Improving the performance of the attribute charts: X¯tn$\bar{X}_{tn}$ and Stn2$S^2_{tn}$

Abstract

This paper proposes a procedure to improve the performance for the attribute control charts: X𝑡𝑛 and 𝑆 2 𝑡𝑛 . In these control charts, a simple size 𝑛 is collected periodically and each item is allocated into one of the five categories defined by a go-no-go gauge. After that, a random value is generated for each item according to a truncated normal distribution with its upper and lower limits defined by the cut points of the go-no-go gauge. With the 𝑛 generated values, the sample mean X𝑡𝑛 and the sample variance 𝑆 2 𝑡𝑛 are calculated and compared with the their respective control limits. In this paper, a procedure was implemented in order to improve the performance of these control charts, which consists of the sequential switches between two sample sizes 𝑛 𝑎 and 𝑛 𝑏 (with 𝑛 𝑎 > 𝑛 𝑏 ) and checking whether the sample mean (or sample variance depending) exceeds the control limits or not. The proposal is relatively easy for practitioners to implement it. Extensive computational experiments showed that the procedure improved both control charts to detect small shifts in term of 𝐴𝑅𝐿 1 . With this procedure, the "Improved X𝑡𝑛 " (shortly X𝑡𝑛(𝐼) ) control chart performs similarly to X chart for small shifts in the process mean provided that the sample sizes are raised by approximately two additional sample units and the "Improved 𝑆 2 𝑡𝑛 " (shortly 𝑆 2 𝑡𝑛(𝐼) ) control chart also has a similar performance to 𝑆 2 chart with more or less double sample size in the range of small shifts of the variance. Two numerical examples are presented to illustrate the use of the procedure.