Minimisation of inspection and rework cost in a BLU factory considering imperfect inspection

Abstract

We address an optimisation problem for minimising the cost of both the inspection and the rework incurred throughout an interconnected inspection-rework system. In order to formulate the relevant cost objective function, assuming imperfect inspection, we make a time-based flow analysis between nodes (or shops), and derive the limiting sizes of flows between nodes and the limiting fraction defective by solving a set of nonlinear balance equations. We provide an enumeration method for determining the optimal frequency of inspection cycles at the end of assembly lines which minimises the relevant cost of inspection and rework. IntroductionA backlight unit (BLU) attached to the back of a display unit is one of the major components of a thin film transistor liquid crystal display. A BLU consisting of several cold cathode fluorescent lamps, a light guide panel and several sheets such as a reflector sheet and a prism sheet can be manufactured by assembling the parts sequentially into a mould frame. Inspections of a BLU can be divided into several functional inspections and external appearance inspections. The functional inspections include a brightness test measured at 13 specified spots on the surface of a BLU, a view angle test and an electrical conformations tests. The external appearance inspections check the surface states of a mould frame, screws, twisted electrical lines,sheets, etc. The final inspection decision can be made only by a single attribute, which is conventionally described as nonconformity.In the Korean BLU industry, even if only one NC (nonconforming) item is found in a lot, the lot is rejected by a source inspector sent by a buyer. Rejected NC items must be 100% inspected later in order to exclude the possibility that even rectified C (conforming) items could be an NC. Hence, three groups of items -one group of items newly produced, another group of items having been rejected and reworked later and the last group of items recalled from the buyer -are accumulated in a clean storage area of a BLU factory. Since three different groups of items with different fraction defectives are circulated in a BLU factory, estimating the fraction defective of items in the storage area and measuring the effect of acceptance sampling plan on preceding and succeeding processes throughout the factory are the current problems to be solved. These problems are basically related to the defective rate of assembly lines. If repeated inspections and reworks are performed at the end of an assembly line, the number of inspections and reworks required in the remaining processes after assembly lines may be reduced. Otherwise, we may inspect and/or rework many more items in the remaining processes.It would be desirable if the proposed production/inspection-rework process mentioned above could be proved to be superior to coexistent ones used in the BLU industry, since optimising a superior process could result in better solution in terms of some criteria than optimising any other inferior processes. However, since a quality contro...

A Nonpolynomial Optimal Algorithm for Sequencing Inspectors in a Repeat Inspection System with Rework

“…= 12 and that the sequence ⟨1, 3⟩ gives the smallest AOQ (=2,534 ppm) of all possible sequences with size 2. In fact, the input data given in the example are partially extracted from the original data sets of a Korean back-light unit supplier, and, from the data sets, the averages of the type I and type II errors were estimated as 0.8641% and 4.5031%, respectively, by Yang and Cho [15].…”

A Study on Overestimating a Given Fraction Defective by an Imperfect Inspector

“…Even if only one NC item is found in a lot, the lot is rejected by the source inspector. The rejected items, even if there are very few NC items, must be 100% reinspected later, in another clean room (Yang and Cho [1]).…”