretically and numerically, that the CDF estimator under HRSS scheme is unbiased and its variance is always less than the variance of the CDF estimator with simple random sampling (SRS). An unbiased estimator of the variance of CDF estimator using HRSS is also derived. Using Monte Carlo simulations, we also study the performances of the proposed and existing CDF estimators under both perfect and imperfect rankings. It turns out that the proposed CDF estimator is by far a superior alternative to the existing CDF estimators with SRS, RSS and L-RSS schemes. For a practical application, a real data set is considered on the bilirubin level of babies in neonatal intensive care.

Bayesian estimation and credible interval of stress–strength reliability for two-parameter bathtub-shaped lifetime (TPBL) distribution are considered based on simple random sampling (SRS), ranked set sampling (RSS) and maximum ranked set sampling with unequal samples (MRSSU). Monte Carlo simulations are used to compare the performances of different proposed methods for Bayesian inferences on R. The results of simulation show that the estimator of the stress–strength reliability based on MRSSU and RSS are more efficient than SRS. Also, we make a comparison between the performance of the proposed methods in this paper and Tarvirdizade and Ahmadpour's [Estimation of the stress–strength reliability for the two-parameter bathtub-shaped lifetime distribution based on upper record values. Stat Methodol. 2016;31:58–72] method, which is based on upper record values. Finally, a real data set has been analyzed for illustrative purposes.

The estimation of the means of the bivariate normal distribution, based on a sample obtained using a modification of the moving extreme ranked set sampling technique (MERSS) is considered. The modification involves using a concomitant random variable. Nonparametric-type methods as well as the maximum likelihood estimation are considered. The estimators obtained are compared to their counterparts based on simple random sampling (SRS). It appears that the suggested estimators are more efficient. Also, MERSS with concomitant variable is easier to use in practice than the usual ranked set sampling (RSS) with concomitant variable. The issue of robustness of the procedure is addressed. Real trees data set is used for illustration.

The terrible operating constraints of many real-world events cause systems to malfunction regularly. The failure of systems to perform their intended duties when they reach their lowest, highest, or both extreme operating conditions is a phenomenon that researchers rarely focus on. The multi-stress strength reliability R=P(W<X<Z) is deemed in this study for a component whose strength X falls between two stresses, W, and Z, where X, W, and Z are independently inverted Kumaraswamy distributed. Both maximum likelihood and maximum product spacing procedures are employed to obtain the reliability estimator under simple random sampling (SRS) and ranked set sampling (RSS) methodologies. Four scenarios for reliability estimators are considered. The reliability estimator in the first and second cases can be determined by applying the same sample design (RSS/SRS) to the strength and stress distributions. When the sample data for W and Z originate from RSS while those for X are acquired from SRS, the third reliability estimator is calculated. The drawn data of the strength and stress random variables, which are obtained from SRS and RSS, respectively, are taken into consideration in the final scenario. The effectiveness of the suggested estimators is compared using a comprehensive computer simulation. Lastly, three real data sets have been used to determine reliability estimators.

In many real-world situations, systems frequently fail due to demanding operating conditions. In particular, when systems reach their lowest, highest, or both extremes operating conditions, they usually fail to accomplish their intended functions. This study considers estimating the stress–strength reliability, for a component with a strength (X) that is independent of the opposing lower bound stress (Y) and upper bound stress (Z). We assumed that the strength and stress random variables followed a generalized inverse exponential distribution with different shape parameters. Under ranked set sampling (RSS) and simple random sampling (SRS) designs, we obtained four reliability estimators using the maximum likelihood method. The first and second reliability estimators were deduced when the sample data of the strength and stress distributions used the sample design (RSS/SRS). The third reliability estimator was determined when the sample data for Y and Z were received from the RSS and the sample data for X were taken from the SRS. The fourth reliability estimator was derived when the sample data of Y and Z were selected from the SRS, while the sample data of X were taken from the RSS. The accuracy of the suggested estimators was compared using a comprehensive computer simulation. Lastly, three real data sets were used to determine the reliability.

