基于差分递减权系数的加权Q控制图

Q控制图的异常检出时间远长于参数已知时控制图的异常检出时间,对此提出了一种加权Q控制图方法.基于单容量样本度量和多容量样本度量,分别给出了相应算法,对算法的正确性给出了数学证明.加权Q控制图方法根据差分递减的权系数构造加权Q控制图的Q统计量,随后对该Q统计量使用Q控制图进行异常分析.仿真结果表明:加权Q控制图的异常检出时间短于Q控制图的异常检出时间,且与参数已知时的控制图的异常检出时间相差不大,综合考虑实用性和检测灵敏度这两个指标,加权Q控制图优于Q控制图和参数已知时的控制图.

Weighted Q control chart based on difference-declining weight parameters

To solve the problem that the ARL (average run length) of Q control chart was much longer than the ARL of control chart with known distribution parameters, the weighted Q control chart was proposed. The method to deal with one-volume-sample metric and the method to deal with multiple-volume-sample metric were both given. The mathematical justification of the method to deal with one-volume-sample metric was given. The Q statistic that the weighted Q control chart used was established by difference-declining weight parameters. The simulation shows that the ARL of the weighted Q control chart is shorter than the ARL of Q control chart and is comparably short to the ARL of control chart with known distribution parameters. Because distribution parameters can not be known in most processes, the weighted Q control chart is better than Q control chart and also better than control chart with known distribution parameters when both of practicability and sensitivity are considered.