Median Ranked Set Sampling Scheme Research Articles

Estimation Study of Multicomponent Stress-Strength Reliability Using Advanced Sampling Approach

In this study, we analyze a multicomponent system with v independent and identical strength components X1,…, Xv and each of these components is exposed to a common random stress Y. The system is considered to be operating only if at least u out of v (1 u  v) strength variables exceed the random stress. The estimate of the system reliability is investigated, assuming the strength and stress random variables follow the exponentiated exponential distribution having different shape parameters. The maximum likelihood estimator for the system reliability is derived from ranked set sampling (RSS), neoteric RSS (NRSS), and median RSS (MRSS). Some accuracy measurements, such as mean squared errors and efficiencies, are used to examine the behaviour of various estimates. Simulation studies demonstrate that the NRSS scheme's reliability estimates are chosen above those of the others under the RSS and MRSS schemes in the majority of situations. Theoretical research is explained through real data analysis.

Monitoring of Location Parameters with a Measurement Error under the Bayesian Approach Using Ranked-Based Sampling Designs with Applications in Industrial Engineering

To detect sustainable changes in the production processes, memory-type control charts are frequently utilized. This study is conducted to assess the performance of the Bayesian adaptive exponentially weighted moving average (AEWMA) control chart using ranked set sampling schemes following two different loss functions in the presence of a measurement error for posterior and posterior predictive distributions using conjugate priors. This study is based on the covariate model and multiple measurement methods in the presence of a measurement error (ME). The performance of the proposed Bayesian-AEWMA control chart with ME has been evaluated through the average run length and the standard deviation of the run length. Finally, a real-life application in semiconductor manufacturing was conducted to evaluate the effectiveness of the proposed Bayesian-AEWMA control chart with a measurement error based on different ranked set sampling schemes. The results demonstrate that the proposed control chart, in the presence of a measurement error, performed well in detecting out-of-control signals compared to the existing control chart. However, the median ranked set sampling scheme (MRSS) proved to be better than the other two schemes in the presence of a measurement error.

Three-fold utilization of supplementary information for mean estimation under median ranked set sampling scheme.

Ranked set sampling (RSS) has created a broad interest among researchers and it is still a unique research topic. It has at long last begun to find its way into practical applications beyond its initial horticultural based birth in the fundamental paper by McIntyre in the nineteenth century. One of the extensions of RSS is median ranked set sampling (MRSS). MRSS is a sampling procedure normally utilized when measuring the variable of interest is troublesome or expensive, whereas it might be easy to rank the units using an inexpensive sorting criterion. Several researchers introduced ratio, regression, exponential, and difference type estimators for mean estimation under the MRSS design. In this paper, we propose three new mean estimators under the MRSS scheme. Our idea is based on three-fold utilization of supplementary information. Specifically, we utilize the ranks and second raw moments of the supplementary information and the original values of the supplementary variable. The appropriateness of the proposed group of estimators is demonstrated in light of both real and artificial data sets based on the Monte-Carlo simulation. Additionally, the performance comparison is also conducted regarding the reviewed families of estimators. The results are empowered and the predominant execution of the proposed group of estimators is seen throughout the paper.

Enhancing the performance of the EWMA control chart for monitoring the process mean using auxiliary information

AbstractWhen using control charts to monitor manufacturing processes, the exponentially weighted moving average (EWMA) control chart is useful for detecting persistent shifts in the process parameter. This paper proposes enhancements to the applications of the EWMA control chart for those scenarios where the exact measurement of process units is difficult and expensive, but the visual ordering of the units can be done easily. The proposed charts use an auxiliary variable that is correlated with the process variable to provide efficient monitoring of shifts in the process mean and are formulated based on ranked set sampling (RSS) and median RSS schemes (MRSS). Simulation results showed that the proposed charting schemes are more efficient in detecting a shift in the process mean than the classical EWMA control chart and its modification. An example is provided to show the application of the proposed charts using a simulated benchmark process: the continuous stirred tank reactor (CSTR).

