On ARL-Unbiased Control Charts

Manufacturing processes are usually monitored by making use of control charts for variables or attributes. Controlling both increases and decreases in a parameter, by using a control statistic with an asymmetrical distribution, frequently leads to an ARL-biased chart, in the sense that some out-of-control average run length (ARL) values are larger than the in-control ARL, i.e., it takes longer to detect some shifts in the parameter than to trigger a false alarm. In this paper, we are going to: explore what Pignatiello et al. (4th Industrial Engineering Research Conference, 1995) and Acosta-Mejia et al. (J Qual Technol 32:89–102, 2000) aptly called an ARL-unbiased chart; provide instructive illustrations of ARL-(un)biased charts of the Shewhart-, exponentially weighted moving average (EWMA)-, and cumulative sum (CUSUM)-type; relate ARL-unbiased Shewhart charts with the notions of unbiased and uniformly most powerful unbiased (UMPU) tests; briefly discuss the design of EWMA charts not based on ARL(-unbiasedness).

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