Some Study On Nonparametric Control Charts

The first Shewhart control chart was proposed by Doctor Shewhart in the 20 th century, Page proposed the Cumulative Sum chart based on likelihood ratio test in 1954, and Roberts proposed the Exponentially Weighted Moving Average chart in 1959. Afterwards, control chart was widely used in production management, and it has become an important management tool, it is mainly used for analyzing the stability of production and service process in a stable state, and for detecting the shifts in the process thus diagnosis the states. Traditional control charts often assumed that data come from a known parametric distribution, mostly assumed the normal distribution. But in the actual production of industrial, the distribution of process is unknown or not normal, so these charts are not available; the nonparametric control charts are needed. In the case of nonparametric, if we continue to use the traditional fixed sampling intervals, the sudden shifts may not be detected. In this situation, we proposed a dynamic nonparametric control chart with variable sampling interval for detecting the shifts in the location parameter; it can timely detect the shifts in process.In this dissertation, we discuss the nonparametric dynamic control charts as follows:1. Due to the fixed sampling interval of nonparametric control charts for sudden shifts are not sensitive enough, so we proposed a nonparametric control charts with two sampling intervals, these charts have variable sampling intervals, which make them much more efficient in detecting various magnitude of shifts. Simulation study demonstrates that: the effect of nonparametric dynamic Shewhart control chart is better than the fixed sampling interval control chart, with the shift increase, the advantage is more obvious, and it is not affected by the distribution. The effect of dynamic nonparametric CUSUM control chart and dynamic nonparametric EWMA control chart are similar to the Shewhart control chart. Besides, they are self-starting nonparametric control charts and we do not require any prior knowledge of the underlying distribution, they can be used to monitor processes at the start stages.2. Inspired by Liu(2013), we develop an adaptive nonparametric dynamic EWMA control chart(NED) for detecting unknown magnitude of shifts. It can automatically adjust the parameter, and choose its sampling interval according to a function of standard order of rank about the current and historical data. The results show that: adaptive nonparametric dynamic EWMA control chart compared to other nonparametric EWMA control chart, the effect is more significant. This control chart is more efficient in detecting unknown various magnitude of shifts, and perform robustly for different continuous distributions.