Design and application of exponential chart for monitoring time-between-events data under random process shift

Abstract

Exponential charts based on time-between-events (TBE) data were developed for monitoring high-yield process like the process which has achieved six-sigma quality level and has 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 (known as TBE random chart) for monitoring time-between-events data; the design algorithm considers the random characteristic of the process shifts and therefore better reflects the real process conditions. The probability distribution of the random process shift is modeled by a Rayleigh distribution based on the sample data acquired during the operation of the control chart. The design of the proposed control chart scheme is demonstrated, and the properties are compared with that of other exponential charts. The results of the numerical studies show that the consideration of the random process shift in designing an exponential chart provides an excellent in-control stability of the charting scheme, which in turn helps in saving time and cost for searching the false alarms. The proposed control chart is easy to understand and operate, and thus the floor operators can utilize and understand it as easily as with a traditional charting scheme. © 2011 Springer-Verlag London Limited.