Industrial engineering applications in metrology: Job scheduling, calibration interval and average outgoing quality

Abstract

This research deals with the optimization of metrology and calibration problems. The optimization involved here is the application scientifically sound operations research techniques to help in solving the problem intended optimally or semi-optimally with a practical time frame. The research starts by exploring the subject of measurement science known as metrology. This involves defining all the constituents of metrology facilities along with their various components. The definitions include the SI units’ history and structure as well as their characteristics. After that, a comprehensive description of most of the operations and parameters encountered in metrology is presented. This involves all sources of uncertainties in most of the parameters that affect the measurements. From the background presented and using all the information within it; an identification of the most important and critical general problems is attempted. In this treatment a number of potential optimization problems are identified along with their description, problem statement definition, impact on the system and possible treatment method. After that, a detailed treatment of the scheduling problem, the calibration interval determination problem and the average outgoing quality problem is presented. The scheduling problem is formulated and modelled as a mixed integer program then solved using LINGO program. A heuristic algorithm is then developed to solve the problem near optimally but in much quicker time, and solution is packaged in a computer program. The calibration interval problem treatment deals with the determination of the optimal CI. Four methods are developed to deal with different cases. The cases considered are the reliability target case, the CI with call cost and failure cost of both first failure and all failures and the case of large number of similar TMDEs. The average out going quality (AOQ) treatment involves the development two methods to assess the AOQ of a calibration facility that uses a certain multistage inspection policy. The two methods are mathematically derived and verified using a simulation model that compares them with an actual failure rate of a virtual calibration facility.