# A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method

## Abstract

**:**

## 1. Introduction

## 2. Neutrosophic Approach

## 3. Design of the Proposed Plan Neutrosophic Interval Method

**Step-1:**Select a random sample of size ${n}_{L}\le {n}_{N}\le {n}_{U}$; ${n}_{N}\in \left\{{n}_{L},{n}_{U}\right\}$ from the lot of product. Compute the statistic ${v}_{N}=\frac{U-{\overline{X}}_{N}}{{s}_{N}}$, where ${\overline{X}}_{N}\in \left\{{\overline{X}}_{L},{\overline{X}}_{U}\right\}$; ${\overline{X}}_{L}={{\displaystyle \sum}}_{i=1}^{n}{x}_{i}^{L}/{n}_{L},$ ${\overline{X}}_{U}={{\displaystyle \sum}}_{i=1}^{n}{x}_{i}^{U}/{n}_{U}$, and ${s}_{N}\in \left\{{s}_{L},{s}_{U}\right\}$, where ${s}_{L}=\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{({x}_{i}^{L}-{\overline{X}}_{L})}^{2}/{n}_{L}}$ and ${s}_{U}=\sqrt{{{\displaystyle \sum}}_{i=1}^{n}{({x}_{i}^{U}-{\overline{X}}_{U})}^{2}/{n}_{U}}$; $i=$1,2,3,…,$n$.**Step-2:**Accept the lot of product of $v\ge {k}_{Na}$; ${k}_{N}\in \left\{{k}_{aL},{k}_{aU}\right\}$ where ${k}_{Na}$ is the neutrosophic acceptance number.

- For the fixed values AQL,${n}_{N}\in \left\{{n}_{L},{n}_{U}\right\}$ decreases as LQL increases.
- For the fixed values AQL,${k}_{Na}\in \left\{{k}_{aL},{k}_{aU}\right\}$ decreases as LQL increases.

#### Comparative Study

## 4. Application of the Proposed Plan

**Step-1:**select a random sample of size ${n}_{N}$ = $\left\{{n}_{L},{n}_{U}\right\}$ from a lot of product. Compute the statistic ${v}_{N}=\frac{U-{\overline{X}}_{N}}{{s}_{N}}=\frac{\left[12,500,12,500\right]-\left[11,715.2,11,719.6\right]}{\left[49.21,49.70\right]}$, so ${v}_{N}\in \left[15.70,15.94\right]$.**Step-2:**Accept a lot of the product of ${v}_{N}\ge {k}_{N}$; ${k}_{Na}\in \left\{{k}_{aL},{k}_{aU}\right\}$. From Table 1, we have ${k}_{Na}\in $ {0.99, 1.02}. So, ${v}_{N}\ge {k}_{Na}$, the lot of product, should be accepted to send to the market.

## 5. Concluding Remarks

## Funding

## Acknowledgments

## Conflicts of Interest

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p_{1} | p_{2} | ${\mathit{n}}_{\mathit{N}}$ | ${\mathit{k}}_{\mathit{N}\mathit{a}}$ | ${\mathit{L}}_{\mathit{N}}\left({\mathit{p}}_{1}\right)$ | ${\mathit{L}}_{\mathit{N}}\left({\mathit{p}}_{2}\right)$ |
---|---|---|---|---|---|

