Chiang Mai Journal of Science

 This paper evaluates performances of the three dual-scheme variable parameters (VP) nonparametric (NP) control charts: the Sign test (ST), the Mann-Whitney Test (MW), and the Hodges-Lehmann estimator (HL)using the Markov chain approach.  From the symmetric discrete probability distribution of each statistic, the regular control scheme has the sample size of 10 observations ( =10) with the predetermined probability distribution classified by control regions using the nearest lesser probability of +/- 3  and  +/- 2  (as in the traditional Shewhart’s type chart) for action limits and warning limits, the tight control schemes have the sample size from 10 to 20 ( =10,11,…,20) with wider both out-of-control region and warning region. The more number of observations, the more choices for the fine probability to be selected fromthe locationsof the nonparametric statistics tosetup the control limits.The results show that among the three VP ( =10, =10,11,…,20), ST has more variation in the average run lengths (ARL) than MW and HL.  In each NP control chart, the average number of samples to signal (ANSS) lies between the ARL of their individual schemes.  The ANSS, the average number of observations to signal (ANOS), and the average number of time to signal (ATS) of the three VPNP control charts, ST has highest variation while MW and HL have varied in a smaller band, and HL has better performances than MW in almost every sample size. By applying variable parameters to nonparametric control charts, their performances can be improved within the regular control scheme and the tight control scheme.