On the Statistical Design of Geometric Control Charts

Abstract

We address several theoretic issues involved in the design of geometric control charts. Primary among these is the question of setting probability limits, based on notions of “unbiasedness” and “conditional power”. A nearly ARL-unbiased design is defined by setting the in-control ARL as near as possible, given the discrete nature of the geometric distribution, to the peak of the ARL curve. An optimal design criterion, based on minimizing the sum of out-of-control ARLs for upward and downward shift is also suggested. These are shown to produce improved conditional power compared with the usual design.

Key Words:

• ARL
• ARL-unbiased
• conditional power
• geometric control chart

Additional information

Notes on contributors

Lingyun Zhang

Lingyun Zhang Postdoctoral Fellow in the Institute of Information Sciences and Technology at Massey University, New Zealand. He received his Ph.D. in Mathematical Statistics from the University of Regina, Canada. His research interests include SPC, applied probability and simulation. He has published papers in Journal of Quality Technology, Communications in Statistics, and The Mathematical Scientist.

K. Govindaraju

K. Govindaraju Received his Ph. D from the University of Madras, India. He is currently working as a senior lecturer in the Institute of Information Sciences and Technology at Massey University. His research interest mainly lies in statistical quality control. Dr. Govindaraju published papers in Journal of Quality Technology, Journal of Applied Statistics, Communications in Statistics, and others.

M. Bebbington

Mark Bebbington Senior Lecturer in stochastic operations research at Massey University, having received his PhD from the University of Cambridge. His research interests are in stochastic modeling and management OR. He has published papers in Economics Letters, European Journal of Operations Research, Communications in Statistics, Journal of Applied Statistics, Journal of Quality Technology, and International Transactions in Operations Research.

C.D. Lai

Chin-Diew Lai Received his PhD in Statistics from Victoria University of Wellington, New Zealand. He held positions at the University of Auckland and National Chiao Tung University, Taiwan, prior taking up the current position at Massey University, New Zealand in 1979. He has published two books and over 80 research papers in Australian Journal of Statistics, Journal of Applied Probability, IEEE Transactions on Reliability, Journal of Mathematical Geology, Communications in Statistics, European Journal of Operational Research, Naval Research Logistics, Reliability Engineering and System Safety, Statistics and Probability Letters, and others. He is an Editor of the Journal of Applied Mathematics and Decision Sciences.