Accurate Test Limits with Estimated Parameters

Abstract

Due to measurement errors, producers are typically forced to set test limits well within specification limits. The methods used in practice are rather informal and usually conservative with respect to consumer loss, thus leading to unnecessary loss of yield. We present approximations for test limits that are still relatively easy to evaluate and moreover very accurate. In addition, the analytical tractability of these approximations allows extension to the more realistic case in which parameters are estimated.

A variety of criteria for setting test limits

“…In OTTEN (1996) (also see ALBERS and KALLENBERG, 1994, and ALBERS, KALLENBERG and OTTEN, 1994a,b, 1997, 1998, the consumer loss is used as criterion to set test limits for measurements of the characteristic itself. In that case our model from (1) has parameters a 0 and b 1 and the error term Z is the measurement error U.…”

“…of every 1000 nonconforming items, on average only one is allowed to be accepted by the test limit. Since we took a 0 and b 1, we can determine a test limit using the technique discussed in ALBERS, KALLENBERG and OTTEN (1994a), in such a way that CL lg 22.75 ppm (approximately). The approximation of a equals a IX 2.445 and the approximated test limit becomes t IX 1.511.…”

Accurate test limits under prescribed consumer risk

“…e.g. Table 3 in Albers et al (1994a). Therefore, our aim is to find a test limit, which minimizes the expected loss up to high-order and with great precision.…”