Grouped Data-Sequential Probability Ratio Tests and Cumulative Sum Control Charts

Abstract

Methodology is proposed for the design of sequential methods when data are obtained by gauging articles into groups, Exact expressions are obtained for the operating characteristics and average sampling number of Wald sequential probability ratio tests and for the average run length of cumulative sum (CUSUM) schemes based on grouped data. Step-by-step design algorithms are provided to assist the practitioner. The methodology is illustrated assuming a normal process with known standard deviation in which we wish to detect shifts in the mean. An example from a progressive die operation is presented. The methods proposed are simple to implement and are an economical alternative to variables-data-based sequential sampling plans and CUSUM control charts.