New Shewhart-EWMA and Shewhart-CUSUM Control Charts for Monitoring Process Mean

In this paper, we propose new Shewhart-EWMA (SEWMA) and Shewhart-CUSUM (SCUSUM) control charts using the varied L ranked set sampling (VLRSS) for monitoring the process mean, namely the SEWMA-VLRSS and SCUSUM-VLRSS charts. The run length characteristics of the proposed charts are computed using extensive Monte Carlo simulations. The proposed charts are compared with their existing counterparts in terms of the average and standard deviation of run lengths. It is found that, with perfect and imperfect rankings, the SEWMA-VLRSS and SCUSUM-VLRSS charts are more sensitive than their analogous charts based on simple random sampling, ranked set sampling (RSS) and median RSS schemes. A real dataset is also used to explain the implementation of the proposed control charts.

Median ranked acceptance sampling plans for exponential distribution

We develop a ranked acceptance sampling plan by attribute for exponential distribution assuming that the life test is truncated at a pre-assigned time. Two main requirements are essential for the proposed ranked sampling plans; namely; the life times of the test units are assumed to follow the exponential distribution; and the data are selected by using a free cost sampling method, the median ranked set sampling scheme from a large lot. The main advantage of using the median rank set sampling is to reduce producer’s risk, and it is one of the ranked scheme that produces a judgment order statistics that are mutually independent and identically distributed random variables to meet the binomial theory assumptions. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; then the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the sampling plans based on the ranked samples and producer’s risk are presented. A comparisons with sampling plan based on simple random sampling and an illustrative example are given.

A new cumulative sum control chart for monitoring the process mean using varied L ranked set sampling

Recently, a varied L ranked set sampling (VLRSS) scheme has been introduced in the literature for estimating the population mean. The VLRSS scheme is a cost-efficient alternative to the classical ranked-set sampling (RSS) and median RSS (MRSS) schemes. In this paper, we construct a new cumulative sum (CUSUM) control chart for efficiently monitoring the process mean using VLRSS, named the CUSUM-VLRSS chart. The CUSUM-VLRSS chart encompasses the existing CUSUM charts based on RSS and MRSS schemes, named the CUSUM-RSS and CUSUM-MRSS charts. We use extensive Monte Carlo simulations to compute the run length characteristics of the proposed CUSUM chart. It is shown that the CUSUM-VLRSS chart is able to perform uniformly better than the CUSUM-RSS and CUSUM-MRSS charts when detecting different kinds of shift in the process mean. A similar trend is observed when the proposed CUSUM chart is constructed under imperfect rankings. A real data-set is also used to explain the implementation of the CUSUM-VLRSS chart.

On Using The Median Ranked Set Sampling for Developing Reliability Test Plans Under Generalized Exponential Distribution

In this article a new single sampling plan based on ranked data scheme is proposed. Two main requirements are considered for the new plan: the lifetime of the test units is assumed to follow the generalized exponential distribution; and the data are selected by using the median ranked set sampling scheme from a large lot. The distribution function characterization under the median ranked set sampling scheme is derived assuming that the set size is known; the minimum number of set cycle and consequently the minimum sample size necessary to ensure the specified average life are obtained and the operating characteristic values of the ranked sampling plans as well as the producer’s risk are presented. An illustrative examples based on the results obtained are given.

New ranked set sampling schemes for range charts limits under bivariate skewed distributions

In this paper, instead of using traditional sampling schemes, we newly introduce to use ranked set, neoteric ranked set and median ranked set sampling to construct range charts control limits under the bivariate skewed distributions. Shewhart, weighted variance and skewness correction methods are considered to construct the range charts in the statistical process control. We have compared the performance of the suggested range charts under simple random and different ranked set sampling schemes by simulation study. The simulation study has showed that range charts based on skewness correction method are the most efficient under neoteric and median ranked set sampling schemes, especially in highly skewed data.

