Optimal allocation of screening inspection effort for nonserial production systems

Graduation date: 1978The economic aspects of quality control have received wide concern since its developmental stages, however, they have not been sufficiently explored. Moreover, as the need for complex products of high precision and reliability increases, most industrial firms have experienced some difficulties in meeting that need at reasonable costs with their limited capabilities. Realizing that one of the most efficient ways of overcoming such difficulties is to properly allocate their inspection efforts within a production process, a mathematical model has been developed for determining the optimal location of screening inspection stations within a nonserial production process. Especially, the effect of imperfect inspection on the probabilistic behaviors of good and defective items is explicitly considered. The model is formulated as a constrained nonlinear zero-one integer program, and it is proved flexible enough to reflect various limitations and requirements existing in general production-inspection systems. As solution techniques, Lawler and Bell's algorithm and Glover's enumeration scheme are proposed with proper fathoming tests obtained by identifying the unique structure of the problem. Glover's scheme is modified to avoid complicated bookkeeping procedures, and FORTRAN programs are developed for both algorithms. The computational efficiencies of the two algorithms are compared with each other by solving randomly generated test problems, and it is shown that Glover's enumeration scheme is more efficient than Lawler and Bell's algorithm under the given conditions for generating test problems. However, it is realized that Glover's scheme is not quite efficient as the problem size increases. Thus, additional research is desired for accelerating enumeration in Glover's scheme. In addition, a nonserial production-inspection system is analyzed by performing some sensitivity analyses showing that the model is adaptive to varying situations