Three Non-parametric Control Charts Based on Ranked Set Sampling
Waliporn Tapang, Adisak Pongpullponsak* and Sukuman Sarikavanij* Author for corresponding; e-mail address: adisak.pon@kmutt.ac.th
Volume: Vol.43 No.4 (JULY 2016)
Research Article
DOI:
Received: 24 May 2015, Revised: -, Accepted: 19 October 2015, Published: -
Citation: Tapang W., Pongpullponsak A. and Sarikavanij S., Three Non-parametric Control Charts Based on Ranked Set Sampling, Chiang Mai Journal of Science, 2016; 43(4): 915-930.
Abstract
In this study, the ranked set sampling (RSS) is applied to the three nonparametric control charts: the Mann – Whitney statistics (U-chart), the Wilcoxon rank sum test (W – chart) and the Hodges - Lehmann estimator (HL – chart) in order to reduce bias in sampling procedure. The data are generated from normal distribution, uniform distribution, and 11 shapes of Weibull distributions with the process mean shift in d times of standard deviation (d = 0.50, 1, 1.5, 2, 2.5, and 3). The results show that the in control average run length (ARL) of the three control charts with RSS are higher than the Shewhart X bar chart at +/-3 standard deviation control limits. When the shift occurs, the out of control ARL of HL – chart is the lowest in every mean shift.