A One-Sided Double Screening Procedure Using Individual Unit Misclassification Error

A double screening procedure (DSP), which controls for individual unit misclassification error (IME) as well as average outgoing quality (AOQ), for quality control applications is developed. Screening involves selecting items whose performance is within specifications based on observing one or more correlated surrogate (screening) variables in lieu of the performance variable directly. In double screening, two screening variables, which are correlated to a performance variable, are observed sequentially, rather than simultaneously as in a single screening plan (SSP); namely, (l) one screening variable is used first to make one of three decisions---accept, reject, or undecided---according to the magnitude of the individual nonconforming probability (equivalent to the IME for an accepted item); (2) after this first screening, the second screening variable is employed to screen the undecided items. Assuming conditions of normality, formulae for computing the selection ratio (proportion of accepted items) and AOQ are derived for a DSP. The impact of the intercorrelation between two screening variables on the sequencing of a DSP and the performance between an SSP versus DSP are examined. A DSP reduces inspection cost considerably relative to an SSP employing two screening variables. Producer's risk is also diminished at a nominal sacrifice in consumer's risk. Implementation of a DSP requires only the use of several simple formulas and readily available standard normal tables.