Performance of t control charts in short runs with unknown shift sizes

Recently, control charts plotting a statistic having a Student’s t distribution have been proposed as an efficient solution to perform Statistical Process Control (SPC) in short production runs where the shift size of the in-control process mean from μ₀ to μ₁ is known a priori. The shift size is usually measured as a multiple δ of the in-control process standard deviation σ₀: but in practice, at the beginning of the production run, both the value of next shift δ and σ₀ are unknown. As a consequence, when the actual shift size differs from the value assumed at the chart design stage, the performance of the control chart can be seriously affected. To overcome this problem, this paper investigates the statistical performance of the Shewhart, EWMA and CUSUM t charts for short production runs when the shift size is unknown and modeled by means of a statistical distribution. An extensive numerical analysis allows the properties of the three charts to be compared and discussed when uniform and triangular distributions are used by quality practitioners to fit the unknown shift size. An illustrative example is utilized to demonstrate a practical implementation of the best performing among the three investigated charts.