scholarly journals Testing of Grouped Product for the Weibull Distribution Using Neutrosophic Statistics

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 403 ◽  
Author(s):  
Muhammad Aslam ◽  
Osama Arif
Keyword(s):  
Sudden Death ◽  
Weibull Distribution ◽  
Failure Time ◽  
Fuzzy Optimization ◽  
Testing Time ◽  
Continuous Variables ◽  
Failure Data ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
Testing Plan

Parts manufacturers use sudden death testing to reduce the testing time of experiments. The sudden death testing plan in the literature can only be applied when all observations of failure time/parameters are crisp. In practice however, it is noted that not all measurements of continuous variables are precise. Therefore, the existing sudden death test plan can be applied if failure data/or parameters are imprecise, incomplete, and fuzzy. The classical statistics have the special case of neutrosophic statistics when there are no fuzzy observations/parameters. The neutrosophic fuzzy statistics can be applied for the testing of manufacturing parts when observations are imprecise, incomplete and fuzzy. In this paper, we will design an original neutrosophic fuzzy sudden death testing plan for the inspection/testing of the electronic product or parts manufacturing. We will assume that the lifetime of the product follows the neutrosophic fuzzy Weibull distribution. The neutrosophic fuzzy operating function will be given and used to determine the neutrosophic fuzzy plan parameters through a neutrosophic fuzzy optimization problem. The results of the proposed neutrosophic fuzzy death testing plan will be implemented with the aid of an example.

scholarly journals A new sudden death chart for the Weibull distribution under complexity

2021 ◽  
Author(s):  
Osama H. Arif ◽  
Muhammad Aslam
Keyword(s):  
Sudden Death ◽  
Control Chart ◽  
Control Process ◽  
Value Addition ◽  
Detection Ability ◽  
Classical Statistics ◽  
Monitoring Reliability ◽  
Neutrosophic Statistics ◽  
Industrial Use ◽  
Run Lengths

AbstractThis article presents a new control chart for monitoring reliability using sudden death testing under the neutrosophic statistics (NS). The average run lengths of the in-control and the out-of-control process have been determined for evaluating the quick detection ability for small and moderate shifts. For the industrial use, tables and figures have been presented for different parameters. The proposed control chart is efficient in comparison with the existing control chart under classical statistics and value addition in the toolkit of the quality control personnel.

scholarly journals Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

2021 ◽  
Author(s):  
Muhammad Aslam ◽  
G. Srinivasa Rao ◽  
Nasrullah Khan
Keyword(s):  
Weibull Distribution ◽  
Shape Parameter ◽  
Sampling Plan ◽  
Sampling Plans ◽  
Interval Method ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
Total Failure ◽  
Life Tests ◽  
Double Group

AbstractIf the sample or population has vague, inaccurate, unidentified, deficient, indecisive, or fuzzy data, then the available sampling plans could not be suitable to use for decision-making. In this article, an improved group-sampling plan based on time truncated life tests for Weibull distribution under neutrosophic statistics (NS) has been developed. We developed improved single and double group-sampling plans based on the NS. The proposed design neutrosophic plan parameters are obtained by satisfying both producer’s and consumer’s risks simultaneously under neutrosophic optimization solution. Tables are constructed for the selected shape parameter of Weibull distribution and various combinations of neutrosophic group size. The efficiency of the proposed group-sampling plan under the neutrosophic statistical interval method is also compared with the crisp method grouped sampling plan under classical statistics.

scholarly journals A new goodness of fit test in the presence of uncertain parameters

2020 ◽  
Author(s):  
Muhammad Aslam
Keyword(s):  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Testing Procedure ◽  
Uncertain Parameters ◽  
Goodness Of Fit Test ◽  
Reliability Data ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
Quality And Reliability ◽  
Anderson Darling

Abstract The Weibull distribution has been widely used in the areas of quality and reliability. The Anderson–Darling test has been popularly used either the data in hand follow the Weibull distribution or not. The existing Anderson–Darling test under classical statistics is applied when all the observations in quality and reliability work are determined, précised, and exact. In the areas of reliability and quality, the data may indeterminate, in-interval and fuzzy. In this case, the existing Anderson–Darling test cannot be applied for testing the assumption of the Weibull distribution. In this paper, we present the Anderson–Darling test under neutrosophic statistics. We present the methodology to fit the neutrosophic Weibull distribution on the data. We discuss the testing procedure with the help of reliability data. We present the comparisons of the proposed test with the existing Anderson–Darling the goodness of fit test under classical statistics. From the comparison, it is concluded that the proposed test is more informative than the existing Anderson–Darling test under an indeterminate environment. In addition, the proposed test gives information about the measure of indeterminacy.

scholarly journals Control Chart for Failure-Censored Reliability Tests under Uncertainty Environment

