A new method of estimating the process capability index with exponential distribution using interval estimate of the parameter. (English) Zbl 1432.62376
Summary: This paper deals with a new method of deriving the Process Capability Index (PCI) when the quality characteristic \(X\) follows a positively skewed distribution. The focus of the paper is to derive a new estimate of PCI by taking into account the \(100(1-{\alpha})\) Confidence Intervals (CI) of the parameter \((s)\) and arriving at a new expression. The formula \(C_{s}\), proposed by P. A. Wright [“A process capability index sensitive to skewness”, J. Stat. Comput. Simul. 52, No. 3, 195–203 (1995; doi:10.1080/00949659508811673)] which contains a component for skewness, is reexamined and a new estimate is constructed by utilizing the lower, middle and upper values of the CI of the parameter. The weighted average of the three possible estimates of \(C_{s}\) is proposed as the new estimate by taking the weights inversely proportional to the squared deviation from the hypothetical value of \(C_{s}\). The properties of the estimate are studied by simulation using one parameter exponential distribution.
MSC:
| 62P30 | Applications of statistics in engineering and industry; control charts |
| 62F25 | Parametric tolerance and confidence regions |
References:
| [1] | C. G. Borroni, M. Cazzaro and P. M. Chiodini, Measuring process capability under non-classical assumptions: A purposive review of the relevant literature, Statist. Appl. 22 (2010), no. 3, 279-306.; Borroni, C. G.; Cazzaro, M.; Chiodini, P. M., Measuring process capability under non-classical assumptions: A purposive review of the relevant literature, Statist. Appl., 22, 3, 279-306 (2010) |
| [2] | J. A. Clements, Process capability calculations for non-normal distributions, Quality Progr. 22 (1989), 95-100.; Clements, J. A., Process capability calculations for non-normal distributions, Quality Progr., 22, 95-100 (1989) |
| [3] | A. J. Duncan, Quality Control and Industrial Statistics, 3rd edition, D B Taraporevala Sons & Co Pvt Ltd., Bombay, 1999.; Duncan, A. J., Quality Control and Industrial Statistics (1999) · Zbl 0047.37901 |
| [4] | G. S. Koch, Jr. and R. F. Link, Statistical Analysis of Geological Data, Dover Publications, New York, 2002.; Koch, Jr., G. S.; Link, R. F., Statistical Analysis of Geological Data (2002) |
| [5] | D. C. Montgomery, Introduction to Statistical Quality Control, 6th edition, John Wiley & Sons, New York, 2009.; Montgomery, D. C., Introduction to Statistical Quality Control (2009) · Zbl 1274.62015 |
| [6] | W. L. Pearn and C. S. Chang, The performance of process capability index \(C}_{{s}}\) on skewed distributions, Comm. Statist. Simulation Comput. 26 (1997), 1361-1377.; Pearn, W. L.; Chang, C. S., The performance of process capability index \(C}_{{s}}\) on skewed distributions, Comm. Statist. Simulation Comput., 26, 1361-1377 (1997) · Zbl 0900.62558 |
| [7] | W. L. Pearn and K. S. Chen, Capability indices for non-normal distributions with an application electrolytic capacitor manufacturing, Microelect. Reliab. 37 (1997), 1853-1858.; Pearn, W. L.; Chen, K. S., Capability indices for non-normal distributions with an application electrolytic capacitor manufacturing, Microelect. Reliab., 37, 1853-1858 (1997) |
| [8] | K. Reddi Rani, V. Sai Sarada and K. V. S. Sarma, A new method of implementing single sampling plan by variables using interval estimates of process mean and variance, Int. J. Sci. Eng. Res. 8 (2017), no. 7, 1702-1705.; Reddi Rani, K.; Sai Sarada, V.; Sarma, K. V. S., A new method of implementing single sampling plan by variables using interval estimates of process mean and variance, Int. J. Sci. Eng. Res., 8, 7, 1702-1705 (2017) |
| [9] | V. Sai Sarada, M. Subbarayudu and K. V. S. Sarma, Estimation of process capability index using confidence intervals of process parameters, Res. Rev. J. Stat. 7 (2018), no. 3, 49-57.; Sai Sarada, V.; Subbarayudu, M.; Sarma, K. V. S., Estimation of process capability index using confidence intervals of process parameters, Res. Rev. J. Stat., 7, 3, 49-57 (2018) · Zbl 1432.62376 |
| [10] | J. Sinsomboonthong, Confidence interval estimations of the parameter for one parameter exponential distribution, IAENG Int. J. Appl. Math. 45 (2015), no. 4, 343-353.; Sinsomboonthong, J., Confidence interval estimations of the parameter for one parameter exponential distribution, IAENG Int. J. Appl. Math., 45, 4, 343-353 (2015) · Zbl 1512.62035 |
| [11] | K. Vännman, A unified approach to capability indices, Statist. Sinica 5 (1995), 805-820.; Vännman, K., A unified approach to capability indices, Statist. Sinica, 5, 805-820 (1995) · Zbl 0824.62091 |
| [12] | R. Vishnu Vardhan and K. V. S. Sarma, Estimation of the area under ROC curve using confidence interval of mean, ANU J. Phys. Sci. 2 (2010), no. 1, 29-39.; Vishnu Vardhan, R.; Sarma, K. V. S., Estimation of the area under ROC curve using confidence interval of mean, ANU J. Phys. Sci., 2, 1, 29-39 (2010) |
| [13] | P. A. Wright, A process capability index sensitive to skewness, J. Stat. Comput. Simul. 52 (1995), 195-203.; Wright, P. A., A process capability index sensitive to skewness, J. Stat. Comput. Simul., 52, 195-203 (1995) |
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