Abstract
In this paper, a control chart scheme has been introduced for the mean monitoring using gamma distribution for belief statistics using multiple dependent (deferred) state sampling under the neutrosophic statistics. The coefficients of the control chart and the neutrosophic average run lengths have been estimated for specific false alarm probabilities under various process conditions. The offered chart has been compared with the existing classical chart through simulation and the real data. From the comparison, it is concluded that the performance of the proposed chart is better than that of the existing chart in terms of average run length under uncertain environment. The proposed chart has the ability to detect a shift quickly than the existing chart. It has been observed that the proposed chart is efficient in quick monitoring of the out-of-control process and a cherished addition in the toolkit of the quality control personnel.
Highlights
Introduction e control chart is a key technique to statistical process control to ensure the quality of the production process. e technique of control chart requires the construction of a central line, and two control limits are known as the lower control limit (LCL) and upper control limit (UCL). e quality characteristic of interest is plotted on this chart for the quick monitoring of an observation falling outside these two limits. e idea of control chart was floated by Shewhart A
E technique of multiple dependent state (MDS) sampling was announced by Wortham and Baker [9] in which the decision for in-control process or out-of-control process is established upon the current information of the process and considers the previous record of the process
By exploring the literature and best of our knowledge, there is no work on the control chart using the belief statistic for MDS. e process monitoring using the belief statistic for neutrosophic statistics under the gamma distribution using MDS sampling has not been studied by any researcher yet
Summary
E evaluation of the functioning of the developed control chart is judged by calculating the average run length (ARL) that is very commonly suggested by the quality control researchers [47]. It is defined as the average of all the samples until the process shows the deterioration. The probability of the out-of-control process for the shifted process at kth sample is calculated as follows: Pin1N PLCL2N ≤ lnZkN ≤ UCL2N,. En, the procedure to compute the control chart coefficient and ARL of the shifted process may be followed as. We observe that as a decreases from aε[1.95, 2.05] to aε[0.95, 1.05 ], the values of NARL increase
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