Determining the optimum process mean under a Gamma distribution

Abstract

Wen and Mergen (1999) presented a trade-off problem, taking both the costs of falling below the lower specification limit and exceeding the upper specification limit into account, to determine the optimum process mean. In Wen and Mergen’s (1999) model, the quality characteristic, X, is assumed to be normally distributed and X is nominal-is-best with a target value. In this paper, we extend Wen and Mergen’s (1999) model to a gamma quality characteristic case by respectively using step loss function and piecewise linear loss function in the cost function. The modified Wen and Mergen’s (1999) model with gamma distribution is developed. A numerical example is provided for illustration.

Keywords:

• Step loss function
• piecewise linear loss function
• specification limits
• process mean
• process standard deviation
• Gamma distribution