Economic and economic statistical designs for three-level control charts

Abstract

In some situations, an appropriate quality measure uses three or more discrete levels to classify a product characteristic. For these situations, some control charts have been developed based on statistical criteria regardless of economic considerations. In this paper, we develop economic and economic statistical designs (ESD) for 3-level control charts. We apply the cost model proposed by Costa and Rahim.[Economic design of X charts with variable parameters: the Markov chain approach, J Appl Stat 28 (2001), 875–885] Furthermore, we assume that the length of time that the process remains in control is exponentially distributed which allows us to apply the Markov chain approach for developing the cost model. We apply a genetic algorithm to determine the optimal values of model parameters by minimizing the cost function. A numerical example is provided to illustrate the performance of the proposed models and to compare the cost of the pure economic and ESD for three-level control charts. A sensitivity analysis is also conducted in this numerical example.

Keywords:

• 3-level control chart
• adjusted average time to signal
• economic design
• economic statistical design
• Markov chain
• genetic algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Mohammad Bameni Moghadam http://orcid.org/0000-0003-1324-8024