Electronic Journal of Differential Equations,
Conference 02 (1999), pp. 105-114.

Title:   Sorting and cost analysis of reworking items in rejected 
 lots based on non-destructive variable sampling plan


Authors: Hadi Y. Alkahby (Dillard Univ., New Orleans, LA, USA)
 Fouad N. Jalbout (Dillard Univ., New Orleans, LA, USA)
 
Abstract: 
A mathematical model for a decision criterion for disposing
an inspection lot is developed. An expression of the posterior cost is
formulated in terms of the quality characteristics $X$ of the items
manufactured, the sample size $n$, the lot size $N$, the upper and
lower limits of $X$ ($U$, $L$) of the individual items, the sample
mean $\overline{x}$, the mean $\mu$ and variance $\sigma^2$ of $X$, also in
terms of the economical cost parameters, Optimizing the posterior cost
equation leads to the estimation of the decision points. A procedure
to accept, reject, screen or scrap the entire lot based on the values
of the decision points is developed. Mathematical expressions are
derived for the expected cost of lot acceptance, screening and
scrapping. In developing the model, the distribution of $X$ and $\mu$
are normal. The tested items can be used for their intended purposes
after testing. The defective items can be repaired or reworked.
Rejected lots are either screened or scrapped. The decision to accept
or reject a lot depends on the upper and lower limits of the sample
mean, which constitutes the decision points.


Published December 9, 1999.
Math Subject Classifications: 62N10.
Key Words: Production cost of an item; 
   upper and lower limit of quality characteristics.