In this paper, a new modification of ranked set sampling (RSS) is suggested, namely; unified ranked set sampling (URSS) for estimating the population mean and variance. The performance of the empirical mean and variance estimators based on URSS are compared with their counterparts in ranked set sampling and simple random sampling (SRS) via Monte Carlo simulation. Simulation results indicate that the URSS estimators perform better than their counterparts using RSS and SRS designs when the ranking is perfect. When the ranking is imperfect, the URSS estimators still are superior than their counterparts in ranked set sampling and simple random sampling methods. Finally, an illustrative example is provided to show the efficiency of the new method in practice.

Ranked Set Sampling and Ranked Set Sampling concomitant are more efficient than Simple Random Sampling. This can be determined by calculating the Relative Precision which is a ratio value from the variance of the mean from each sampling technique. From the research of Ranked Set Sampling, obtained , and so Ranked Set Sampling is more efficient than Simple Random Sampling. For the research of Ranked Set Sampling concomitant, obtained , and so Ranked Set Sampling concomitant is more efficient than Simple Random Sampling, and for simple linear regression analysis obtained , , , so simple linear regression model of Ranked Set Sampling is more efficient than simple linear regression model of Simple Random Sampling

In the case of contamination for skewed distributions, the modified Shewhart, modified weighted variance, and modified skewness correction methods are newly introduced by Karagoz (Hacet J Math Stat 47(1):223–242, 2018). In this study, we propose to modify these methods by considering simple random sampling (SRS), ranked set sampling (RSS) and median ranked set sampling (MRSS) designs under the contaminated type I Marshall–Olkin bivariate Weibull and lognormal distributions. These bivariate distributions are chosen since they can represent a wide variety of shapes from nearly symmetric to highly skewed. We evaluate the performance of proposed modified methods based on different ranked set sampling designs by using Monte Carlo Simulation. The type I risks of $${\bar{X}}$$ charts for existing and newly proposed modified methods by using SRS, RSS and MRSS designs in the case of contamination for these distributions are obtained via simulation study. The proposed modified methods using RSS and MRSS designs for the $${\bar{X}}$$ chart can be a favorable substitute in process monitoring when the distribution is highly skewed and contaminated.

The ranked set sampling (RSS) is an effective scheme popularly used to produce more precisely estimators. Despite its popularity, RSS suffers from some drawbacks which includes high sensitivity to outliers and it cannot sometimes be applicable when the population is relatively small. To overcome these limitations, varied L ranked set sampling (VLRSS) is recently introduced. It is shown that VLRSS scheme enjoys with many interesting properties over RSS and also encompasses several existing RSS schemes. In addition, it is also helpful for providing precise estimates of several population parameters. To fill this gap, this article extends the work and address the estimation of based ℛ on VLRSS when the strength and stress both follow exponential distribution. Maximum likelihood approach as well as Bayesian method are considered for estimating ℛ. The Bayes estimators are obtained by using gamma distribution under general entropy loss function and LINEX loss function. The performance of the estimators based on VLRSS are investigated by a simulation study as well as a real dataset relevant to industrial field. The results reveal that the proposed estimators are more efficient relative to their analogues estimators under L ranked set sampling given that the quality of ranking is fairly good.

ABSTRACTIn this paper, ranked set sampling is proposed for constructing a non-parametric quality control chart based on sign statistic for monitoring the process center when the units are difficult and costly to measure. The characteristics of run length such as average, median and standard deviation are used as criteria to compare two sampling schemes: ranked set sampling and simple random sampling. Cauchy, double exponential and normal distributions are applied to investigate the performance of sign control chart based on studied sampling schemes. The proposed control chart is illustrated with a real data set. The results indicate that when the process starts to get out of control, the chart based on ranked set sampling reduces the run length characteristics values.

