A new sudden death chart for the Weibull distribution under complexity

Osama H Arif,Muhammad Aslam

doi:10.1007/s40747-021-00316-x

Osama H Arif, Muhammad Aslam

Open Access

https://doi.org/10.1007/s40747-021-00316-x

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Abstract

This article presents a new control chart for monitoring reliability using sudden death testing under the neutrosophic statistics (NS). The average run lengths of the in-control and the out-of-control process have been determined for evaluating the quick detection ability for small and moderate shifts. For the industrial use, tables and figures have been presented for different parameters. The proposed control chart is efficient in comparison with the existing control chart under classical statistics and value addition in the toolkit of the quality control personnel.

Highlights

A control chart is an important tool of statistical process control for maintaining and improving the quality of the product to compete in the market [1]
Life testing experiments are very common in the statistical process control literature when a random sample of items is selected and put on testing for possible failure [2]
Let XN ∈ XL, XU denote the lifetime of a part, where XL is lower value of indeterminacy interval and XU be the upper value of the indeterminacy interval, which follows, the neutrosophic Weibull distribution with neutrosophic scale parameter N ∈ L, L and neutrosophic shape parameter mN ∈ mL, mL, the cumulative distribution function can be written as: F xN = 1 − exp − NxN mN ; mN ∈ mL, mL, N ∈ L, L (2)

Summary

Introduction

A control chart is an important tool of statistical process control for maintaining and improving the quality of the product to compete in the market [1]. By exploring the literature and to the best of our knowledge, there is no work on the control sudden death control chart for monitoring the process of having incomplete, imprecise, and vague production data. We will propose the sudden death control chart for monitoring the reliability when the lifetime of the product follows the Weibull distribution under the uncertainty environment. We hope that the proposed control chart will be more adequate, adequate, and informative than the sudden death chart under classical statistics in an uncertain environment. In "Example", an example is given and some concluding remarks are given in the last section

Design of proposed control chart

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Conclusion