# Monitoring a Process of Exponentially Distributed Characteristics through Minimizing the Sum of the Squared Differences

Monitoring a Process of Exponentially Distributed Characteristics through Minimizing the Sum of... This study presents an optimal exponent for transforming the exponentials for statistical process control (SPC) applications. The optimal exponent, 3.5454, is determined by minimizing the sum of the squared differences between two distinct cumulative probability functions. The normal distribution closely approximates the transformed distribution. The study investigates an interval of indifference for the exponent using two criteria, the square root of sum of the squared differences ( $${\sqrt D )}$$ and the Kullback-Leibler distance (K-L). This interval is [3.4, 3.77], which implies that exponents falling in this interval have very similar results in transforming the exponentials. The study explores an example of flash memory wafer. The individual chart using the transformed data eliminating location the parameter has better detection power than that without eliminating the location parameter. Moreover, the control chart is also easier for practitioners to interpret and implement than probabilistic control limits. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Quality & Quantity Springer Journals

# Monitoring a Process of Exponentially Distributed Characteristics through Minimizing the Sum of the Squared Differences

, Volume 41 (1) – Dec 29, 2005
13 pages

/lp/springer_journal/monitoring-a-process-of-exponentially-distributed-characteristics-ywm2mKL0a2
Publisher
Subject
Social Sciences; Methodology of the Social Sciences; Social Sciences, general
ISSN
0033-5177
eISSN
1573-7845
D.O.I.
10.1007/s11135-005-6214-8
Publisher site
See Article on Publisher Site

### Abstract

This study presents an optimal exponent for transforming the exponentials for statistical process control (SPC) applications. The optimal exponent, 3.5454, is determined by minimizing the sum of the squared differences between two distinct cumulative probability functions. The normal distribution closely approximates the transformed distribution. The study investigates an interval of indifference for the exponent using two criteria, the square root of sum of the squared differences ( $${\sqrt D )}$$ and the Kullback-Leibler distance (K-L). This interval is [3.4, 3.77], which implies that exponents falling in this interval have very similar results in transforming the exponentials. The study explores an example of flash memory wafer. The individual chart using the transformed data eliminating location the parameter has better detection power than that without eliminating the location parameter. Moreover, the control chart is also easier for practitioners to interpret and implement than probabilistic control limits.

### Journal

Quality & QuantitySpringer Journals

Published: Dec 29, 2005

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