Cumulative Conforming Control Chart Assuming Discrete Weibull Distribution

Sajid Ali,Ismail Shah,Lichen Wang,Tanzila Zafar

doi:10.1109/access.2020.2964602

Abstract

Time Between Events (TBE) charts have advantages over the traditional control charts when monitoring high quality processes with very low defect rates. This article introduces a new discrete TBE control chart following discrete Weibull distribution. The design of the proposed chart is derived analytically and discussed numerically. Moreover, the performance is assessed by using the Average Run Length (ARL) and the Coefficient of Variation of Run Length (CVRL). Besides simulation studies, the proposed scheme is also illustrated using four real data examples.

Highlights

Statistical process control (SPC) is a quality control method, which is used to monitor a process by using statistical methods
PERFORMANCE EVALUATION USING Average Run Length (ARL) AND Coefficient of Variation of Run Length (CVRL) There are many criteria which can be used to assess the performance of control charts at a particular shift or for a range of shifts
CONCLUDING REMARKS In time-between-events (TBE) charts, the occurrence of an event follows Poisson process and it is assumed that the time between two non-conformities follows exponential distribution, which is only suitable for constant failure rate

Summary

INTRODUCTION

Statistical process control (SPC) is a quality control method, which is used to monitor a process by using statistical methods. Variable control charts like X , S, S2, are commonly used to monitor the continuous data. S. Ali et al.: CCC Chart Assuming Discrete Weibull Distribution binomial and suggested rules of approximation, including np > 15 or p ≥ 0.1 and np ≥ 10. The number of runs/cycles to failure when the components are prior to cyclical loading or on/off switching devices, etc In such situations, the lifetime of a component or a device is modeled as a discrete random variable and geometric and negative binomial are the most common models used in reliability analysis. The main aim of this study is to introduce a new CCC chart using discrete Weibull distribution and to study its performance assuming average run length (ARL) and coefficient of variation of run length (CVRL) as the performance measures. The performance of the discrete Weibull chart using ARL is discussed in Section 5 whereas Section 6 concludes the study

THE DISCRETE WEIBULL DISTRIBUTION

CONTROL CHARTS BASED ON DISCRETE WEIBULL

REAL DATA APPLICATIONS

PERFORMANCE EVALUATION USING ARL AND CVRL

CONCLUDING REMARKS