The maximum livelihood estimator (MLE) using a ranked set sample (RSS) usually has no closed expression because the maximum likelihood equation involves both hazard and inverse hazard functions, and may no longer be efficient when the judgment ranking is imperfect. In this paper, we consider a modified MLE (MMLE) using RSS for general parameters, which has the same expression as the MLE using a simple random sample (SRS), except that the SRS in the MLE is replaced by the RSS. The results show that, for the location parameter, the MMLE is always more efficient than the MLE using SRS, and for the scale parameter, the MMLE is at least as efficient as the MLE using SRS, when the same sample size is used. Under the perfect judgment ranking, numerical examples also show that the MMLE has good efficiency relative to the MLE based on RSS. When the judgment error is present, we conduct simulations to show that the MMLE is more robust than the MLE using RSS.

There are many situations where it is costly to measure the variable under the study, but this variable can be easily ranked. Ranked set sampling (RSS) utilizes the information of the ranks in addition to the measurements. It was proved that RSS is more efficient than simple random sampling (SRS) when estimating the population arithmetic mean for the same sample size. Because of its efficiency, RSS was employed to a wide range of applications and becoming an interesting method for many researchers. It was studied parametrically and non-parametrically and several estimators based on different statistical distributions were investigated. This research adopts Rician distribution and several measurements from this distribution were investigated based on RSS. The estimations include the arithmetic, geometric, harmonic, quadratic means as well as the median, variance, mean deviation, coefficient of variation, coefficient of skewness and kurtosis. Simulation study shows that the estimators based on RSS are more efficient than those based on SRS. However, the gain in the efficiency with variance and coefficient of kurtosis is not too much and even worse for small sample size.

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. In the current paper, several traditional and ad hoc estimators of the scale and shape parameters $$\theta $$ and $$\alpha $$ from the Pareto distribution $$p(\theta ,\alpha )$$ will be respectively studied in cases when one parameter is known and when both are unknown under simple random sampling, RSS and some of its modifications such as extreme RSS(ERSS) and median RSS(MRSS). It is found for estimating of $$\theta $$ from $$p(\theta ,\alpha )$$ in which $$\alpha $$ is known, the best linear unbiased estimator (BLUE) under ERSS is more efficient than the other estimators under the other sampling techniques. For estimating of $$\alpha $$ from $$p(\theta ,\alpha )$$ in which $$\theta $$ is known, the modified BLUE under MRSS is more efficient than the other estimators under the other sampling techniques. For estimating of $$\theta $$ and $$\alpha $$ from $$p(\theta ,\alpha )$$ in which both are unknown, the ad hoc estimators under ERSS are more efficient than the other estimators under the other sampling techniques. All efficiencies of these estimators are simulated under imperfect ranking. A real data set is used for illustration.

The article introduces a novel Bayesian AEWMA Control Chart that integrates different loss functions (LFs) like the square error loss function and Linex loss function under an informative prior for posterior and posterior predictive distributions, implemented across diverse ranked set sampling (RSS) designs. The main objective is to detect small to moderate shifts in the process mean, with the average run length and standard deviation of run length serving as performance measures. The study employs a hard bake process in semiconductor production to demonstrate the effectiveness of the proposed chart, comparing it with existing control charts through Monte Carlo simulations. The results underscore the superiority of the proposed approach, particularly under RSS designs compared to simple random sampling (SRS), in identifying out-of-control signals. Overall, this study contributes a comprehensive method integrating various LFs and RSS schemes, offering a more precise and efficient approach for detecting shifts in the process mean. Real-world applications highlight the heightened sensitivity of the suggested chart in identifying out-of-control signals compared to existing Bayesian charts using SRS.

The method of maximum likelihood estimation based on ranked set sampling (RSS) and some of its modifications is used to estimate the unknown parameters of the new Weibull-Pareto distribution. The estimators are compared with the conventional estimators based on simple random sampling (SRS). The biases, mean squared errors, and confidence intervals are used to the comparison. The effect of the set size and number of cycles of the RSS schemes are addressed. Monte Carlo simulation is carried out by using R. The results showed that the RSS estimators are more efficient than their competitors using SRS.