Comparisons of Shewhart-type rank based control charts for monitoring location parameters of univariate processes

Abstract

The nonparametric (distribution-free) control charts are robust alternatives to the conventional parametric control charts when the form of underlying process distribution is unknown or complicated. In this paper, we consider two new nonparametric control charts based on the Hogg-Fisher-Randle (HFR) statistic and the Savage rank statistic. These are popular statistics for testing location shifts, especially in right-skewed densities. Nevertheless, the control charts based on these statistics are not studied in quality control literature. In the current context, we study phase-II Shewhart-type charts based on the HFR and Savage statistics. We compare these charts with the Wilcoxon rank-sum chart in terms of false alarm rate, out-of-control average run-length and other run length properties. Implementation procedures and some illustrations of these charts are also provided. Numerical results based on Monte Carlo analysis show that the new charts are superior to the Wilcoxon rank-sum chart for a class of non-normal distributions in detecting location shift. New charts also provide better control over false alarm when reference sample size is small.

Performance evaluation of joint monitoring control charts

“…The values of the plotting statistics for SC and SL charts, along with test samples, are reported in Table 6 and their corresponding control charts are given in Figure 4. [4] which concluded that there is no scale shift in the process.…”

“…[5]). The shift in location is noted when p 3 is very low except p 4 ; if p 3 is relatively high except p 4 , then there is the indication of a shift in scale. If both p 3 and p 4 are very low, shift is noted in both location and scale.…”

“…Normality is a typical assumption needed for parametric charts, while non-parametric charts are free from any such constraints. Reference can be made for further check out to Chakraborti et al [1,2], Chowdhury et al [3], and Mukherjee and Sen [4] in the literature. Moreover, a traditional approach used in SPC is to monitor each parameter separately; however, simultaneous monitoring of more than one parameter is also becoming popular in industry.…”

Nonparametric cost‐minimized Shewhart‐type process monitoring with restricted false alarm probability

“…Qiu and Hawkins, Bakir, Qiu, and Chatterjee and Qiu, among others, paid lots of attention to NSPM tools and techniques in the initial years of the 21st century. Among the more recent articles, we recommend Li et al, Qiu and Li, Graham et al, Abbasi et al, Mukherjee et al, Graham et al, Liu et al, Chowdhury et al, Mukherjee and Sen, Qiu and Zhang, Mukherjee, Chong et al, and Huang et al Clearly, in the last few years, research on NSPM techniques has gained considerable momentum. Mukherjee and Marozzi outlined the phenomenal growth of works on NSPM schemes.…”

Design and implementation issues for a class of distribution-free Phase II EWMA exceedance control charts

“…They noted a nearly 200% growth on research in nonparametric process control charts in the first half of the current decade. Interested readers may see Chakraborti and Graham (2007), Chakraborti et al (2011), Graham et al (2012Graham et al ( , 2014, Mukherjee and Chakraborti (2012), Mukherjee et al (2013), Balakrishnan et al (2015) Mukherjee and Sen (2015), Li et al (2016) and Mukherjee and Marozzi (2016b) among others for various aspects of nonparametric control charts. Some other recent works include Hawkins and Deng (2010) who considered a nonparametric control chart under a change-point set-up and Abbasi et al (2013) who considered a nonparametric control chart for the progressive mean.…”