The operating characteristic of double sampling plans by variables when the standard deviation is unknown

Abstract

Double sampling plan by variables, double-stage t-test, JEL C00, C12,

Double ASN Minimax sampling plans by variables when the standard deviation is unknown

“…Numerical examples will be presented in the doctoral dissertation of A. Rohr. Krumbholz and Rohr (2006) showed that the one-sided two-stage t-test may be interpreted as a special double plan by variables in Case (ii). The OC procedure of Krumbholz/Rohr can also be used to calculate the OC of the two-sided two-stage t-test.…”

“…But their formula seems to be not constructive enough in that sense that it could serve as basis for an algorithm. Krumbholz and Rohr (2006) proved a formula expressing P (A 2 ) as a triple integral which could be implemented in an algorithm. This algorithm led to the first available procedure, as far as we know, allowing to calculate the OC L δ (p) exactly for an arbitrary p. Throughout the present paper, this procedure will be employed.…”

“…For this we use the socalled five-point-stencil obtained from a Taylor series with a residual of h 4 , where h denotes the stepwidth away from k 1 and k 2 , respectively. Using the exact calculation of the OC, provided by Krumbholz and Rohr (2006), we are now able to determine precisely the ASN Minimax plan δ * in a reasonable amount of time. Thus, there is no longer need for approximations like the Wallis approximation.…”

“…In some cases, there occur minor differences in the plans while the ASN maximum is almost at the same level, as could be expected. Krumbholz and Rohr (2006) succeeded in developing an algorithm allowing to calculate exactly the OC of the Bowker and Goode plans in the case of unknown σ . They showed that the plans of Sommers, obtained by Wallis approximation, tend to violate considerably the given bound β for the error of the second kind.…”

Minimax versions of the two-stage t test

“…Sommers (1981)) to calculate L(θ ) using normal approximations. Krumbholz and Rohr (2006) succeeded in programming an algorithm to calculate exactly the OCL of the double sampling plan for variables with unknown variance and a one-sided tolerance limit. This tolerance limit U may be assumed to be an upper one without any restriction.…”