Weibull Quantile Function and Application in Missing Data

Itrat Batool Naqvi, Muhammad Aslam, Mansour Sattam Aldosari

Abstract



In this research paper Weibull Quantile function constructed through which tables for different quantiles developed with known shape and scale parameters. Sometime the exact sampling distribution of the sample statistics of interest is not available especially in case of quantiles and situation become complicated/ worst when the data contain missing observations due to some certain reasons, under such situations the determination of the experimental results and further analysis not possible. The limits are difficult to construct when the distribution of its quality characteristic of interest is unknown as well data contain missing observations. This research paper addressed the said problem. A number of quantile control limits could be constructed through purposed method but for analysis purpose few of them discussed. The results explore, both graphically and numerically, that the missing data limits widened than the full data in each case. It is known fact that due to the reduction into the original sample size researcher loss some significant information and gained of wider control limits not an astonished fact to us rather obvious and comply with the usual practices /expectations. Although to the best of our knowledge the quantile control limits for missing data not constructed in literature, the way as constructed in this research paper through the gateway of quantile function. The Average Run Length (ARL) table also provided through which the efficiency for different quantiles can examine.

Keywords


Control chart; Weibull distribution; average run length



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