This thesis is concerned with the design of control charts applying a sequential probability ratio test(SPRT) at every sampling point. Existing SPRT control charts are constructed under the assumption that there is no restriction on the number of observations at any sampling point. For situations where the time(or cost) required to sample and test an item is long(or high), they can not be directly applied.
Two SPRT control charts are proposed for situations in which there exists an upper bound on sample size. When the number of observations in a sampling point reaches the upper bound, one chart makes in-control/out-of-control decision based on the current value of SPRT statistic, and the other chart defers the decision to the next sampling point of which starting value is the value of the current SPRT statistic. A Markov chain approach is used to derive the formulas for evaluating the performances of the proposed charts. The proposed SPRT charts are compared with the existing SPRT charts, $\bar{X}$ charts, and cumulative sum charts. Guidelines are given for the design of the proposed charts.
