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Trimmed samples are widely employed in several areas of statistical practice, especially when some sample values at either or both extremes might have been contaminated. The problem of estimating the parameters of Burr distribution type III based on a trimmed samples and prior information will be considered. In this paper, we study the estimation of unknown parameters based on doubly censored type II. The problem discussed using maximum likelihood method and Bayesian approach to estimate the shape parameters of Burr type III distribution. The numerical illustration requires solving nonlinear equations, therefore, MathCAD (2001) statistical package used to asses these effects numerically.

To detect indeterminacy effect in the manufacturing process, attribute control chart using neutrosophic Weibull distribution is proposed in this paper. To make the attribute control chart more efficient for persistent shifts in the industrial process, an attribute control chart using Weibull distribution has been proposed recently. In this study, a neutrosophic Weibull distribution-based attribute control chart develop for efficient monitoring of the process. The indeterminacy effect was studied with the control chart's performance using characteristics of run length. In addition, the proposed chart effectively detected shifts in uncertainty. The relative efficiency of the proposed structure is compared with the existing attribute control chart under the Weibull timetruncated life test. The relative analysis reveals that the proposed time-truncated control chart for Weibull distribution under uncertainty design performance more efficiently than the existing counterparts. From the comparison, the proposed chart provides smaller values for the out-of-control average run length as compared to the existing attribute control chart. An illustrative application related to automobile manufacturing is also incorporated to demonstrate the proposal.

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