联合监测过程位置参数和尺度参数的非参数Shewhart控制图

用于检测生产服务过程的传统控制图多数都假定过程的分布是已知的。这些控制困经常是在正态分布的假设下构建的,然而在服务质量实时监控中数据往往是非正态的。在这种情况下,基于正态分布假设的控制图的结果是不可靠的。为了解决这个问题,通常考虑非参数方法,因为在过程分布未知情况下,非参数控制图比参数图更加稳健有效。本文提出一个新的基于Van der Waerden和Klotz检验的Lepage型非参数Shewhart控制图(称为LPN图)用于同时检测未知连续过程分布的位置参数和尺度参数。文中给出了LPN图在不同参数下的控制限。依据运行长度分布的均值,方差和分位数,分析了LPN图在过程受控和失控时的性能,并与其他一些现有的非参数控制图进行比较。基于蒙特卡洛的模拟结果表明,LPN图对非正态分布具有很好的稳健性,并且在不同的过程分布下对检测位置参数和尺度参数,尤其对检测尺度参数的漂移都具有很好的性能。最后通过监控出租车服务质量说明LPN图在实际中的应用。

A Distribution-free Shewhart Control Chart for Joint Monitoring of Location and Scale Parameters

Most traditional control charts used for sequential monitoring assume that full knowledge is available regarding the distribution of the process.These charts are constructed under the assumption of normality,nevertheless,in on-line monitoring of service quality,the data are often non-normal.In such cases,the results from the charts based on the assumption of normality would be unreliable.To address this problem,the nonparametric approach is often considered,because when the process distribution is unknown,a nonparametric chart is generally more robust and effective than a parametric chart.In this paper,we propose a new Shewhart-Lepage control chart based on the Van der Waerden test and the Klotz test(referred to as LPN chart)for joint monitoring of location and scale.Control limits are tabulated for some charting parameters.The in-control and out-of-control performance properties and a comparison with some other existing nonparametric charts are presented in terms of the average,the standard deviation and some percentiles of the run length distribution.Numerical results based on Monte Carlo analysis show that the proposed LPN chart is quite robust to non-normally distributed data,and moreover,it provides quite a satisfactory performance for a class of location-scale models in detecting varying magnitude of shifts in the process location and/or scale,especially when the shift is mainly from the scale.The application of our proposed chart is illustrated by a real data example in monitoring cab services.