Ranked Set Sampling Scheme Research Articles

Reliability test for degradation data based on ranked set sampling

AbstractIn this article, we consider test for the two null hypotheses for and , two widely useful tests in reliability, based on ranked set sampling (RSS). We derive the likelihood ratio test as well as the associated exact and asymptotic results. Considering a fixed significance level and power of the test, we show that the proposed test statistic outperforms the existing test. In small sample cases, the proposed test leads to a much narrower confidence interval for the reliability function . Then, the test statistics obtained from simple random sampling and RSS schemes are compared through which, the efficiency of using RSS is demonstrated. For illustration, we apply the proposed test to a degradation data from the reliability literature. Upon using RSS, the cost of measurement gets reduced and efficiency gets improved, suggesting the importance and use of RSS data in reliability experiments and their design.

Reliability Estimation in Stress Strength for Generalized Rayleigh Distribution Using a Lower Record Ranked Set Sampling Scheme

This paper explores the likelihood and Bayesian estimation of the stress–strength reliability parameter (R) based on a lower record ranked set sampling scheme from the generalized Rayleigh distribution. Maximum likelihood and Bayesian estimators as well as confidence intervals of R are derived and their properties are studied. Furthermore, two parametric bootstrap confidence intervals are introduced in the paper. A comparative simulation study is conducted to assess the effectiveness of these four confidence interval methodologies in estimating R. The application of the methods is demonstrated using real data on fiber strength to showcase their practicability and relevance in the industry.

A Refinement of Ratio Estimation in Ranked Set Sampling and Stratified Ranked Set Sampling Approaches

Estimation of population mean is a persistent subject issue in sampling surveys and many discrete efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this an improved version of ratio estimator are presented in this paper under the ranked set sampling scheme and stratified ranked set sampling scheme. Comparison amongst estimators is made in terms of Mean Square Errors ( ) and Percentage Relative Efficiencies ( ). The expression for of the proposed estimator is pinned-down to first order of approximations. It turns out from both simulation studies as well as real data set that the proposed estimator dominates its existing counterpart estimators.

Enhanced exponential ratio-cum-ratio estimator in ranked set sampling using transformed auxiliary information

Estimation of population mean is a determined subject issue in sampling surveys and many efforts have been paid by various researchers to enhance the precision of the estimates by utilizing the correlated auxiliary information. In connection with this, we suggest an improved exponential ratio-cum-ratio estimator using transformed auxiliary variables under ranked set sampling scheme. Theoretical comparison between estimators is made in terms of mean square errors (MSEs), percentage relative efficiencies (PREs), and percentage relative root mean squared error (PRRMSE). The numerical expression for the bias and MSE of the suggested estimator is derived up to first order of approximation. Based on the results of actual data sets and a simulation study, it is found that the suggested estimator perform well as compared to its existing counterparts.

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.

Inference for a general family of exponentiated distributions under ranked set sampling with partially observed complementary competing risks data

ABSTRACT Ranked set sampling (RSS) acts as an efficient way for collecting failure information due to its ability of saving testing time and cost, and this paper discusses statistical inference for complementary competing risks model under a modified RSS scheme called the maximum ranked set sampling procedure with unequal samples (MRSSU). When the lifetimes of causes of failure are characterized by a general family of exponentiated distributions with partially observed failure causes, parameter estimation is explored from classical likelihood and Bayesian approaches. Existence and uniqueness of maximum likelihood estimators for model parameters are established, and approximate confidence intervals are constructed in consequence. With respect to general flexible priors, Bayes point and interval estimates are constructed, and associated Monte-Carlo sampling is proposed for complex posterior computation. In addition, when there is extra restriction information available, likelihood and Bayes estimates are also proposed in this regard. Extensive simulation studies are conducted to investigate the performance of different methods, and a real-life example is carried out to demonstrate the applications of our results.