0.001 | 0.002 | {388,569} | {1.062,1.068} | {0.0151,0.065} | {0.9501,0.9502} |

0.003 | {213,268} | {1.05,1.055} | {0.000,0.000} | {0.9501,0.9502} | |

0.004 | {180,213} | {1.046,1.05} | {0.000,0.000} | {0.9500,0.9502} | |

0.006 | {139,150} | {1.039,1.041} | {0.000,0.000} | {0.9504,0.9508} | |

0.008 | {103,130} | {1.03,1.037} | {0.000,0.000} | {0.9500,0.9506} | |

0.010 | {78,117} | {1.02,1.034} | {0.000,0.026} | {0.9501,0.9506} | |

0.015 | {61,100} | {1.01,1.029} | {0.000,0.007} | {0.9500,0.9512} | |

0.020 | {50,80} | {0.99,1.02} | {0.000,0.010} | {0.9527,0.6983} | |

0.0025 | 0.030 | {143,233} | {0.696,0.706} | {0.0173,0.0847} | {0.9501,0.9504} |

0.050 | {138,213} | {0.695,0.705} | {0.0214,0.0937} | {0.9504,0.9506} | |

0.005 | 0.050 | {77,83} | {0.708,0.711} | {0.9999,1.000} | {0.0791,0.0990} |

0.100 | {15,22} | {0.77,0.795} | {0.0012,0.0118} | {0.9545,0.9577} | |

0.01 | 0.020 | {184,210} | {0.812,0.814} | {0.0731,0.0985} | {0.9500,0.9536} |

0.030 | {95,102} | {0.794,0.796} | {0.0275,0.0358} | {0.9502,0.9508} | |

0.03 | 0.060 | {127,149} | {0.669,0.673} | {0.0638,0.0992} | {0.9516,0.9520} |

0.090 | {112,121} | {0.666,0.668} | {0.0010,0.0018} | {0.9502,0.9507} | |

0.05 | 0.100 | {125,132} | {0.60,0.614} | {0.0029,0.0551} | {0.9501,0.9503} |

0.150 | {38,40} | {0.557,0.559} | {0.0812,0.0921} | {0.9512,0.9519} |

**Table 2.**The comparison of neutrosophic plan with plan under classical Statistics, when$\alpha =0.05$, $\beta $ = 0.05.

p_{1} | p_{2} | Proposed Plan | Existing Plan |
---|---|---|---|

${\mathit{n}}_{\mathit{N}}$ | $\mathit{n}$ | ||

0.001 | 0.002 | {388,569} | 388 |

0.001 | 0.010 | {78,117} | 78 |

0.001 | 0.020 | {50,80} | 50 |

0.005 | 0.050 | {77,83} | 77 |

0.005 | 0.100 | {15,22} | 15 |

0.01 | 0.020 | {184,210} | 184 |

0.01 | 0.030 | {95,102} | 95 |

0.05 | 0.100 | {125,132} | 125 |

[11,816.7,11,816.7] | [11,710.1,11,710.1] | [11,722.6,11,823.5] | [11,744.1,11,744.1] | [11,681.1,11,681.1] | [11,728.4,11,728.4] |

[11,712.6,11,712.6] | [11,775.2,11,775.2] | [11,743.3,11,743.3] | [11,786.1,11,786.1] | [11,760.6,11,760.6] | [11,723.6,11,723.6] |

[11,721.7,11,721.7] | [11,698,11,698] | [11,695.9,11,695.9] | [11,726.4,11,726.4] | [11,797.2,11,797.2] | [11,773.1,11,773.1] |

[11,769.1,11,769.1] | [11,800.8,11,800.8] | [11,780.7,11,780.7] | [11,670.9,11,675.9] | [11,692.3,11,692.3] | [11,666.2,11,666.2] |

[11,755.2,11,762.5] | [11,712.7,11,712.7] | [11,775.5,11,775.5] | [11,731.2,11,731.2] | [11,625.6,11,625.6] | [11,757.5,11,757.5] |

[11,674.7,11,674.7] | [11,729.2,11,729.2] | [11,681.3,11,681.3] | [11,636.4,11,636.4] | [11,682.1,11,690.7] | [11,667.9,11,667.9] |

[11,722.9,11,722.9] | [11,655.3,11,655.3] | [11,700.2,11,700.2] | [11,754.2,11,754.2] | [11,769.9,11,769.9] | [11,705.9,11,705.9] |

[11,589.8,11,589.8] | [11,738.4,11,745.6] | [11,745.4,11,745.4] | [11,727.7,11,727.7] | [11,664.3,11,664.3] | [11,647.2,11,647.2] |

[11,755,11,755] | [11,671.8,11,671.8] | [11,705.8,11,705.8] | [11,664.2,11,664.2] | [11,677.0,11,695.2] | [11,680.5,11,687.4] |

[11,633.6,11,633.6] |

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Aslam, M.
A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method. *Symmetry* **2019**, *11*, 114.
https://doi.org/10.3390/sym11010114

**AMA Style**

Aslam M.
A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method. *Symmetry*. 2019; 11(1):114.
https://doi.org/10.3390/sym11010114

**Chicago/Turabian Style**

Aslam, Muhammad.
2019. "A Variable Acceptance Sampling Plan under Neutrosophic Statistical Interval Method" *Symmetry* 11, no. 1: 114.
https://doi.org/10.3390/sym11010114