New difference-cum-ratio and exponential type estimators in median ranked set sampling

This paper suggests difference-cum-ratio and exponential type estimators of population mean using first or third quartiles and mean of auxiliary variable under median ranked set sampling scheme and we have extended our study in double sampling scheme when the population parameters are unknown. The bias and mean square error of estimators are derived by theoretically both of sampling designs. Empirical studies have been done to demonstrate the efficiency of proposed estimators over the existing estimators. We have found that difference-cum-ratio estimator is always more efficient than regression estimator and both of the estimators are considerable efficient than existing estimators.

New Synthetic EWMA and Synthetic CUSUM Control Charts for Monitoring the Process Mean

Exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are potentially powerful statistical process monitoring tools because of their excellent speed in detecting small to moderate persistent process shifts. Recently, synthetic EWMA (SynEWMA) and synthetic CUSUM (SynCUSUM) control charts have been proposed based on simple random sampling (SRS) by integrating the EWMA and CUSUM control charts with the conforming run length control chart, respectively. These synthetic control charts provide overall superior detection over a range of mean shift sizes. In this article, we propose new SynEWMA and SynCUSUM control charts based on ranked set sampling (RSS) and median RSS (MRSS) schemes, named SynEWMA-RSS and SynEWMA-MRSS charts, respectively, for monitoring the process mean. Extensive Monte Carlo simulations are used to estimate the run length characteristics of the proposed control charts. The run length performances of these control charts are compared with their existing powerful counterparts based on SRS, RSS and MRSS schemes. It turns out that the proposed charts perform uniformly better than the Shewhart, optimal synthetic, optimal EWMA, optimal CUSUM, near-optimal SynEWMA, near-optimal SynCUSUM control charts based on SRS, and combined Shewhart-EWMA control charts based on RSS and MRSS schemes. A similar trend is observed when constructing the proposed control charts based on imperfect RSS schemes. An application to a real data is also provided to demonstrate the implementations of the proposed SynEWMA and SynCUSUM control charts. Copyright © 2014 John Wiley & Sons, Ltd.

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

Exponentially weighted moving average (EWMA) control charts have been widely accepted because of their excellent performance in detecting small to moderate shifts in the process parameters. In this paper, we propose new EWMA control charts for monitoring the process mean and the process dispersion. These EWMA control charts are based on the best linear unbiased estimators obtained under ordered double ranked set sampling (ODRSS) and ordered imperfect double ranked set sampling (OIDRSS) schemes, named EWMA-ODRSS and EWMA-OIDRSS charts, respectively. We use Monte Carlo simulations to estimate the average run length, median run length, and standard deviation of run length of the proposed EWMA charts. We compare the performances of the proposed EWMA charts with the existing EWMA charts when detecting shifts in the process mean and in the process variability. It turns out that the EWMA-ODRSS mean chart performs uniformly better than the classical EWMA, fast initial response-based EWMA, Shewhart-EWMA, and hybrid EWMA mean charts. The EWMA-ODRSS mean chart also outperforms the Shewhart-EWMA mean charts based on ranked set sampling (RSS) and median RSS schemes and the EWMA mean chart based on ordered RSS scheme. Moreover, the graphical comparisons of the EWMA dispersion charts reveal that the proposed EWMA-ODRSS and EWMA-OIDRSS charts are more sensitive than their counterparts. We also provide illuminating examples to illustrate the implementation of the proposed EWMA mean and dispersion charts. Copyright © 2014 John Wiley & Sons, Ltd.

Inference about the Regression Parameters Using Median-Ranked Set Sampling

The ranked set samples and median ranked set samples in particular have been used extensively in the literature due to many reasons. In some situations, the experimenter may not be able to quantify or measure the response variable due to the high cost of data collection, however it may be easier to rank the subject of interest. The purpose of this article is to study the asymptotic distribution of the parameter estimators of the simple linear regression model. We show that these estimators using median ranked set sampling scheme converge in distribution to the normal distribution under weak conditions. Moreover, we derive large sample confidence intervals for the regression parameters as well as a large sample prediction interval for new observation. Also, we study the properties of these estimators for small sample setup and conduct a simulation study to investigate the behavior of the distributions of the proposed estimators.