Sign control charts with variable sampling intervals

Abstract

Nonparametric procedures with variable sampling intervals (VSI) are presented for the problem of detecting changes in the process median (or mean), and also changes in process variability. The proposed procedures are based on sign-test statistics computed for each sample, and are used in Shewhart control charts. The sampling interval between samples is allowed to vary depending on what is being observed in the current sample. When the process is in control the run length distribution for the proposed sign control chart does not depend on the distribution of the observations. An additional advantage of the proposed sign charts is the fact that the variance of the process does not need to be established in order to set up a control chart. This makes such charts useful for start-up of new processes where not much information is available yet on the variability. Comparisons between parametric and sign control charts with fixed sampling intervals (FSI) and variable sampling intervals (VSI) are presented. Numerical results show the advantages of using sign charts, especially when a VSI chart is used. It is also shown that it is possible to combine the VSI feature with curtailed sampling plans that are based on the attained sample size. Curtailed sampling plans can considerably reduce the expected number of observations used in the Shewhart control schemes based on the sign statistic.