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An economic design for variable sampling interval MA control charts

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Abstract

Most of the studies done on the economic design of control charts focus on a fixed-sampling interval (FSI); however, it has been discovered that variable-sampling-interval (VSI) control charts are substantially quicker in detecting shifts in the process than FSI control charts due to a higher frequency in the sampling rate when a sample statistic shows some indication of a process change. In this paper, an economic design for a VSI moving average (MA) control chart is proposed. The results of a numerical example adopted from an actual case indicate that the loss cost of VSI MA control charts is consistently lower than that of the FSI scheme.

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Abbreviations

n :

Sampling size for each moving plot

h a :

Subsequent sampling interval when preceding sample mean is located at sub-control region I a , a=1,2,...,η

η :

Number of different sampling-interval lengths, η≥2

k a :

Threshold limit expressed in units of \({\sqrt n }{\left( {\overline{x} - \mu _{0} } \right)}/\sigma ,\;\;a = 2,3,...,\eta \)

k 1 :

Control limit expressed in units of \({\sqrt n }{\left( {\overline{x} - \mu _{0} } \right)}/\sigma \)

µ 0 :

Target mean

σ :

True-process standard deviation

δ :

Magnitude of an assignable cause expressed in units of σ

λ :

Occurrence rate of an assignable cause per unit time

D :

Average time taken to find and repair an assignable cause after detection

e :

Time for a sample to be taken, transmitted to laboratory, and results phoned back to process control room

M :

Income reduction when μ=μ 0+δσ

T :

Average cost of looking for an assignable cause when a false alarm occurs

W :

Average cost of looking for and repairing an assignable cause when one does exist

F c :

Fixed cost per subgroup of sampling, inspecting, evaluating and plotting

V c :

Variable cost per subgroup of sampling, inspecting, evaluating and plotting

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Acknowledgments

The authors wish to express appreciation for the support by National Sciences Council of the Republic of China, Grant No. NSC90-2218-E-212-001, and to Dr. Cheryl Rutledge for her editorial assistance.

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Authors and Affiliations

  1. Department of Industrial Engineering, Da-Yeh University, 112 Shan-Jiau Road, Da-Tsuen, Chang-Hua 51505, Taiwan R.O.C

    F.-J. Yu

  2. Department of Business Administration, National Changhua University of Education, Changhua, 500, Taiwan R.O.C.

    H.-H. Wu

Authors
  1. F.-J. Yu
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  2. H.-H. Wu
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Correspondence to F.-J. Yu.

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Yu, FJ., Wu, HH. An economic design for variable sampling interval MA control charts. Int J Adv Manuf Technol 24, 41–47 (2004). https://doi.org/10.1007/s00170-003-1625-y

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  • DOI: https://doi.org/10.1007/s00170-003-1625-y

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