Exponentially weighted moving average Lepage-type schemes based on the lower-order percentile of the run-length metrics and their use in monitoring time-occupancy in Google applications

ABSTRACT

Many existing monitoring schemes in the literature are based on the in-control (IC) average or median run-length. Several Phase-II schemes frequently fail to protect against the high rate of early false alarms. The problem may worsen when the average run-length metric is used, and the scheme is based on unknown and estimated parameters. Early false alarms can be avoided using monitoring schemes based on the lower-order percentiles of the IC run-length distribution. The exponentially weighted moving average (EWMA)-Lepage scheme is presented in this paper. The new design is based on a percentile-based approach that can effectively reduce and control the rate of early false alarms. The run-length properties of the EWMA scheme with the lower-order percentile-based design were investigated and compared with the double EWMA-Lepage and homogeneously weighted moving average-Lepage schemes. Detailed simulation studies show no clear winner among the three schemes for given sample sizes for the unknown shift. Instead, the size of the Phase-I and Phase-II samples heavily influences the choice of a potentially beneficial scheme. A case study on monitoring the time occupation of users on the Google application is presented to demonstrate the design and implementation of lower-percentile-based techniques. Some future research directions are offered.

KEYWORDS:

• Exponentially weighted moving average (EWMA)
• false alarm
• Lepage statistic
• percentile-based
• steady-state run-length

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Ministry of Higher Education (MoHE) Malaysia through Fundamental Research Grant Scheme project. FRGS/1/2019/STG06/UTAR/02/2.

Notes on contributors

Kok Ming Chan

Kok Ming Chan is currently a lecturer for BSc. (Hons) Actuarial Sciences degree program at Quest International University, Malaysia. He received his B.App.Sc. (Hons), majoring in Applied Statistics from Universiti Sains Malaysia in 2019, and MSc., majoring in Statistical Quality Control from Universiti Tunku Abdul Rahman, Malaysia in 2022. His current research interests include statistical modelling and statistical quality control.

Zhi Lin Chong

Zhi Lin Chong is an assistant professor in Lee Kong Chian Faculty of Engineering and Science, Universiti Tunku Abdul Rahman (UTAR). In the past, he served as a senior lecturer in the School of Mathematical Sciences, Universiti Sains Malaysia (USM), and as a lecturer in the Faculty of Science, UTAR, for some years. He received his PhD in 2015 from the School of Mathematical Sciences, USM. His research interests include, but not limited to, parametric and nonparametric statistical process monitoring and control.

Amitava Mukherjee

Amitava Mukherjee is a full professor in the Production, Operations, and Decision Sciences Area of XLRI—Xavier School of Management, Jamshedpur, India. He is an elected member of the International Statistical Institute (ISI), a member of its committee on Risk Analysis, a life member of the International Indian Statistical Association, Indian Science Congress Association, Calcutta Statistical Association, and a regular member of the American Society for Quality, American Statistical Association, among others. Prof. Mukherjee is currently an Associate Editor of Sequential Analysis—Design, Methods and Applications and Journal of Statistical Computation and Simulation. He also served as a guest editor of Quality and Reliability Engineering International and Quality Technology and Quantitative Management. He has published over 65 articles on Web of Science and Scopus enlisted journals in diverse research areas, including sequential analysis, nonparametric inference, statistical process control, and Geostatistics. His current research interest includes but is not limited to applied sequential methodology, nonparametric hypothesis testing, methodologies for high-dimensional data, and statistical process control.