Failure rate monitoring in generalized gamma-distributed process

ABSTRACT

Advancement in technology brings a revolutionary change in the quality of the final product or items. Most of the manufacturing processes produce a large number of conforming items along with a few non-conforming items. For real-time monitoring of these highly efficient processes, monitoring of time-between-events is a well-known approach adopted in the literature of statistical process control. Usually, it is assumed that the time-between-events follows an exponential or gamma distribution. However, the generalized gamma distribution is the most popular choice for modelling skewed data. In this article, we consider a two-sided monitoring scheme based on the generalized gamma distribution. Two-sided monitoring schemes for skewed distributions often encounter bias in its run length properties. Therefore, we address this problem with modified control limits in a more general distributional setup. A Monte Carlo simulation-based study is designed, and results showed encouraging performance properties. A couple of practical applications in connection to monitoring renewable energy and coal mine explosions have been discussed.

KEYWORDS:

• Average time to signal
• generalized gamma distribution
• high-quality processes
• statistical process control
• time-between-events

Disclosure statement

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

Additional information

Notes on contributors

Niladri Chakraborty

Niladri Chakraborty is currently a lecturer at the Department of Mathematical Statistics and Actuarial Science, University of the Free State, Free State, South Africa. Dr Chakraborty received PhD in Mathematical Statistics in 2017 from the University of Pretoria, South Africa. He spent a few years as a postdoctoral fellow at the City University of Hong Kong, Hong Kong. His current research interest includes nonparametric inference, statistical process control, reliability and life testing.

Tahir Mahmood

Tahir Mahmood was born in Sargodha, Punjab, Pakistan in 1990. He got his degree of BS (Hons.) in Statistics with distinction (Gold Medalist) from the Department of Statistics, University of Sargodha, Sargodha, Pakistan. In 2015, he secured a scholarship from the Deanship of Graduate Studies, King Fahd University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia. In April 2017, he received his MS (Applied Statistics) degree from the Department of Mathematics and Statistics, KFUPM. In June 2020, he received his PhD (Applied Statistics) from the Department of Systems Engineering and Engineering Management, City University of Hong Kong, Hong Kong. Nowadays, he is a Lecturer in the Department of Technology, School of Science and Technology, The Open University of Hong Kong, Hong Kong. His current research interests include Statistical Process Monitoring, Data Mining and Generalized Linear Modelling.