Monitoring of semiconductor manufacturing process on Bayesian AEWMA control chart under paired ranked set sampling schemes

Quality control often employs memory-type control charts, including the exponentially weighted moving average (EWMA) and Shewhart control charts, to identify shifts in the location parameter of a process. This article pioneers a new Bayesian Adaptive EWMA (AEWMA) control chart, built on diverse loss functions (LFs) such as the square error loss function (SELF) and the Linex loss function (LLF). The proposed chart aims to enhance the process of identifying small to moderate as well as significant shifts in the mean, signifying a notable advancement in the field of quality control. These are implemented utilizing an informative prior for both posterior and posterior predictive distributions, employing various paired ranked set sampling (PRSS) schemes. The effectiveness of the suggested chart is appraised using average run length (ARL) and the standard deviation of run length (SDRL). Monte Carlo simulations are employed to contrast the recommended approach against other control charts. The outcomes demonstrate the dignitary performance of the recommended chart in identifying out-of-control signals, especially applying PRSS designs, in comparison to simple random sampling (SRS). Finally, a practical application was conducted in the semiconductor manufacturing context to appraise the efficacy of the offered chart using various paired ranked set sampling strategies. The results reveal that the suggested control chart performed well in capturing the out-of-control signals far better than the already in use control charts. Overall, this study interposes a new technique with diverse LFs and PRSS designs, improving the precision and effectiveness in detecting process mean shifts, thereby contributing to advancements in quality control and process monitoring.

Bayesian AEWMA control chart under ranked set sampling with application to reliability engineering

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.

General weighted cumulative residual (past) extropy of minimum (maximum) ranked set sampling with unequal samples

The general weighted cumulative residual extropy (GWCRJ) and general weighted cumulative past extropy (GWCPJ) are introduced in this article. There are some results in relation to GWCPJ and GWCRJ. We take into account GWCRJ-based uncertainty measures for the minimal ranked set sampling technique with unequal samples (minRSSU). Additionally, we take into account GWCPJ-based uncertainty measures for the maximum ranked set sampling technique with unequal samples (maxRSSU). Stochastic comparison for simple random sampling (SRS) is discussed. We looked at the monotone properties of minRSSU and maxRSSU as well as stochastic comparison. The empirical estimators of GWCPJ and GWCRJ are obtained and a simulation study for comparing the proposed estimator will be given involving the proposed ranked set sampling schemes under perfect ranking.

Monitoring of manufacturing process using bayesian EWMA control chart under ranked based sampling designs

Control charts, including exponentially moving average (EWMA) , are valuable for efficiently detecting small to moderate shifts. This study introduces a Bayesian EWMA control chart that employs ranked set sampling (RSS) with known prior information and two distinct loss functions (LFs), the Square Error Loss function (SELF) and the Linex Loss function (LLF), for posterior and posterior predictive distributions. The chart's performance is assessed using average run length (ARL) and standard deviation of run length (SDRL) profiles, and it is compared to the Bayesian EWMA control chart based on simple random sampling (SRS). The results indicate that the proposed control chart detects small to moderate shifts more effectively. The application in semiconductor manufacturing provides concrete evidence that the Bayesian EWMA control chart, when implemented with RSS schemes, demonstrates a higher degree of sensitivity in detecting deviations from normal process behavior. Comparison to the Bayesian EWMA control chart using SRS, it exhibits a superior ability to identify and flag instances where the manufacturing process is going out of control. This heightened sensitivity is critical for promptly addressing and rectifying issues, which ultimately contributes to improved quality control in semiconductor production.

Adaptive EWMA control chart for monitoring the coefficient of variation under ranked set sampling schemes

In this study, we introduce an Adaptive Exponentially Weighted Moving based Coefficient of Variation (AEWMCV) control chart, designed to address situations where the process mean fluctuates over time and the standard deviation of the process changes linearly with the process mean. To enhance the efficiency and effectiveness of the control chart, we integrate the ranked set sampling method and its modified schemes, such as Simple Random Sampling, Quartile RSS, Median RSS, and Extreme RSS. The performance of the proposed AEWMCV control chart and the studied CV control charts are evaluated using the Average Run Length and Standard Deviation of Run Length metrics. Our findings reveal that the proposed control chart outperforms the existing CV control charts, especially in detecting slight to moderate changes in the process CV. To illustrate the practical applicability of the suggested control chart, we present an example demonstrating its use on a real dataset. The results highlight the superior performance of the AEWMCV control chart in accurately detecting and responding to changes in the process CV. In conclusion, our study introduces an innovative AEWMCV control chart that combines ranked set sampling and its modified schemes to enhance performance in scenarios with fluctuating process means and changing standard deviations. The proposed control chart proves to be more effective in detecting subtle variations in the process CV compared to traditional CV control charts. This research provides a valuable contribution to the field of control chart methodology, especially when dealing with challenging or costly data collection scenarios.

