Nonparametric control schemes for profiles with attribute data

Attribute data are very common in the real production and service processes. Therefore, many kinds of control charts for attribute data have been studied in the literature. On the other hand, profile monitoring has been a popular statistical process control (SPC) problem recently. Moreover, in some cases, the response variables of profiles are attribute data, such as binary or Poisson data. Thus, the research on SPC for profiles with attribute data is very important, which motivates us to undertake this current research and try to develop a unified framework for monitoring such kind of profiles. In this paper, the unified framework of control schemes based on the nonparametric regression is proposed, including the generalized likelihood ratio chart, the T2 chart and the exponential weighted moving average chart. These schemes could tackle linear or nonlinear profiles with a wide class of response variables belonging to the exponential family of distributions. The performance of the proposed control charts is studied under the binomial and Poisson profiles by numerical simulations. Furthermore, two examples are used for illustrating the implementation of the proposed control charts.