Transforming the exponential by minimizing the sum of the absolute differences

Shih Chou Kao, Chuan Ching Ho, Ying Chin Ho

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This work presents an optimal value to be used in the power transformation to transform the exponential to normality for statistical process control (SPC) applications. The optimal value is found by minimizing the sum of absolute differences between two distinct cumulative probability functions. Based on this criterion, a numerical search yields a proposed value of 3.5142, so the transformed distribution is well approximated by the normal distribution. Two examples are presented to demonstrate the effectiveness of using the transformation method and its applications in SPC. The transformed data are almost normally distributed and the performance of the individual charts is satisfactory. Compared to charts that use the original exponential data and probability control limits, the individual charts constructed using the transformed distribution are superior in appearance, ease of interpretation and implementation by practitioners.

Original languageEnglish
Pages (from-to)691-702
Number of pages12
JournalJournal of Applied Statistics
Issue number7
StatePublished - Aug 2006


  • Exponential distribution
  • Individual chart
  • Normal distribution
  • Probability control limits
  • Weibull distribution


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