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2021•Maǧallaẗ al-rāfidayn li-ʿulūm al-ḥāsibāt wa-al-riyāḍiyyāẗ/˜Al-œRafidain journal for computer sciences and mathematicsOpen access

Estimation of Non-Normal Process Capability Indices

Huda Mohamed Taib, Ban Al-Ani

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Abstract

The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

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The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

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Available abstract

The important and common applications of process capability indices (PCI’s) is the process capability ratio and the process capability index , and the use of these measures in practical applications is based on the assumption that the process is under statistical control and that the outputs of that process follow the normal distribution. In practice, however, there are many cases in which the outputs of the process are not follow normal distribution, in such cases, calculating PCI’s will lead to misleading results. In this paper, the non-normal production process capability was evaluated. The evaluation process was conducted using four methods: The first method involved the use of Box-Cox power transformation to normal distribution of data and then calculating indicators of the capability process by traditional methods. The second method is by using the weighted variance method, and the third method is by using the Clements’ method based on the percentiles calculation of data, and the fourth method is based on the use of the Darling-Anderson goodness of fit test to accommodate some of the probability distributions of the original data, this test shows that the log-normal distribution is the most appropriate distribution for the data The results showed that although the process is stable and under statistical control, it is not capable based on the value of the process capability index that did not exceed (65%), as the percentage defect units, which is outside the specifications, is large and located between (3.6%) and (13.4%). The results also showed that there is a convergence in the results of the PCI’s calculated by all methods, and that the Clements’ method is the best method as it gives the highest values ​​for the PCI’s. The research recommended studying and calculating other PCI’s like, , , and CMA(τ,v). One of the recommendations for future research and studies is to do a theoretical study to compare the mentioned methods and choose the best ones based on some statistical criteria.

Key concepts: Process capability index, Process capability, Percentile, Normal distribution, Process (computing), Anderson–Darling test, Computer science, Statistics

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