A new approach to optimal design of control charts based on change point estimation and total time on test plot

Abstract

Estimation of the change point of a process may be the most important result and application of control charts in the literature of statistical process control. The time to the change point called process failure mechanism may have the most vital role in optimal design of control charts. Applying the total time on test plot as a supreme tool for the failure rate shape identification is proposed in this paper to pick out an appropriate failure model. The unknown parameters of the fitted distribution then can be estimated by some common statistical methods like maximum likelihood based on the estimated change point data. The generalized cost model of Rahim and Banerjee (1993) adapted for fitted shock model will determine eventually the optimal design parameters of control charts economically and statistically. A numerical study on the optimal design of $\overline{X}$-control chart illustrates our practical approach for production systems with bathtub-shaped failure rate.

Keywords:

• Bathtub-shaped hazard rate
• change point estimation
• control chart design
• integrated hazard over sampling intervals
• total time on test plot