Abstract
Process capability indices (PCIs) are often used to assess process performance. Higher PCIs do not mean lower rejection rates. Thus, loss-based PCIs are better for process capability measurement. This study introduces a new capability index, \(\mathcal S^{\prime }_{pk}\), based on a symmetric loss function for normal process, to include loss into capability analysis. We then estimate PCI \({\mathcal {S}}^{\prime }_{pk}\) employing six standard techniques of estimation and compare their mean squared errors (MSEs) through simulation analysis. For the index \({\mathcal {S}}^{\prime }_{pk}\), asymptotic confidence intervals (ACI), generalized confidence intervals (GCI), and parametric bootstrap confidence intervals (BCIs) are used to construct confidence intervals . Monte Carlo simulation evaluates ACI, GCI, and BCIs average widths and coverage probabilities. Our experiments showed that MPSE produced the smallest width. \({\mathcal {B}}{\mathcal {C}}_p\)-boot outperformed its competitors. For most sample sizes and estimation methodologies, \(\mathcal {P}\)-boot has a greater CP. Two electronic industry data sets are evaluated to demonstrate the accuracy of the suggested estimating methodologies, ACI, GCI, and BCIs.
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References
Abdel Ghaly AA, Aly H, Salah R (2016) Different estimation methods for constant stress accelerated life test under the family of the exponentiated distributions. Qual Reliab Eng Int 32(3):1095–1108
Bansal S (2021) Nature-inspired hybrid multi-objective optimization algorithms in search of near-OGRs to eliminate FWM noise signals in optical WDM systems and their performance comparison. J Inst Eng India: Series B 102:743–769
Boyles RA (1994) Process capability with asymmetric tolerances. Commun Stat - Simul Comput 23:613–643
Chan LK, Cheng SW, Spiring FA (1988) A new measure of process capability: \(C_{pm}\). J Qual Technol 30:162–175
Chen JP, Tong LI (2003) Bootstrap confidence interval of the difference between two process capability indices. Int J Adv Manuf Technol 21:249–256
Chen JP, Tong LI (2003) Bootstrap confidence interval of the difference between two process capability indices. Int J Adv Manuf Technol 21:249–256
Cheng RCH, Amin NAK (1983) Estimating parameters in continuous univariate distributions with a shifted origin. J Roy Stat Soc: Ser B (Methodol) 45(3):394–403
Cheng RCH, Amin NAK (1979) Maximum product-of-spacings estimation with applications to the log-normal distribution. Math Report, 79
Dennis JE, Schnabel RB (1983) Numerical methods for unconstrained optimization and non-linear equations. Prentice-Hall, Englewood Cliffs, NJ
Dey S, Ali S, Park C (2015) Weighted exponential distribution: properties and different methods of estimation. J Stat Comput Simul 85:3641–3661
Dey S, Josmar MJ, Nadarajah S (2017b) Kumaraswamy distribution: different methods of estimation. Comput Appl Math. https://doi.org/10.1007/s40314-017-0441-1
Dey S, Kumar D, Ramos PL, Louzada F (2017a) Exponentiated Chen distribution: properties and estimation. Commun Stat- Simul Comput 46:8118–8139
Dey S, Saha M (2019) Bootstrap confidence intervals of generalized process capability index \(C_{pyk}\) using different methods of estimation. J Appl Stat 46(10):1843–1869
Dey S, Saha M (2020) Bootstrap confidence intervals of process capability index \(S_{pmk}\) using different methods of estimation. J Stat Comput Simul 90(1):28–50
Gupta S, Garg R, Singh A (2020) ANFIS-based control of multi-objective grid connected inverter and energy management. J Inst Eng India: Series B 101:1–14
Hsiang TC, Taguchi G (1985) A tutorial on quality control and assurance. Las Vegas, NV (unpublished presentation), Annual Meeting on the American Statistical Association
Ihaka R, Gentleman R (1996) R: a language for data analysis and graphics. J Comput Graph Stat 5:299–314
Ihaka R, Gentleman R (1996) R: a language for data analysis and graphics. J Comput Graph Stat 5:299–314
Juran JM (1974) Juran’s Quality Control Handbook, 3rd edn. McGraw-Hill, New York, USA
Kane VE (1986) Process capability indices. J Qual Technol 18:41–52
