# Time-Truncated Group Plan under a Weibull Distribution based on Neutrosophic Statistics
## 1 Introduction  
The ambition of each producer is to globalize their business by means of marketing the products. However, few producers reach this goal since they only make sincere efforts in improving and controlling the product's quality to accomplish this target. The producer who enhances the product's quality need not concern its globalization because the continuous improvement in quality helps to increase the positive opinion of the products and to fulfill the consumer's expectations. Hence, the involvement of the producers with great efforts supports to attain the desired result and to achieve the ambition. For quality improvement and maintenance purposes, the producer uses certain statistical techniques, namely control charts and acceptance sampling (see [PERSON] [1] and [PERSON] [2]). In spite of the application of control charts in quality maintenance via monitoring the manufacturing process, it is not suitable for assuring the quality of the finished products. But there is a necessity to provide quality assurance for the products before they are received by the consumer. Under this situation, the manufacturers may prefer complete inspection. However, complete inspections are not appropriate for all situations because they are costly, require quality inspectors, and are time consuming. Therefore, in most of the cases, manufacturers adopt sampling inspections to provide quality assurance. In sampling inspection, a sample of items is selected randomly from the entire lot for inspection. Acceptance sampling is also a form of sampling inspection, in which the decision to accept or reject a lot is made based on the results of sample items taken from the concerned lot. Obviously, acceptance sampling overcomes the drawbacks of complete inspections, such as inspection cost and time consumption, since it inspects only a part of the items of the lot for making decisions. Acceptance sampling plans yield the sample size and acceptance criteria associated with the sampling rules to be implemented. For further details on acceptance sampling, one may refer to [PERSON] [3] and [PERSON] [2]. In the literature, several sampling plans are available for lot sentencing with different sampling procedures; however, a single-sampling plan (SSP) is the most basic, as well as the easiest, sampling plan in terms of the implementation process. In SSP, a single sample of size \(n\) is taken for lot sentencing, and the acceptance/rejection decision is made immediately by comparing the sample results with acceptance numbers determined from attribute inspections or with acceptance criteria from variables inspections. Many authors have investigated SSPs under various situations (see, for example, [PERSON] et al. [4], [PERSON] and [PERSON] [5], [PERSON] [6], and [PERSON] and [PERSON] [7]). In SSP implementation, a sample of \(n\) items is distributed to \(n\) testers, and the decision is made after consolidating the information obtained from all the testers. Obviously, it requires much time to make a decision, and the inspection cost is also high. One can overcome these drawbacks by implementing a group acceptance sampling plan (GASP) instead of using SSP. In GASP, a certain number of sample items are allocated to a single tester, and the test is conducted simultaneously on the sample items. Therefore, the testing time and inspection cost are reduced automatically under GASP when compared to SSP. It is to be mentioned that the number of testers involved in the inspection is frequently referred to as the number of groups, and the number of sample items allocated to each group is defined as the group size. For the purposes of making a decision on the lot by utilizing minimum cost and time, GASP has been used for the inspection of different quality characteristics by several authors (see, for example, [PERSON] and [PERSON] [8]). When industrial practitioners are uncertain about the parameters, the inspection cannot be done using traditional sampling plans.