Developing a Constrained Mathematical Model to Optimize the Expected Total Costs of Life Testing

Abstract

The subjects of reliability acceptance sampling plans and failure-censored life tests have usually been investigated from the viewpoint of statistical properties; indeed, few researchers have shed light on the economic aspects of these issues. In this research, a constrained mathematical model is developed to optimally design a reliability sampling plan under failure censoring life testing. Minimizing the expected total cost (ETC) involved in the sampling and life testing is considered as the objective function of the model. Ensuring the producer’s and the consumer’s risks is taken into consideration as the constraint of the model. To minimize the ETC, the model optimally determines three decision variables including the total number of the items put to the life test, the number of the failed items to terminate the test, and a criterion to make decisions about the acceptance or rejection of the lot. Examples are provided and analyses are conducted to gain some insight regarding the model performance.