Abstract
In this article, a repetitive sampling control chart for the gamma distribution under the indeterminate environment has been presented. The control chart coefficients, probability of in-control, probability of out-of-control, and average run lengths have been determined under the assumption of the symmetrical property of the normal distribution using the neutrosophic interval method. The performance of the designed chart has been evaluated using the average run length measurements under different process settings for an indeterminate environment. In-control and out-of-control nature of the proposed chart under different levels of shifts have been described. The comparison of the proposed chart has been made with the existing chart. A real-world example from the healthcare department has been included for the practical application of the proposed chart. It has been observed from the simulation study and real example that the proposed control chart is efficient in quick monitoring of the out-of-control process. It can be concluded that the proposed control chart can be applied effectively in uncertainty.
Highlights
Repetitive sampling scheme (RSS) is an efficient sampling scheme for the statistical process control techniques that attracted the attention of many researchers during the last two decades. e RSS was basically introduced by Journal of Mathematics
Many control charts have been developed for monitoring the skewed statistic and proved to be effective and useful, for example, Jearkpaporn et al [30] developed a monitoring scheme to detect a shift in the shape parameter, Zhang et al [31] developed the gamma chart based on the random shift model for monitoring the out-of-control process, Chen and Yeh [32] developed an X-bar chart for nonnormal distribution using the gamma distribution, and Gonzalez and Viles [33] presented the method to monitor the variable quality characteristic using the r-chart under the gamma distribution
We will measure the efficiency of the proposed control chart under the neutrosophic average run length (NARL) which shows on the average when the process is out-ofcontrol and is defined by
Summary
Let the neutrosophic failure time be TN ∈ [TL, TU], where TL and TU represent the indeterminacy interval of lower and upper failures of an item that follows the neutrosophic gamma distribution with neutrosophic scale parameter bN ∈ [bL, bU] and neutrosophic shape parameter aN ∈ [aL, aU]. en, the neutrosophic probability density function (npdf ) of the neutrosophic gamma distribution is given as f tN. Let the neutrosophic failure time be TN ∈ [TL, TU], where TL and TU represent the indeterminacy interval of lower and upper failures of an item that follows the neutrosophic gamma distribution with neutrosophic scale parameter bN ∈ [bL, bU] and neutrosophic shape parameter aN ∈ [aL, aU]. En, the neutrosophic probability density function (npdf ) of the neutrosophic gamma distribution is given as f tN. > 0; aN ∈ aL, aU, bN ∈ bL, bU, where Γ(x) describes the neutrosophic gamma function; for more details, readers may refer to [20]. E resultant neutrosophic cumulative distribution (ncd) of the neutrosophic Gamma distribution (NGD) is. It is to be noted that the NGD under the classic statistics is the generalization of the traditional gamma distribution. E mean and variance of the neutrosophic statistics can be written as μN aN; bN aN ∈ aL, aU, bN ∈ bL, bU,
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