Interval shrinkage estimation of process performance capability index in gamma distribution

Authors
Parviz Nasiri
Hedar Mokhdari
Masoud Yrmohhmadi
Abstract
Evaluation of production products is a process of necessity to check product quality. One of the criteria for evaluating the quality of the manufactured product is the quality characteristic of the process performance index, which has recently considered a number of researchers in statistical articles. Estimation of process performance index can be done according to the type of statistical distribution of product quality by different methods, including the maximum likelihood method, the least error squared method, the maximum product of distances and quantization. In this article, the estimation of the process performance index is presented using the gamma distribution using method of estimation, moment, maximum likelihood and interval shrinkage estimator. To provide the interval contraction estimator, after proving the unbiasedness of the torque estimators asymptotically, it is shown that the performance index estimator is also unbiased. Next, the efficiency of the estimators is compared using the square error criterion.
Keywords
Gamma distribution
process performance index
classical estimation
for interval shrinkage
Mean squared error
Ahmadi, M. V., and M. Doostparast. 2021. Evaluating the lifetime performance index of products based on pro-aggressively Type-II censored Pareto samples: A new Bayesian approach. Quality and Reliability Engineering Q3 International doi:10.1002/qre.3040.

Golosnoy, V. and Liesenfeld, R. 2011. Interval shrinkage estimators, J. Appl. Stat. 38, 465-477.

Hong, C. W., J. W. Wu, and C.-H. Cheng. 2007. Computational procedure of performance assessment of lifetime index of businesses for the Pareto lifetime model with the right type II censored sample. Applied Mathematics and Computation 184 (2):336–50. Doi: 10.1016/j.amc.2006.05.199.

J. Shaabani & A. A. Jafari. 2022. Inference on the lifetime performance index of gamma distribution: point and interval estimation, Communications in Statistics - Simulation and Computation, DOI: 10.1080/03610918.2022.2045498.

Lee, W. C. 2010. Assessing the lifetime performance index of gamma lifetime products in the manufacturing industry. Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 224 (10):1571–9. Doi:10.1243/09544054JEM1783

Lee, W. C. 2011. Inferences on the lifetime performance index for Weibull distribution based on censored observations using the max p-value method. International Journal of Systems Science 42:931–7. doi:10.1080/00207720903260168.

Lee, W. C., J. W. Wu, and C. W. Hong. 2009. Assessing the lifetime performance index of products from progressively type II right censored data using Burr XII model. Mathematics and Computers in Simulation 79: 2167–79. Doi: 10.1016/j.matcom.2008.12.001.

Montgomery, D. C. 1985. Introduction to statistical quality control. John Wiley & Sons.

Thompson, J. R. 1968. Accuracy borrowing in the estimation of the mean by shrinkage to an interval, J. Amer. Statist. Assoc., 63, 953-963.

Nasiri, P., Ebrahimi, F. 2022. Interval Shrinkage Estimation Reliability System of Stress-Strengths

Models in two parameter Lindley distribution. Mathematical Researches, 8 (1), 72-88

Tong, L. I., K. S. Chen, and H. T. Chen. 2002. Statistical testing for assessing the performance of lifetime index of electronic components with exponential distribution. International Journal of Quality & Reliability Management 19 (7):812–24. doi:10.1108/02656710210434757.