Enhanced nonparametric control charts under simple and ranked set sampling schemes

Abstract

Investigation and removal of unnatural variation in the processes of manufacturing, production and services require application of statistical process control. Control charts are the most famous and commonly used statistical process control tools to trace changes in the manufacturing and nonmanufacturing processes parameter(s). The nonparametric control charts become necessary when the distribution of underlying process is unknown or questionable. The nonparametric charts are robust alternative along with holding property of quick shift detection ability in process parameter(s). In this article, we have proposed nonparametric double exponentially weighted moving average chart based on Wilcoxon signed rank test under simple and ranked set sampling schemes for efficient monitoring of the process location. The proposed control charts are compared with classical exponentially weighted moving average, double exponentially weighted moving average, nonparametric exponentially weighted moving average sign, nonparametric exponentially weighted moving average signed rank, nonparametric cumulative sum signed rank charts using average run length and some other characteristics of run length distribution as performance measures. Comparison reveals that the proposed control charts performs better to detect all kinds of shifts in the process location than existing counterparts. A real-life application related to manufacturing process (the variable of interest is the diameter of piston ring) is also provided for the practical implementation of the proposed chart.

On developing sensitive nonparametric mixed control charts with application to manufacturing industry

“…Large values indicate the chart's efficiency relative to its competitors (cf. Abbas et al 45 ).…”

“…The following continuous, symmetric distributions have been used in this proposed study: (a) normal distribution with zero mean and unit variance, ) (e), and CN distribution to monitor the behavior of the proposed scheme in the presence of outliers. The detailed formulation of the CN distribution can be seen in Abbas et al 45 The distributions mentioned above are adjusted with zero mean and unit variance for ease in comparisons. The density functions of these distributions are given in Table 3.…”

“…The following continuous, symmetric distributions have been used in this proposed study: (a) normal distribution with zero mean and unit variance, N (0, 1) that is bell‐shaped, Meso‐kurtic, and symmetrical distribution, (b) Student's t ‐distribution with () degrees of freedom that has a heavy tail, platy‐kurtic shaped; symmetrical distribution, (c) Laplace distribution, DE(0, 1/) (double exponential distribution), (d) Logistic Distribution, LOG (0, ) (e), and CN distribution to monitor the behavior of the proposed scheme in the presence of outliers. The detailed formulation of the CN distribution can be seen in Abbas et al 45 . The distributions mentioned above are adjusted with zero mean and unit variance for ease in comparisons.…”

The effect of measurement error on the performance of Mann‐Whitney and Signed‐Rank nonparametric control charts

“…Chakraborti and Graham 22 reviewed nonparametric control charts considering both univariate and multivariate ones. Raza et al 23 proposed a new nonparametric double exponentially weighted moving average control chart on the basis of the Signed‐Rank statistic, and Abbas et al 24 developed nonparametric double exponentially weighted moving average charts based on Wilcoxon Signed‐Rank test under simple and ranked set sampling schemes.…”

A non‐parametric double homogeneously weighted moving average control chart under sign statistic

“…suggested a new mixed EWMA–CUSUM chart based on arcsine statistic and after that named as NPAS–MEC chart. There are many other studies on non‐parametric charts under different scenarios, which can be seen in the work of Qui and Li, 20 Abid et al., 21 Chakraborti and Graham, 22 Li et al., 23 Qiu, 24 Abbas et al 25 and Li et al 26 …”