A comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes

Abstract

Distribution-free charting schemes for process monitoring are more robust and reliable than their parametric counterparts when the process distributions are unknown and complicated. Most of the existing control charts are uni-aspect schemes because they can detect a shift in only one aspect of the process distribution, like location or scale. Research on schemes for simultaneous surveillance of location and scale parameters has been very active in recent years, leading to many bi-aspect schemes. These schemes do not explicitly deal with the shape of the process distribution. However, a shift in the shape parameter with or without a location or scale shift can occur in practice, especially in production or time-to-event processes. Note that there are nonparametric schemes for detecting general shifts based on goodness-of-fit test statistics or empirical likelihood ratio statistics, which cannot isolate if there is a shift in location, scale, shape, or combination of these parameters. This article introduces a new distribution-free process monitoring scheme that can detect a shift in the location, scale or shape parameters, or any combinations of them. The new scheme is based on a combined statistic designed via Euclidean distance of the standardized Wilcoxon statistic for location, the standardized Ansari-Bradley statistic for scale, and the standardized Savage-type statistic for shape. We discuss the implementation design using the average run-length as the performance metric and investigate the proposed scheme's in-control performance. It is shown that the new charting scheme is in-control robust irrespective of the underlying process distribution and therefore applicable to monitor any univariate continuous processes. An out-of-control performance comparison study of the new scheme with many existing schemes shows that the new scheme is preferable to the existing schemes. We illustrate the proposed chart with real data to monitor a passenger train's arrival delays in Italy's regional route. The proposed scheme is comprehensive because it integrates the follow-up procedure via integrated sub-charts for classifying the signaling component.

An optimally designed distribution‐free CUSUM procedure for tri‐aspect surveillance of continuous processes

“…Interested readers may also see Mukherjee et al 29 for more details. In many time-to-event processes, among others, shifts are not always limited to location and scale, but the shift may happen to shape parameters.…”

“…An example is the inverse ) 𝜚 ′ , among other. Some motivations for why a multi-aspect statistic should include the shape were already discussed by Mukherjee et al 29 Our main task is to consider the null hypothesis 𝐹 𝑋 (𝑥) = 𝐹 𝑌 (𝑥). In symbols, monitoring the equality in distribution is analogous to monitoring a deviation in process location, scale or shape parameters, that is…”

“…It is easy to note that 𝑊 𝑡 and 𝐴 𝑡 are linearly independent, while 𝑆 𝑡 is not independent of 𝑊 𝑡 and 𝐴 𝑡 . Mukherjee et al 29 introduced a distribution-free Shewhart-type chart using the statistic as in (18). In the current context, based on the above statistic, we propose a tri-aspect nonparametric CUSUM scheme, denoted hereafter as tri-aspect nonparametric CUSUM (TNC).…”

“…In this subsection, we facilitate performance comparisons with the TNS scheme proposed in Mukherjee et al, 29 the BNC-L scheme proposed in Chowdhury et al 17 and the CUSUM-CvM scheme based on Cramér-von Mises Statistic. The TNS scheme is Shewhart-type and plots 𝑇 𝑡 against 𝑡.…”

Mean control chart based on ranked set schemes for unknown skewed probability distribution and parameters

“…Chong et al 33 evaluated and compared the performance of distribution‐free Shewhart‐type lepage and cucconi schemes in monitoring complex process distributions. Mukherjee et al 34 derived comprehensive distribution‐free scheme for tri‐aspect surveillance of complex processes.…”