IJPAM: Volume 80, No. 3 (2012)

EXPLICIT FORMULAS OF AVERAGE RUN LENGTH FOR
A MOVING AVERAGE CONTROL CHART FOR MONITORING
THE NUMBER OF DEFECTIVE PRODUCTS

Yupaporn Areepong
Department of Applied Statistics
Faculty of Applied Science
King Mongkut's University of Technology North Bangkok
Bangkok 10800, THAILAND


Abstract. The objective of this paper is to study Statistical Process Control (SPC) with a Moving Average control chart (MA). The main characteristics of a control chart are the Average Run Length (ARL) (mean of false alarm times) and the Average Delay time (AD) (mean delay of true alarm times). The ARL should be sufficiently large while the process is still in-control and the AD should be small when the process goes out-of-control. Explicit MA-based formulas for ARL and AD are presented for observations from a binomial distribution. In particular, formulas are developed for the number of defective products in a production line. The new formulas are simple, and easy to implement and use by practitioners. The ARL and AD calculated from these new formulas are compared with numerical simulation results for the Shewhart np and EWMA charts. The results show that the new MA formulas perform better than the np and EWMA charts when the shifts in parameter values from in-control to out-of-control are moderate or large.

Received: April 15, 2012

AMS Subject Classification: 60A05

Key Words and Phrases: average run length, average delay time, moving average control chart, alarm time

Download paper from here.



Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 80
Issue: 3