An Improved Half Normal Probability Plot Approach with Application in Outlier Detection of Lifetime Data

Half normal probability plot (HNPP) has been widely used in designed experiments for identifying the factors and interactions with significant effects on the response. The effects of all the factors and interactions form a univariate dataset and the significant factors and interactions can be viewed as large outliers. A main drawback with the HNPP approach is its subjectivity in drawing the straight line through the origin and those points with small effect values based on visual evaluation. In the context of outlier detection, another drawback with the HNPP approach is that it cannot effectively detect small outliers. This chapter aims to address these two issues by proposing an improved HNPP approach and a two-step outlier detection method. To address the first issue, we fit the $$m$$ m data points on the left-hand-side of HNPP to a straight line without intercept and fit the other data points to another straight line with a non-zero intercept. The value of $$m$$ m is determined by maximizing the average of two correlation coefficients associated with the two straight lines. To address the second issue, the ordered dataset is divided into two subsets by the median. The small-value [large-value] subset contains possibly small [large] outliers. The improved HNPP approach is applied separately to each subset. Two real-world examples are included to illustrate the proposed approach and method as well as their appropriateness.