Comparison between Nonnormal Process Capability Study Based on Two Kinds of Transformations

Yang, Jie; Song, Xiang dong; Zhe, Ming

doi:10.1109/cdee.2010.103

Cited by 1 publication

(3 citation statements)

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“…After the transformation, process capability can be evaluated. Box & Cox (1964) When the optimum value of λ is obtained, for all the quality characteristic values of X, upper and lower specification limits are transformed to normal variables (Yang, Song & Ming, 2010). Therefore, the corresponding PCIs, C p and C pk , can be computed from the mean and standard deviation of the transformed data just like computations of C p and C pk under normality.…”

Section: Box-cox Power Transformation (Bct)mentioning

confidence: 99%

“…Define the quantile ratio (QR) as Bounded System (S B ) and Unbounded System (S U ) can be selected according to the following general Table 1. Summary of Johnson transformation system (Yang et al, 2010) However, in the case of s = 3, if the suitable value of z is identified, Johnson system that fits the data is identified as well. Based on the transformed data, the quality control technique under the normal assumption can be applied.…”

Section: Jonhson Transformation System Using Pearson Curves (Jt)mentioning

confidence: 99%

“…The quantiles x 0.00135 , x 0.50 , x 0.99865 that correspond the probabilities 0.00135, 0.5 and 0.99865 can be obtained. Hence, the corresponding process capability index can be evaluated (Yang et al, 2010).…”

Section: Jonhson Transformation System Using Pearson Curves (Jt)mentioning

confidence: 99%

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Comparing performances of clements, box-cox, Johnson methods with weibull distributions for assessing process capability

Şenvar

Şennaroğlu

2016

JIEM

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Abstract:Purpose: This study examines Clements' Approach (CA), Box-Cox transformation (BCT), and Johnson transformation (JT) methods for process capability assessments through Weibull-distributed data with different parameters to figure out the effects of the tail behaviours on process capability and compares their estimation performances in terms of accuracy and precision.Design/methodology/approach: Usage of process performance index (PPI) P pu is handled for process capability analysis (PCA) because the comparison issues are performed through generating Weibull data without subgroups. Box plots, descriptive statistics, the root-mean-square deviation (RMSD), which is used as a measure of error, and a radar chart are utilized all together for evaluating the performances of the methods. In addition, the bias of the estimated values is important as the efficiency measured by the mean square error. In this regard, Relative Bias (RB) and the Relative Root Mean Square Error (RRMSE) are also considered. Findings:The results reveal that the performance of a method is dependent on its capability to fit the tail behavior of the Weibull distribution and on targeted values of the PPIs. It is observed that the effect of tail behavior is more significant when the process is more capable.-634-Journal of Industrial Engineering and Management -http://dx.doi.org/10.3926/jiem.1703Research limitations/implications: Some other methods such as Weighted Variance method, which also give good results, were also conducted. However, we later realized that it would be confusing in terms of comparison issues between the methods for consistent interpretations. Practical implications:Weibull distribution covers a wide class of non-normal processes due to its capability to yield a variety of distinct curves based on its parameters. Weibull distributions are known to have significantly different tail behaviors, which greatly affects the process capability. In quality and reliability applications, they are widely used for the analyses of failure data in order to understand how items are failing or failures being occurred. Many academicians prefer the estimation of long term variation for process capability calculations although Process Capability Indices (PCIs) C p and C pk are widely used in literature. On the other hand, in industry, especially in automotive industry, the PPIs P p and P pk are used for the second type of estimations.Originality/value: Performance comparisons are performed through generating Weibull data without subgroups and for this reason, process performance indices (PPIs) are executed for computing process capability rather than process capability indices (PCIs). Box plots, descriptive statistics, the root-mean-square deviation (RMSD), which is used as a measure of error, and a radar chart are utilized all together for evaluating the performances of the methods. In addition, the bias of the estimated values is important as the efficiency measured by the mean square error.In this regard, Relative Bias (RB) and the Relativ...

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Section: Box-cox Power Transformation (Bct)mentioning

confidence: 99%

Section: Jonhson Transformation System Using Pearson Curves (Jt)mentioning

confidence: 99%