An Extension of Banerjee and Rahim's Model for an Economic X-Bar Control Chart for Non-Normally Distributed Data Under Gamma Failure Models

Abstract

This study compares an x-bar control chart economic design with a variable sampling interval (VSI) and a fixed-length sampling (FSI) for non-normal data under gamma (λ, 2) shock models. In earlier investigations, most control chart economic designs assumed the failure mechanism, which belongs to the Poisson distribution. Furthermore, these subgroup measurements were assumed to be normally distributed. However, these assumptions may not be tenable. Hence, this study employs Rahim and Banerjee (1993) model and a numerical example to indicate the solution procedure and to implement the sensitivity analysis while comparing the results of using various sampling avenues in non-normally data.

Keywords:

• Burr distribution
• Economic design
• Fixed-length sampling interval
• Gamma failure mechanism
• Non-normal distribution
• Variable sampling interval

Mathematics Subject Classification:

• 90C30
• 34A34

Notes

^aUtilizing fixed sampling interval approach.

() Indicates utilizing fixed sampling interval scheme.

() Indicates utilizing fixed sampling interval scheme.

() Indicates utilizing fixed sampling interval scheme.

() Indicates utilizing fixed sampling interval scheme.

() Indicates utilizing fixed sampling interval scheme.