Economic design of exponential chart for monitoring time-between-event data under random process shift

Abstract

Control charts based on time-between-event data have recently shown to be very useful in manufacturing systems, in reliability and maintenance monitoring, and also in service related applications in general. This article develops an economic model of the exponential chart for monitoring time-between-event data under random process shift. The probability density function for the occurrence of process shift follows Rayleigh distribution. The design of the proposed control chart scheme has been demonstrated. A comparison between economic design and statistical design is conducted. The results of the numerical example show that the exponential chart designed under random process shift is more realistic than the exponential chart designed under fixed process shift.