Kao JHK (1958) Computer methods for estimating Weibull parameters in reliability studies. Trans IRE-Reliab Quality Control 13:15–22
Kao JHK (1959) A graphical estimation of mixed Weibull parameters in life testing electron tube. Technometrics 1:389–407
MacDonald PDM (1971) Comment on an estimation procedure for mixtures of distributions by Choi and Bulgren. J Royal Stat Soc: Series B 33(2):326–329
Mathew T, Sebastian G, Kurian KM (2007) Generalized confidence intervals for process capability indices. Qual Reliab Eng Int 23:471–481
Mehr AD, Ghiasi AR, Yaseen ZM, Sorman AU, Abualigah L (2023) A novel intelligent deep learning predictive model for meteorological drought forecasting. J Ambient Intell Humaniz Comput 14:10441–10455
Muruganantham B, Gnanadass R (2021) Solar integrated time Series load flow analysis for practical distribution system. J Inst Eng India: Series B 102:829–841
Nassar M, Dey S (2018) Different estimation methods for exponentiated Rayleigh distribution under constant-stress accelerated life test. Quality Reliabil Eng Int. https://doi.org/10.1002/qre.2349
Nayak JR, Shaw B, Sahu BK (2023) A fuzzy adaptive symbiotic organism search based hybrid wavelet transform-extreme learning machine model for load forecasting of power system: a case study. J Ambient Intell Humaniz Comput 14:10833–10847
Padhi S, Panigrahi BP, Dash D (2020) Solving dynamic economic emission dispatch problem with uncertainty of wind and load using whale optimization algorithm. J Inst Eng India: Series B 101:65–78
Pearn WL, Kotz S, Johnson NL (1992) Distributional and inferential properties of process capability indices. J Qual Technol 24:216–231
Peng C (2010) Parametric lower confidence limits of quantile-based process capability indices. J Qual Technol Quant Manag 7(3):199–214
Ranneby B (1984) The maximum spacing method an estimation method related to the maximum likelihood Method. Scandinavian J Stat 11(2):93–112
Saha M (2022) Applications of a new process capability index to electronic industries. Commun Stat 8(4):574–587
Saha M, Dey S, Yadav AS, Ali S (2021) Confidence intervals of the index \(C_{pk}\) for normally distributed quality characteristics using classical and Bayesian methods of estimation. Brazilian J Probab Stat 35(1):138–157
Swain J, Venkatraman S, Wilson J (1988) Least squares estimation of distribution function in Johnsons translation system. J Stat Comput Simul 29:271–297
Vannman K (1995) A unified approach to capability indices. Statistica Sinika 5:805–820
Wang X, Wang Y, Peng J et al (2023) Multivariate long sequence time-series forecasting using dynamic graph learning. J Ambient Intell Humaniz Comput 14:7679–7693
Weerahandi S (1993) Generalized confidence intervals. J Am Stat Assoc 88:899–905
Weerahandi S (1995) Exact statistical methods for data analysis. Springer, New York
Weerahandi S (2004) Generalized inference in repeated measures. Wiley, New York
Wu CW, Pearn WL (2008) A variables sampling plan based on \(C_{pmk}\) for product acceptance determination. Eur J Oper Res 184:549–560
Wu CW, Pearn WL (2008) A variables sampling plan based on \(C_{pmk}\) for product acceptance determination. Eur J Oper Res 184:549–560
Xiao Z, Xu X, Xing H, Luo S, Dai P, Zhan D (2021) RTFN: a robust temporal feature network for time series classification. Inf Sci 571:65–86
Xiao Z, Zhang H, Tong HX, Xu X (2022). An efficient temporal network with dual self-distillation for electroencephalography signal classification. IEEE International Conference on Bioinformatics and Biomedicine (BIBM), Las Vegas, NV, USA, pp 1759-1762
Xing H, Xiao Z, Qu R, Zhu Z, Zhao B (2022) An efficient federated cistillation learning system for multitask time series classification. IEEE Trans Instrum Meas 71:1–12
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Saha, M., Devi, A., Yadav, A.S. et al. Evaluation of a novel loss-based process capacity index \({\mathcal {S}}^{\prime }_{pk}\) and its applications. Int J Syst Assur Eng Manag 15, 2188–2201 (2024). https://doi.org/10.1007/s13198-023-02235-1
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DOI: https://doi.org/10.1007/s13198-023-02235-1