Range Control Charts Revisited: Simpler Tippett-like Formulae, It´s Practical Implementation and the Study of False Alarm

This paper presents simpler alternative formulae and procedures of implementation to deal with the relative range statistic (moments, distribution and quantiles) used in the construction of range control charts for process dispersion monitoring. The Tippett's integral formulae for sample relative range moments and distribution are revisited and simpler new alternative expressions are proposed together with an easy computational implementation procedure based on it's relation with the Tukey maximum studentized range statistic. Also, such proposed methods are applied in the assessment of the range chart performance considering false alarm comparison between exact control limits charts versus normal approximated versions (3-sigma Shewhart procedure), which show the serious drawbacks of such misplaced control limits. These much simple tools introduced here, we believe, will permit the presentation of R control charts more transparently and without unrealistic normal approximations or blind dependence on tables, avoiding the serious limitations of such \ad hoc" practice.