Designing of Gini-chart for Exponential, t, Logistic and Laplace Distributions

Abstract

This article extended the work of Saghir and Lin (2012) to develop the probability limits of Gini chart, a process dispersion chart based on gini's mean difference proposed by Riaz and Saghirr (2007), for the exponential, t₍₅₎, Logistic and Laplace distributions. The asymmetrical control limits of the Gini chart are proposed for the distributions under study. The estimated factors and quantile points used in the construction of the Gini chart are provided for the exponential, t₍₅₎, Logistic and Laplace distributions. The effect of improper use of constants and quantile points in the construction of Gini chart is studied in terms of the associated false alarm rates. The performance of the asymmetrical control limits of the given chart is evaluated in terms of average run length (ARL) for the exponential, t₍₅₎, Logistic and Laplace distributions and compared with the 3σ limits proposed by Saghir and Lin (2012). The ARL performance of the proposed probability limits is compared with the existing limits of R and S charts for the under study parent distributions. Finally, the design scheme of chart associated with Gini chart is developed.

Keywords:

• ARL
• Control charts
• False Alarm rate
• Gini-Chart
• Logistic Distribution