Control charts with variable sampling rates

Abstract

This thesis is concerned with the design of statistical process control charts in which sampling rates are allowed to vary based on the values of the preceding sample statistics. This thesis is divided into the following four parts. (i) Variable sampling interval(VSI) $\bar{X}$ control charts with an improved switching rule which uses past sample means in addition to the current sample mean in the determination of the next sampling interval are proposed. The proposed control charts use long sampling interval if $l_2(≥2)$ consecutive sample means fall close to centerline and short interval otherwise. The expressions of the average time to signal and the average number of switches to signal are derived with a Markov chain approach. The proposed charts are compared with the existing VSI control charts, and a similar comparison is made for the case where warning limits are added to the $\bar{X}$ control charts. (ii) Two VSI schemes in $\bar{X}$ control charts with runs rules are proposed. One determines the next sampling interval based on the number of consecutive sample means falling in the regions specified by the runs rules for signaling, and the other based on the number of consecutive sample means belonging to the regions complementary to the ones used in the first scheme. A Markov chain approach is used to derive the formulas for evaluating the performances of the proposed schemes. Numerical comparisons are made between the VSI and fixed sampling interval(FSI) $\bar{X}$ control charts with runs rules. (iii) Variable stream and sample size(VSSS) group control charts(GCCs) in which both the number of streams selected for sampling and sample size are allowed to vary based on the values of the preceding sample statistics are proposed. The proposed charts select a large portion of streams and take samples of size n>1 from the selected streams if both the largest and smallest of sample means observed at the current sampling point fall between the lower and upper th...