## Quality Control Charts using Ranked Set Sampling

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**Hassen
A. Muttlak **

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Different
quality control charts for the sample mean are developed using ranked set
sampling (RSS) and median ranked set sampling (MRSS). These new charts are
compared to the usual control charts based on simple random sampling (SRS)
data. The charts based on RSS and MRSS are shown to have smaller average run
length (ARL) than the classical chart especially if the process starts to get
out of control. The MRSS is compared with RSS and SRS data, it turns out that
MRSS dominates all other methods in terms of the ARL if the process starts to
get out of control. Real data are collected using the SRS, RSS and MRSS. These
data sets are used to construct the corresponding control charts. These charts are compared to usual SRS chart.
It turns out that the newly developed charts are more efficient in estimating
the population mean and the process is more stable. Through this study we are
assuming that the underlying distribution is normal. A check of the normality
for our data set indicated that the normality assumption is reasonable.

*Key Words*: Average run length, lower
confidence limit, median ranked set sampling, simple random sampling and upper
confidence limit.