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 690 ◽  
Author(s):  
Muhammad Aslam ◽  
Nasrullah Khan ◽  
Mohammed Albassam
Keyword(s):  
Weibull Distribution ◽  
Control Chart ◽  
Control Charts ◽  
Scale Parameter ◽  
Type Ii ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
Uncertainty Environment

Existing control charts based on failure-censored (Type-II) reliability tests were designed using classical statistics. Classical statistics was applied for the monitoring of the process when observations in the sample or the population were determined. Neutrosophic statistics (NS) are applied when there is uncertainty in the sample or population. In this paper, a control chart for failure-censored (Type-II) reliability tests was designed using NS. The design of a control chart for the Weibull distribution, which is applied when there is a lack of symmetry using neutrosophic statistics, is given. The proposed control chart was used to monitor the neutrosophic mean and neutrosophic variance, which are related to the neutrosophic scale parameter. The advantages of the proposed control chart over the existing control chart are discussed.

A Reliability Data Analysis Method Using Mixture Weibull Distribution Model

2011 ◽  
Vol 148-149 ◽  
pp. 1449-1453 ◽  
Author(s):  
Ying Kui Gu ◽  
De Liang Ge ◽  
Yao Gang Xiong
Keyword(s):  
Weibull Distribution ◽  
Failure Time ◽  
Likelihood Estimation ◽  
Weibull Model ◽  
Distribution Model ◽  
Time Data ◽  
Failure Rate Function ◽  
Failure Data ◽  
Wide Range ◽  
Rod System

The weibull distribution plays a crucial role in reliability theory and life-testing experiments. Weibull mixtures are widely used to model lifetime and failure time data, since they exhibit a wide range of shapes for the failure rate function. In this paper, the failure data of crank rod system was analyzed by using mixture weibull distribution model. The distribution parameters of the mixture weibull distribution model were estimated by using maximum likelihood estimation and drawing method. The comparison of fitting degree of failure location between standard weibull distribution model and mixture weibull model was given. Results show that the fitting degree of the failure data in the mixture weibull distribution model is higher than that of the simple weibull distribution model, and it can more accurately described the failure distribution curve of the system in life cycle.

scholarly journals Neutrosophic ratio-type estimators for estimating the population mean

2021 ◽  
Author(s):  
Zaigham Tahir ◽  
Hina Khan ◽  
Muhammad Aslam ◽  
Javid Shabbir ◽  
Yasar Mahmood ◽  
...  
Keyword(s):  
Minimum Mean Square Error ◽  
Auxiliary Information ◽  
Population Parameter ◽  
Uncertain Information ◽  
Population Mean ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
The Mean ◽  
Type Data ◽  
First Time

AbstractAll researches, under classical statistics, are based on determinate, crisp data to estimate the mean of the population when auxiliary information is available. Such estimates often are biased. The goal is to find the best estimates for the unknown value of the population mean with minimum mean square error (MSE). The neutrosophic statistics, generalization of classical statistics tackles vague, indeterminate, uncertain information. Thus, for the first time under neutrosophic statistics, to overcome the issues of estimation of the population mean of neutrosophic data, we have developed the neutrosophic ratio-type estimators for estimating the mean of the finite population utilizing auxiliary information. The neutrosophic observation is of the form $${Z}_{N}={Z}_{L}+{Z}_{U}{I}_{N}\, {\rm where}\, {I}_{N}\in \left[{I}_{L}, {I}_{U}\right], {Z}_{N}\in [{Z}_{l}, {Z}_{u}]$$ Z N = Z L + Z U I N where I N ∈ I L , I U , Z N ∈ [ Z l , Z u ] . The proposed estimators are very helpful to compute results when dealing with ambiguous, vague, and neutrosophic-type data. The results of these estimators are not single-valued but provide an interval form in which our population parameter may have more chance to lie. It increases the efficiency of the estimators, since we have an estimated interval that contains the unknown value of the population mean provided a minimum MSE. The efficiency of the proposed neutrosophic ratio-type estimators is also discussed using neutrosophic data of temperature and also by using simulation. A comparison is also conducted to illustrate the usefulness of Neutrosophic Ratio-type estimators over the classical estimators.

scholarly journals KAJIAN RELIABILITAS PADA SISTEM SERI-PARALEL DENGAN EMPAT KOMPONEN

2018 ◽  
Vol 7 (1) ◽  
pp. 73-83
Author(s):  
Farhah Izzatul Jannah ◽  
Sudarno Sudarno ◽  
Alan Prahutama
Keyword(s):  
Weibull Distribution ◽  
System Reliability ◽  
Failure Time ◽  
Likelihood Estimation ◽  
Parallel System ◽  
Operating Conditions ◽  
Failure Time Data ◽  
Time Data ◽  
Rank Regression ◽  
Load Resistor

