Efficient designs of modeling attribute control charts for a Weibull distribution under truncated life tests

Abstract

In this paper, the designs of the attribute control chart for the Weibull distribution under the time truncated life tests are investigated. Thus, some models are presented for the determination of optimal parameters. All models have the same cost function to be minimized. However, in the economic-statistical model and multi-objective model, the producer’s risk and the consumer’s risk must be satisfied as constraints. These risks are also considered as simultaneous objective functions in the multi-objective model. Therefore, different algorithms are proposed to specify design parameters. For the multi-objective model, the concept of data envelopment analysis (DEA) is utilized in the proposed algorithm. DEA is a powerful non-parametric approach to evaluate the relative efficiency of a group of decision-making units (DMUs) with multiple inputs and outputs. Through simulation studies and comparisons, the results of the proposed models are investigated. Besides, a real example for the inspection of chip products is provided to illustrate and compare the performance of various models.