DETERMINING THE CONSTANTS OF RANGE CHART FOR SKEWED POPULATIONS
DOI:
https://doi.org/10.23055/ijietap.2012.19.2.347Keywords:
Range chart, skewed distribution, normality, type I riskAbstract
The probability of a false alarm rate (type I risk) in Shewhart control charts based on a normal distribution will increase as the skewness of a process increases. However, the distribution of a range is a positively–skewed one. It is unstable for monitoring range values by using three-sigma control limits that is from the concept of a normal assumption. Moreover, most studies employ a simulation method to compute the type I risks of the range control chart for non–normal processes. To provide an alternative method, this study utilizes the probability density function of the distribution of the range to construct the appropriated control limits of a range control chart for a skewed process. The control limits of the range chart were determined by setting that the type I risk is equal to 0.0027 and the standardized Weibull, lognormal and Burr distributions. Furthermore, compared to range charts that use type I risks and type II risks, weighted variance (WV), skewness correction (SC) and traditional Shewhart control charts, the proposed range chart is superior to other control chart, in terms of the type I risks and type II risks for a skewed process. An example of the yield strength for the deformed bar in coil is presented to illustrate these findings.Published
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