VARIANCE ESTIMATORS USING NON-PARAMETRIC APPROACH UNDER DIFFERENT RANKED SET SAMPLING SCHEMES

Estimation of variance is a commonly discussed topic under simple random sampling (SRS) scheme. The current article deals the issue of variance estimation utilizing supplementary information with the nonparametric approach under different ranked set sampling (RSS) schemes. We propose a class of nonparametric variance estimators utilizing kernel regression [1] with different bandwidths (Plug-in and Cross-validation), under RSS schemes. Simulation study is provided utilizing diverse data sets. The comparison of simulation results has been made between the members of the proposed class with respect to the unbiased variance estimator.

Performance of Bayesian EWMA control chart with measurement error under ranked set sampling schemes with application in industrial engineering

The objective of this study is to investigate the behavior of the Bayesian exponentially weighted moving average (EWMA) control chart in the presence of measurement error (ME). It explores the impact of different ranked set sampling designs and loss functions on the performance of the control chart when ME is present. The analysis incorporates a covariate model, multiple measurement methods, and a conjugate prior to account for ME. The performance evaluation of the proposed Bayesian EWMA control chart with ME includes metrics such as average run length and standard deviation of run lengths. The findings, obtained through Monte Carlo simulation and real data application, indicated that ME significantly affects the performance of the Bayesian EWMA control chart when RSS schemes are employed. Particularly noteworthy is the superior performance of the median RSS scheme compared to the other two schemes in the presence of ME.

Dual-rank ranked set sampling

In this paper, we propose a new sampling design extending the well-known ranked set sampling, which we named dual-rank ranked set sampling. Unlike the original ranked set sampling scheme, dual-rank ranked set sampling is based on two ranking sets stages, as the double ranked set sampling design. Dual-rank ranked set sampling differs from double ranked set sampling, however, since it requires only n 2 initially selected units to draw a sample of size n, whereas double ranked set sampling is based on n 3 units to provide a sample of similar size. We verified that the dual-rank ranked set sampling sample estimator of the population mean is an unbiased estimator for the corresponding population parameter when the underlying distribution is symmetric. A simulation study was carried out to evaluate the efficiency of dual-rank ranked set sampling. The simulation results pointed out that dual-rank ranked set sampling estimation is more efficient than simple random sampling and ranked set sampling, and it is a cost-effective alternative to double ranked set sampling estimation. The problem of interval estimation for dual-rank ranked set sampling was also addressed. An application based on fish ageing data is finally presented.

Improved model fitting approaches under ranked set sampling schemes with application to forest data

In this paper, we address the problem of fitting probabilistic models based on several sampling designs that originated from the ranked set sampling (RSS) scheme. Although these sampling designs have been proved to be efficient and/or economical alternatives to simple random sampling (SRS) and RSS, the problem of model fitting still should be properly studied for a complete understanding of their advantages. In this study, we investigated the performance of eight RSS-based designs, among them the recently proposed modified neoteric RSS (Taconeli & Cabral, 2019), combined with six estimation methods in model fitting. Through extensive simulations, we could identify the combinations that provided higher efficiency. The simulated results showed that the RSS-based designs outperformed SRS in model fitting, whereas the Anderson-Darling and maximum product of spacings were the most efficient among the estimation methods. In addition, the Anderson-Darling and maximum product of spacings estimation, combined with the neoteric RSS design and its variants, allowed the highest efficiency under both perfectand imperfect ranking. Additional simulations based on real data set from a forest inventory corroborated these findings.

