A more accurate representation of the expected number of false alarms in statistical quality control

E. A. Silver, T. R. Rohleder

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We explain deviations away from the usual estimate of the expected number of false alarms per unit time in the use of a Statistical Process Control (SPC) chart. Using applied probability we develop an exact analytic expression for the expected number of false alarms per unit time. The derivation involves determining the expected value of a modulus function of a random variable. Results depend upon the probability distribution of a key random variable: the time from when an out-of-control signal is observed (and an assignable cause is present) until the process is put back into control. For the cases of normal and Erlang distributions, the usual estimate used in the design of economic control charts is biased somewhat low. The bias becomes more important when there is an appreciable chance of the process going out of control within a single inter-sampling interval.

Original languageEnglish (US)
Pages (from-to)5589-5599
Number of pages11
JournalInternational Journal of Production Research
Volume45
Issue number23
DOIs
StatePublished - Dec 2007
Externally publishedYes

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Quality control
Random variables
Statistical process control
Probability distributions
Sampling
Economics
Statistical quality control
Control charts
Expected value
Probability distribution
Deviation
Applied probability

Keywords

  • Control charts
  • False alarms
  • Modulus function

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering

Cite this

A more accurate representation of the expected number of false alarms in statistical quality control. / Silver, E. A.; Rohleder, T. R.

In: International Journal of Production Research, Vol. 45, No. 23, 12.2007, p. 5589-5599.

Research output: Contribution to journalArticle

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