Design of Sampling Plan Using Regression Estimator under Indeterminacy

The acceptance sampling plans are one of the most important tools for the inspection of a lot of products. Sometimes, it is difficult to study the variable of interest, and some additional or auxiliary information which is correlated to that variable is available

Capability Indices for Non-Normal Distribution using Gini’s Mean Difference as Measure of Variability

This paper investigates the efficiency of Gini's mean difference (GMD) as a measure of variability in two commonly used process capability indices (PCIs), i.e., Cp and Cpk. A comparison has been carried out to evaluate the performance of GMD-based PCIs and Pearn and Chen quantile-based PCIs under low, moderate, and high asymmetry using Weibull distribution. The simulation results, under low and moderate asymmetric condition, indicate that GMD-based PCIs are more close to target values than quantile approach. Beside point estimation, nonparametric bootstrap confidence intervals, such as standard, percentile, and bias corrected percentile with their coverage probabilities also have been calculated. Using quantile approach, bias corrected percentile (BCPB) method is more effective for both Cp and Cpk, where as in case of GMD, both BCPB and percentile bootstrap method can be used to estimate the confidence interval of Cp and Cpk, respectively.1133Ysciescopu

A Nonparametric HEWMA-p Control Chart for Variance in Monitoring Processes

Control charts are considered as powerful tools in detecting any shift in a process. Usually, the Shewhart control chart is used when data follows the symmetrical property of a normal distribution. In practice, the data from the industry may follow a non-symmetrical distribution or an unknown distribution. The average run length (ARL) is a significant measure to assess the performance of the control chart. The ARL may mislead when the statistic is computed from an asymmetric distribution. To handle this issue, in this paper, an ARL-unbiased hybrid exponentially weighted moving average proportion (HEWMA-p) chart is proposed for monitoring the process variance for a non-normal distribution or an unknown distribution. The efficiency of the proposed chart is compared with the existing chart in terms of ARLs. The proposed chart is more efficient than the existing chart in terms of ARLs. A real example is given for the illustration of the proposed chart in the industry.11Ysciescopu

Evaluation of Modified Non-Normal Process Capability Index and Its Bootstrap Confidence Intervals

Process capability index (PCI) is used to quantify the process performance and is becoming an attracted area of research. A variability measure plays an important role in PCI. The interquartile range (IQR) or the median absolute deviation (MAD) is commonly used for a variability measure in estimating PCI when a process follows a non-normal distribution In this paper, the efficacy of the IQR and MAD-based PCIs was evaluated under low, moderate, and high asymmetric behavior of the Weibull distribution using different sample sizes through three different bootstrap confidence intervals. The result reveals that MAD performs better than IQR, because the former produced less bias and mean square error. Also, the percentile bootstrap confidence interval is recommended for use, because it has less average width and high coverage probability.11Ysciescopu

A Multiple Dependent State Repetitive Sampling Plan Based on Performance Index for Lifetime Data with Type II Censoring

In this paper, a multiple dependent state repetitive (MDSR) sampling plan based on the lifetime performance index C-L is proposed for lifetime data with type II censoring when the lifetime of a product follows the exponential distribution or Weibull distribution. The optimal parameters of the proposed plan are determined by minimizing the average sample number while satisfying the producer's risk and consumer's risk at corresponding quality levels. Besides, the performance of the proposed plan is compared with that of the existing lifetime sampling plan in terms of the average sample number and operating characteristic curve. Two illustrative examples are given for the demonstration of the proposed plan.11Ysciescopu

Design of Sampling Plan Using Regression Estimator under Indeterminacy

The acceptance sampling plans are one of the most important tools for the inspection of a lot of products. Sometimes, it is difficult to study the variable of interest, and some additional or auxiliary information which is correlated to that variable is available. The existing sampling plans having auxiliary information are applied when the full, precise, determinate and clear data is available for lot sentencing. Neutrosophic statistics, which is the extension of classical statistics, can be applied when information about the quality of interest or auxiliary information is unclear and indeterminate. In this paper, we will introduce a neutrosophic regression estimator. We will design a new sampling plan using the neutrosophic regression estimator. The neutrosophic parameters of the proposed plan will be determined through the neutrosophic optimization solution. The efficiency of the proposed plan is discussed. The results of the proposed plan will be explained using real industrial data. From the comparison, it is concluded that the proposed sampling plan is more effective and adequate for the inspection of a lot than the existing plan, under the conditions of uncertainty

A New X-Bar Control Chart for Using Neutrosophic Exponentially Weighted Moving Average

The existing Shewhart X-bar control charts using the exponentially weighted moving average statistic are designed under the assumption that all observations are precise, determined, and known. In practice, it may be possible that the sample or the population observations are imprecise or fuzzy. In this paper, we present the designing of the X-bar control chart under the symmetry property of normal distribution using the neutrosophic exponentially weighted moving average statistics. We will first introduce the neutrosophic exponentially weighted moving average statistic, and then use it to design the X-bar control chart for monitoring the data under an uncertainty environment. We will determine the neutrosophic average run length using the neutrosophic Monte Carlo simulation. The efficiency of the proposed plan will be compared with existing control charts

Design of Variable Sampling Plan for Pareto Distribution Using Neutrosophic Statistical Interval Method

The sampling plans have been widely used for the inspection of a lot of the product. In practice, the measurement data may be imprecise, uncertain, unclear or fuzzy. When there is uncertainty in the observations, the sampling plans designed using classical statistics cannot be applied for the inspection of a lot of the product. The neutrosophic statistic, which is the generalization of the classical statistics, can be used when data is not precise, uncertain, unclear or fuzzy. In this paper, we will design the variable sampling plan under the Pareto distribution using the neutrosophic statistics. We used the symmetry property of the normal distribution. We assume uncertainty in measurement data and sample size required for the inspection of a lot of the product. We will determine the neutrosophic plan parameters using the neutrosophic optimization problem. Some tables are given for practical use and are discussed with the help of an example

Time-Truncated Group Plan under a Weibull Distribution based on Neutrosophic Statistics

The aim of reducing the inspection cost and time using acceptance sampling can be achieved by utilizing the features of allocating more than one sample item to a single tester. Therefore, group acceptance sampling plans are occupying an important place in the literature because they have the above-mentioned facility. In this paper, the designing of a group acceptance sampling plan is considered to provide assurance on the product’s mean life. We design the proposed plan based on neutrosophic statistics under the assumption that the product’s lifetime follows a Weibull distribution. We determine the optimal parameters using two specified points on the operating characteristic curve. The discussion on how to implement the proposed plan is provided by an illustrative example