Reliability analysis is the analysis of the possibility that the product or service will function properly for a certain period of time under operating conditions without failure. One configuration of components that can be formed is a series-parallel system on a filter capacitor circuit using 4 components consisting of 2 rectifier diodes, 1 capacitor, and 1 load resistor. The data used to obtain the value of system reliability is the time of failure based on the assumption of failure of the independent component. The function of the form on the system can be expressed by Ф(x)= x1x3 + x1x4 + x2x3 + x2x4 - x1x3x4 - x2x3x4 - x1x2x3 - x1x2x4 + x1x2x3x4. The parameter values of each distribution are calculated using the Median Rank Regression Estimation (MRRE) and Maximum Likelihood Estimation (MLE) methods. To test the data following a certain distribution or not, the calculation is manually done with the Anderson-Darling (AD) test so that it is known that the failure time data of rectifier diode 1 follows the weibull distribution with parameters  and , failure time data of rectifier diode 2 follows weibull distribution with parameters  and , failure time data of capacitors follow normal distribution with parameters  and , and the failure time data of the load resistor following the gamma distribution with parameters  and . From the calculation of system reliability, it shows that the higher the intensity of the system fails it will affect the value of reliability to be lower. A serial system from a parallel system functions if there is at least one component j in one subsystem that functions. Keywords: Reliability, Series-Parallel, MRRE, MLE, AD.

scholarly journals On Estimation of Number of Detectable Software Faults under Budget Constraint

2017 ◽  
Vol 2 (3) ◽  
pp. 135-139 ◽  
Author(s):  
Shinji Inoue ◽  
Kenta Hotta ◽  
Shigeru Yamada
Keyword(s):  
Software Reliability ◽  
Budget Constraint ◽  
Testing Time ◽  
Software System ◽  
Software Faults ◽  
Testing Phase ◽  
Software Reliability Model ◽  
Software Reliability Growth ◽  
Reliable Software ◽  
Testing Plan

Checking software quality and reliability of developed software system is one of the important activities for developing highly-reliable software system. In software testing phase, which is located in the final stage of software development process, software faults remaining the developed software system must be eliminated as possible as the testing manager could. Further, it is also important to develop testing plan to conduct testing activities efficiently under the certain constraints because there are some constraints, such as cost and delivery, in the actual testing phase. This paper discusses method to estimate the number of detectable faults under constant budget constraint by applying a two-dimensional Weibull type software reliability model, in which the software reliability growth process depends on testing time and testing effort factors. We finally show numerical examples of our method by using actual data.

scholarly journals Test of Association in the Presence of Complex Environment

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Muhammad Aslam ◽  
Osama H. Arif
Keyword(s):  
Contingency Tables ◽  
Complex Environment ◽  
Test Statistic ◽  
Test Of Independence ◽  
The Real ◽  
Classical Statistics ◽  
Neutrosophic Statistics

A new test of independence under neutrosophic statistics for testing the association between two criteria of classification is presented in this paper. The necessary contingency tables for the neutrosophic population and the neutrosophic sample are presented. The test statistic of the proposed test is introduced under neutrosophic statistics. A real example from education is selected to explain the proposed test. From the real example, it is concluded that the proposed test of independence is more informative, flexible, and suitable to be applied under uncertainty as compared to the existing test under classical statistics.

scholarly journals New Diagnosis Test under the Neutrosophic Statistics: An Application to Diabetic Patients

2020 ◽  
Vol 2020 ◽  
pp. 1-7 ◽  
Author(s):  
Muhammad Aslam ◽  
Osama H. Arif ◽  
Rehan Ahmad Khan Sherwani
Keyword(s):  
Gold Standard ◽  
Medical Science ◽  
Diabetic Patients ◽  
Medical Field ◽  
Classification Analysis ◽  
Classical Statistics ◽  
Neutrosophic Statistics ◽  
New Diagnosis ◽  
Uncertainty Environment ◽  
Standard Tests

The diagnosis tests (DT) under classical statistics are applied under the assumption that all observations in the data are determined. Therefore, these DT cannot be applied for the analysis of the data when some or all observations are not determined. The neutrosophic statistics (NS) which is the extension of classical statistics can be applied for the data having uncertain, unclear, and fuzzy observations. In this paper, we will present the DT, and gold-standard tests under NS are called neutrosophic diagnosis tests (NDT). Therefore, the proposed NDT is the generalization of the existing DT and can be applied under the uncertainty environment. We will present the NDT table and present a real example from the medical field. The use of the proposed method will be more effective and adequate to be used in medical science, biostatistics, decision, and classification analysis.

Sign in / Sign up

Export Citation Format

Share Document