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

Abstract

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...

Objective Bayesian inference for the capability index of the Gamma distribution

“…For nonnormally distributed data, a quantile approach to measure the parametric estimation of process capability indices was developed by Clements 12 . Hence, more researchers focused on the study of the process capability analysis of the nonnormal data; for more details, refer Kashif et al, 13 Panichkitkosolkul, 14 Leiva et al., 15 Senvar and Sennaroglue, 16 Saha et al., 17,18 Meng et al., 19 Mahmoud et al, 20 and Wu 21 …”

Control Charts for Monitoring Process Capability Index Using Median Absolute Deviation for Some Popular Distributions

“…Hosseinifard et al [11] claimed that the study of process capability indices for non-normal data may lead to erroneous results. Therefore, the study of non-normal data has long been a great challenge for researchers [7][8][9][10]12,13].…”

Evaluation of Bootstrap Confidence Intervals Using a New Non-Normal Process Capability Index

“…Process capability indices are used to assess the given production process, or whether not to produce items according to the given specifications. The efficiency of these indices required that the process follows a normal distribution [1][2][3]. However, the involvement of different noise factors, sometime may result in the non-normal behaviors of the production process [4].…”

“…In case of non-normal processes, the normality based classical process capability index (PCI) may give unreliable and misleading results [5]. Several methods have been proposed [1,[3][4][5][6][7] to estimate PCIs and deal with non-normality issue. However, until now, we could not rely ona single method that creates efficiently under all situations [4].…”

“…However, until now, we could not rely ona single method that creates efficiently under all situations [4]. Moreover, it is also argued that all methods showed a variable performance under different non-normal distributions [3]. Therefore, the evaluation of different non-normal PCIs, under different distributions, is an important research area for practitioners and statisticians.…”