A weighted likelihood ratio test-based chart for monitoring process mean and variability |
| |
| Authors: | Zhi Song Yanchun Liu Zhonghua Li |
| |
| Institution: | 1. Department of Mathematics, Liaoning University, Shenyang, People's Republic of China;2. College of Science, Shenyang Agricultural University, Shenyang, People's Republic of China;3. Business School, Liaoning University, Shenyang, People's Republic of China;4. Institute of Statistics and LPMC, Nankai University, Tianjin, People's Republic of China |
| |
| Abstract: | In this paper, a new single exponentially weighted moving average (EWMA) control chart based on the weighted likelihood ratio test, referred to as the WLRT chart, is proposed for the problem of monitoring the mean and variance of a normally distributed process variable. It is easy to design, fast to compute, and quite effective for diverse cases including the detection of the decrease in variability and individual observation case. The optimal parameters that can be used as a design aid in selecting specific parameter values based on the average run length (ARL) and the sample size are provided. The in-control (IC) and out-of-control (OC) performance properties of the new chart are compared with some other existing EWMA-type charts. Our simulation results show that the IC run length distribution of the proposed chart is similar to that of a geometric distribution, and it provides quite a robust and satisfactory overall performance for detecting a wide range of shifts in the process mean and/or variability. |
| |
| Keywords: | Weighted likelihood ratio test exponentially weighted moving average average run length run length distribution statistical process control |
|
|