Adaptive EWMA control chart using Bayesian approach under ranked set sampling schemes with application to Hard Bake process

The memory-type control charts, such as cumulative sum (CUSUM) and exponentially weighted moving average control chart, are more desirable for detecting a small or moderate shift in the production process of a location parameter. In this article, a novel Bayesian adaptive EWMA (AEWMA) control chat utilizing ranked set sampling (RSS) designs is proposed under two different loss functions, i.e., square error loss function (SELF) and linex loss function (LLF), and with informative prior distribution to monitor the mean shift of the normally distributed process. The extensive Monte Carlo simulation method is used to check the performance of the suggested Bayesian-AEWMA control chart using RSS schemes. The effectiveness of the proposed AEWMA control chart is evaluated through the average run length (ARL) and standard deviation of run length (SDRL). The results indicate that the proposed Bayesian control chart applying RSS schemes is more sensitive in detecting mean shifts than the existing Bayesian AEWAM control chart based on simple random sampling (SRS). Finally, to demonstrate the effectiveness of the proposed Bayesian-AEWMA control chart under different RSS schemes, we present a numerical example involving the hard-bake process in semiconductor fabrication. Our results show that the Bayesian-AEWMA control chart using RSS schemes outperforms the EWMA and AEWMA control charts utilizing the Bayesian approach under simple random sampling in detecting out-of-control signals.

On Cox proportional hazards model performance under different sampling schemes.

Cox's proportional hazards model (PH) is an acceptable model for survival data analysis. This work investigates PH models' performance under different efficient sampling schemes for analyzing time to event data (survival data). We will compare a modified Extreme, and Double Extreme Ranked Set Sampling (ERSS, and DERSS) schemes with a simple random sampling scheme. Observations are assumed to be selected based on an easy-to-evaluate baseline available variable associated with the survival time. Through intensive simulations, we show that these modified approaches (ERSS and DERSS) provide more powerful testing procedures and more efficient estimates of hazard ratio than those based on simple random sampling (SRS). We also showed theoretically that Fisher's information for DERSS is higher than that of ERSS, and ERSS is higher than SRS. We used the SEER Incidence Data for illustration. Our proposed methods are cost saving sampling schemes.

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.

Generalized Power Transformation Estimators in Stratified Ranked Set Sampling using Auxiliary Information

Auxiliary variable is commonly used in survey sampling to improve the precision of estimates. Whenever there is auxiliary information available, the researchers want to utilize it in the method of estimation to obtain the most efficient estimator. Stratified simple random sampling (SSRS) is used in certain types of surveys because it combines the conceptual simplicity of simple random sampling (SRS) with potentially significant gains in efficiency. It is a convenient technique to use whenever we wish to ensure that our sample is representative of the, population and also to obtain separate estimates for parameters of each sub domain of the population. Stratified Ranked Set Sampling combines the advantages of Stratification and Ranked set sampling (RSS) to obtain an unbiased estimator for the population mean, with potentially significant gains in efficiency. Under Stratified ranked set sampling scheme, we have suggested two general estimators using power transformation to estimate the population mean of the study variable. These methods are highly beneficial to the estimation based on Stratified Simple Random Sampling (SSRS). The first order approximation to the bias and mean square error (MSE) of the proposed estimators are obtained. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in Stratified simple random sampling. A numerical illustration is also included to demonstrate the merits of the proposed estimator using SRSS over the corresponding estimators in SSRS.

Hybrid EWMA Control Chart under Bayesian Approach Using Ranked Set Sampling Schemes with Applications to Hard-Bake Process

A memory-type control chart is an important tool of statistical process control for monitoring small to moderate shifts in the manufacturing process. Using the prior information by the Bayesian approach is helpful in control charts. In this paper, a new hybrid exponentially weighted moving average (HEWMA) control chart is suggested under the Bayesian theory using ranked set sampling (RSS) schemes for posterior and posterior predictive distribution with informative prior and different loss functions (LFs). The extensive Monto Carlo simulation is conducted to evaluate the overall performance of the proposed Bayesian HEWMA control chart through average-run-length (ARL) and standard-deviation of the run-length (SDRL). Finally, a numerical example of the hard-bake process in semiconductor manufacturing is used to check the working and execution of the proposed Bayesian HEWMA control-chart under different RSS schemes. The results reveal that the suggested Bayesian HEWMA control-chart under RSS schemes is more sensitive in detecting out-of-control signals than the Bayesian HEWMA and Bayesian AEWMA control-charts under simple random sampling.