Method of using of the Box-Cox transformation at the application of the xbar and s chart

Nicolae Eftimie

doi:10.1051/matecconf/20179404005

Abstract

The application of the most statistical process control techniques is based on the assumption that the distribution of the measurements is normal. However, there are many situations in practice when the process data distribution is not normal. In certain cases, the Box-Cox transformation can be used for converting the process data distribution into a normal distribution. Considering these aspects, the paper presents a method of application for the xbar and s chart that can be used in the case when the measurements distribution is not normal. The proposed method consists of the following stages: the testing of normality of the process data, the application of the Box-Cox transformation and the testing of normality of the transformed data. In the case when the distribution of the transformed data is normal, they are used at the application of the xbar and s control chart.

Highlights

%R[ DQG &R[ >@ GHYHORSHG D PHWKRG WKDW FDQ EH XVHG IRU FRQYHUWLQJ WKH SURFHVV GDWD GLVWULEXWLRQ LQWR D QRUPDO GLVWULEXWLRQ $FFRUGLQJ WR WKLV PHWKRG HDFK PHDVXUHPHQW xi ZLOO EH WUDQVIRUPHG E\ PHDQV RI WKH IROORZLQJ V\VWHP RI HTXDWLRQV yi ° ̄°®OQxiOxi.
%R[ DQG &R[ >@ GHYHORSHG D PHWKRG WKDW FDQ EH XVHG IRU FRQYHUWLQJ WKH SURFHVV GDWD GLVWULEXWLRQ LQWR D QRUPDO GLVWULEXWLRQ $FFRUGLQJ WR WKLV PHWKRG HDFK PHDVXUHPHQW xi ZLOO EH WUDQVIRUPHG E\ PHDQV RI WKH IROORZLQJ V\VWHP RI HTXDWLRQV
Q WKH FDVH ZKHQ WKH GLVWULEXWLRQ RI WKH WUDQVIRUPHG GDWD LV QRUPDO WKH\ DUH XVHG DW WKH DSSOLFDWLRQ RI WKH xbar DQG s FRQWURO FKDUW RWKHUZLVH DQRWKHU PHWKRG PXVW EH DSSOLHG IRU WKH FRQWURO FKDUW DSSOLFDWLRQ

Summary

Introduction

%R[ DQG &R[ >@ GHYHORSHG D PHWKRG WKDW FDQ EH XVHG IRU FRQYHUWLQJ WKH SURFHVV GDWD GLVWULEXWLRQ LQWR D QRUPDO GLVWULEXWLRQ $FFRUGLQJ WR WKLV PHWKRG HDFK PHDVXUHPHQW xi ZLOO EH WUDQVIRUPHG E\ PHDQV RI WKH IROORZLQJ V\VWHP RI HTXDWLRQV yi ° ̄°®OQxiOxi.

Results

Conclusion