Economic Design of Variable Sampling Interval X-Bar Control Charts for Monitoring Correlated Non Normal Samples

Abstract

Recent studies have shown the X-bar control chart with variable sampling interval detects shifts in the process mean faster than the traditional X-bar chart. These studies are usually based on the assumption that the process data are independently and normally distributed. However, many situations in practice violate these assumptions. In this study, a methodology is developed to economically design a variable sampling interval X-bar control chart that takes into consideration correlated non normal sample data. An example is provided to illustrate the solution procedure. A sensitivity analysis on the input parameters (i.e., the cost and the process parameters) is performed taking into account the non normality and the correlation on the optimal design of the chart.

Keywords:

• Correlated process data
• Economic design
• Genetic algorithms
• Non normality
• Variable sampling interval
• X-bar control chart

Mathematics Subject Classification:

• Primary 62-XX
• Secondary 62P30

Acknowledgment

The authors are thankful for the constructive comments of the reviewers that helped improve the presentation of this article.

Notes

ρ = 0.77.

ρ = 0.77.

Fixed cost parameters: λ = 0.01, δ = 1, t ₁ = 0.1, t ₂ = 0.3, c ₁ = 10, c ₂ = 30, c ₃ = 100, c ₄ = 0.5, c ₅ = 0.1.