Assume that each random variable of a sequence had a density which is a Polya frequency function of order two. To this sequence we apply the Jirina sequential procedure to determine a tolerance interval. In this paper we find some sufficient conditions on the type of trend permissible for this sequence which enable us to show that when the Jirina procedure is used the sampling will stop sooner and the tolerance interval cover more of the population (in a stochastic sense) than would occur in the case without trend. Similar considerations are shown to hold when the sequences of observations have densities which have non-decreasing hazard rates.
"Some Applications of the Jirina Sequential Procedure to Observations with Trend." Ann. Math. Statist. 34 (3) 857 - 865, September, 1963. https://doi.org/10.1214/aoms/1177704008