Evaluation of the Behavior of Robust Process Capability Estimators Based on Their Bootstrap Confidence Intervals for Gamma Distribution
Subject Areas : Statistical Quality Control
Hosein Ebrahimi
1
,
Davood Shishebori
2
*
1 - Department of Industrial Engineering, Yazd University, Yazd, Iran
2 - Department of Industrial Engineering, Yazd University, Yazd, Iran
Keywords: Robust estimators, Gamma distribution, Process capability indices, Bootstrap confidence intervals,
Abstract :
Today, producing a product with high quality, according to the customer needs requires a clear strategy of the manufacturers in the market. To produce a good product, measures are taken to measure and control products at all production levels among, which the analysis of process capability indices is of great importance in the industry. In this context, the usability indicators can be effective when the data follow a normal distribution. On the other hand, if the data aren't standard normal, evaluation of the process's capability based on these indices will typically be confronted with the problem. In this paper, after investigating the behavior and characteristics of the median absolute deviation (MAD) and interquartile range (IQR) and (Q_n), their analysis is conducted for the Gamma distribution. Then, the bias errors and standard errors are obtained using the jackknife method. Three estimators are evaluated in three different modes according to the bootstrap methods and based on their confidence intervals. Finally, by analyzing the results of this research, the reliability, and performance of the estimators are evaluated in different states.
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