Bootstrap confidence intervals of C<sub><i>Npk</i></sub>for inverse Rayleigh and log-logistic distributions

Rao, G. Srinivasa; Aslam, Muhammad; Kantam, R. R. L.

doi:10.1080/00949655.2015.1040799

Cited by 38 publications

(15 citation statements)

References 26 publications

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“…Peng (2010a, b) developed parametric lower confidence limits of quantile-based PCIs and also studied PCIs for 1 3 processes with skewed distributions. Similar developments can be seen from Kantam et al (2010) and Wararit and Somchit (2012) for half-logistic distribution, and from Rao et al (2015) for inverse Rayleigh and log-logistic distributions. The main aim behind the development of PCIs is to give indication on the quality process whether it is moving in line with the predefined standards.…”

Section: Introductionsupporting

confidence: 81%

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

2019

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This paper deals with construction of confidence intervals for process capability index using bootstrap method (proposed by Chen and Pearn in Qual Reliab Eng Int 13(6):355-360, 1997) by applying simulation technique. It is assumed that the quality characteristic follows type-II generalized log-logistic distribution introduced by Rosaiah et al. in Int J Agric Stat Sci 4(2):283-292, (2008). Discussed different bootstrap confidence intervals for process capability index. Maximum likelihood method is considered for obtaining the estimators of the parameter. Monte Carlo simulation technique is applied to find out the coverage probabilities and average widths of the bootstrap confidence intervals. The results are illustrated with real data sets.

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Section: Introductionsupporting

confidence: 81%

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

2019

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“…It allows checking the distribution of parameters in relation to the initial sample [49]. The bootstrap method is useful when the form of the distribution of the variable in the population is not known and when the quality or amount of information collected does not allow the use of classic statistical methods [50]. Due to the fact that it does not make assumptions about the distribution in the population, it is included in the non-parametric methods.…”

Section: Bootstrap Methodsmentioning

confidence: 99%

Bootstrap Analysis of the Production Processes Capability Assessment

Stoma¹,

Stoma

Dudziak

et al. 2019

Applied Sciences

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The high customer requirements for appropriate product quality pose a challenge for manufacturers and suppliers and also cause them many problems related to ensuring a sufficiently high product quality throughout the entire production cycle. For the above reasons, it is so important to assess the capability of monitored processes, and shaping, analyzing and controlling the capability of processes is an important aspect of managing an organization that uses a process approach to management. The use of an appropriate method to analyze the course of production processes is a necessity imposed by quality standards, e.g., ISO 9001: 2015. That is why it is so important to propose a quick and low-cost method of assessing production processes. For this purpose, a method of assessing the capability of the manufacturing process using bootstrap analysis was used. The article presents the analysis of inherent properties of the production process based on the results of measurements of the characteristic features of the process or the characteristics of the manufactured products (process variables) for the shafts with grooves. The main goals of the work are to develop a procedure for determining process capability based on the bootstrap method, including criteria for the classification of production process capability; to develop the criterion values for confidence intervals of production process capability; as well as to demonstrate the practical application of bootstrap analysis in manufacturing. Moreover, comparative analyses of process capabilities using bootstrap and classic methods were carried out. They confirm both the narrowing of the confidence interval when using the bootstrap method and the possibility of determining a better estimator of the lower limit of this range compared to the results obtained using the classic method. The tests carried out for the unit production of shafts with grooves showed that the analysis of the process capability for measuring tests n = 10 is possible. Finally, new criterion values for the assessment of process capability for the bootstrap method were proposed. The model for assessing the capability of production processes presented in the paper was implemented in low-volume production in the defense industry.

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“…Since then, several researchers have developed numerous techniques for constructing CIs. In this regard, readers may refer to Peng 16,17 ; Leiva et al 18 ; Pearn et al 19,20 ; Kashif et al 21,22 ; Weber et al 23 ; Pina-Monarrez et al 24 ; Rao et al 25 ; Dey et al 26 ; Dey and Saha 27,28 ; Park et al 29 ; Saha et al [30][31][32] , Alomani et al 33 and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Parametric inference of the loss based index Cpm for normal distribution

Saha

Dey²,

Wang

2021

Quality & Reliability Eng

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The process capability index (PCI) has been introduced as a tool to aid in the assessment of process performance and most of the traditional PCIs performed well when process follows the normal behavior. In this article, we consider a PCI,  𝑝𝑚 for normal random variables. The objective of this article is five fold: First, six different methods of estimation of the PCI  𝑝𝑚 are addressed from frequentist approaches and compare them in terms of their mean squared errors using extensive numerical simulations. Second, we compare three bootstrap confidence intervals (BCIs) of the PCI  𝑝𝑚 including standard bootstrap, percentile bootstrap, and bias-corrected percentile bootstrap. Third, Bayesian estimation is considered under four loss functions (symmetric as well as asymmetric) using normal prior for location parameter and inverse gamma prior for the scale parameter for the considered model. Also, we obtain highest posterior density (HPD) credible intervals of the PCI  𝑝𝑚 . Fourth, a new cost effective PCI, namely,  𝑝𝑚𝑐 is introduced by incorporating tolerance cost function in the index  𝑝𝑚 . Fifth, the power of the test is obtained, and Monte Carlo simulation study has been carried out to compare the performances of the classical BCIs and HPD credible intervals of PCIs  𝑝𝑚 and  𝑝𝑚𝑐 in terms of average widths and coverage probabilities. Finally, two real data sets have been analyzed for illustrative purposes.

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Bootstrap confidence intervals of C_Npkfor inverse Rayleigh and log-logistic distributions

Cited by 38 publications

References 26 publications

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Bootstrap Analysis of the Production Processes Capability Assessment

Parametric inference of the loss based index Cpm for normal distribution

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Bootstrap confidence intervals of CNpkfor inverse Rayleigh and log-logistic distributions

Cited by 38 publications

References 26 publications

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Bootstrap confidence intervals of CNpk for type-II generalized log-logistic distribution

Bootstrap Analysis of the Production Processes Capability Assessment

Parametric inference of the loss based index Cpm for normal distribution

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Bootstrap confidence intervals of C_Npkfor inverse Rayleigh and log-logistic distributions