Abstract

The well-known variable control charts for mean and range of sub-groups for the half normal distribution were constructed by three different approaches. One from the first principles of using percentiles of the sampling distribution of the sample mean and sample range, the second from Shewhart control limits, and the third approach was a skewness correction procedure depending on the skewness coefficient. The coverage probabilities of the three different approaches were computed through simulation and compared.

Issue Section:
Research Papers
Keywords:
most probable, equi-tailed, HND

References

1.
Edgeman
,
R. L.
, “
Inverse Gaussian Control Charts
,”
Aust. J. Stat.
, Vol.
31
, No.
1
,
1989
, pp.
435
–
446
. https://doi.org/10.1111/j.1467-842X.1989.tb00500.x
Google Scholar
Crossref
Search ADS
 
2.
Gonzalez
,
I.
 and
Viles
,
I.
, “
Semi-Economic Design of Mean Control Charts Assuming Gamma Distribution
,”
Econ. Qual. Control
, Vol.
15
,
2000
, pp.
109
–
118
.
3.
Kantam
,
R. R. L.
 and
Sriram
,
B.
, “
Variable Control Charts on Gamma Distribution
,”
IAPQR Trans.
, Vol.
26
, No.
2
,
2001
, pp.
63
–
67
.
4.
Kantam
,
R. R. L.
,
Vasudeva Rao
,
A.
, and
Srinivasa Rao
,
G.
, “
Control Charts for Log-Logistic Distribution
,”
Econ. Qual. Control
, Vol.
21
, No.
1
,
2006
, pp.
77
–
86
. https://doi.org/10.1515/EQC.2006.77
Google Scholar
Crossref
Search ADS
 
5.
Betul
,
K.
 and
Berna
,
Y.
, “
The Individual Control Charts for BURR Distributed Data
,”
Proceedings of the Ninth WSEAS International Conference on Applied Mathematics
, Istanbul, Turkey, May 27–29, 2006,
WSEAS
,
Stevens Point, WI
, pp.
645
–
649
.
6.
Srinivasa Rao
,
B.
 and
Sarath Babu
,
G.
, “
Variable Control Charts Based on Linear Failure Rate Model
,”
Int. J. Stat. Syst.
, Vol.
7
, No.
3
,
2012
, pp.
331
–
341
.
7.
Srinivasa Rao
,
B.
, “
Mean and Range Charts for Skewed Distributions—A Comparison Based on Half-Logistic Distribution
,”
Pakistan J. Stat.
, Vol.
28
, No.
4
,
2012
, pp.
437
–
444
.
8.
Chan
,
L. K.
 and
Heng
,
J. C.
, “
Skewness Correction x¯ and R Charts for Skewed Distributions
,”
Naval Res. Log.
, Vol.
50
, No.
6
,
2003
, pp.
1
–
19
. https://doi.org/10.1002/nav.10042
Google Scholar
Crossref
Search ADS
 
This content is only available via PDF.
All rights reserved. This material may not be reproduced or copied, in whole or part, in any printed, mechanical, electronic, film, or other distribution and storage media, without the written consent of ASTM International.
You do not currently have access to this content.