Statistical Process Control on the Circle: A Review and Some New Results

Statistical process control (SPC) is an important and mature area of statistics which finds application in many diverse disciplines. Until quite recently, virtually all developments and applications were restricted to data in Euclidean spaces. In this paper, we review some SPC methodology that has been developed to deal with data lying on the unit circle. With regard to parametric methods, a review of sequential probability ratio tests and Page-type CUSUMs is provided. A Shiryaev–Roberts-type sequential procedure is also proposed. Nonparametric rank-based CUSUMs for detecting location and/or concentration changes are also reviewed.