A study of Weibull shape parameter: Properties and significance

The two-parameter Weibull distribution has been widely used for modelling the lifetime of products and components. In this paper we study the effect of the shape parameter on the failure rate and three variables of importance in the context of maintenance and reliability improvement. These variables are (i) time to failure, (ii) age at replacement based on risk and (iii) residual life. We propose a classification scheme for the distribution based on the shape parameter and discuss the application of the results.

[1]  Abolfazl Saghafi,et al.  Improved linear regression method for estimating Weibull parameters , 2009 .

[2]  P. D. Warren,et al.  Fracture of brittle materials: effects of test method and threshold stress on the Weibull modulus , 2001 .

[3]  Dallas R. Wingo,et al.  The left-truncated Weibull distribution: theory and computation , 1989 .

[4]  Dongsu Ryu,et al.  Novel concepts for reliability technology , 2005, Microelectron. Reliab..

[5]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[6]  R. Jiang,et al.  Aging property of unimodal failure rate models , 2003, Reliab. Eng. Syst. Saf..

[7]  Joel E. Michalek,et al.  Determination of Reliability Functions by the TTT Transform , 1985, IEEE Transactions on Reliability.

[8]  M. M. Siddiqui,et al.  Residual lifetime distribution and its applications , 1994 .

[9]  Xiaowei Xu,et al.  Multi-criteria decision making approaches for supplier evaluation and selection: A literature review , 2010, Eur. J. Oper. Res..

[10]  J. Moubray.  Reliability-centred maintenance , 1995 .

[11]  A. K. S. Jardine,et al.  Maintenance, Replacement, and Reliability , 2021 .

[12]  P. L Hall,et al.  Probabilistic physics-of-failure models for component reliabilities using Monte Carlo simulation and Weibull analysis: a parametric study , 2003, Reliab. Eng. Syst. Saf..

[13]  Tiedo Tinga,et al.  Application of physical failure models to enable usage and load based maintenance , 2010, Reliab. Eng. Syst. Saf..

[14]  Vallayil N. A. Naikan,et al.  Reliability strength design through inverse distributions—exponential and Weibull cases , 1996 .

[15]  Anil K. Jain.  Data clustering: 50 years beyond K-means , 2008, Pattern Recognit. Lett..

[16]  Wenyuan Li,et al.  Evaluating mean life of power system equipment with limited end-of-life failure data , 2004 .

[17]  Seong-woo Woo,et al.  Improving the reliability of a water dispenser lever in a refrigerator subjected to repetitive stresses , 2009 .

[18]  Philip A. Scarf,et al.  On reliability criteria and the implied cost of failure for a maintained component , 2005, Reliab. Eng. Syst. Saf..

[19]  Suk Joo Bae,et al.  Lifetime prediction through accelerated degradation testing of membrane electrode assemblies in direct methanol fuel cells , 2010 .

[20]  Wen-Chuan Lee,et al.  Computational procedure of assessing lifetime performance index of Weibull lifetime products with the upper record values , 2011, Math. Comput. Simul..

[21]  Min Xie,et al.  On the upper truncated Weibull distribution and its reliability implications , 2011, Reliab. Eng. Syst. Saf..

[22]  Pra Murthy.  New research in reliability, warranty and maintenance , 2010 .

[23]  H. Kaebernick,et al.  Remaining life estimation of used components in consumer products: Life cycle data analysis by Weibull and artificial neural networks , 2007 .

[24]  Albert H. Moore,et al.  An Evaluation of Exponential and Weibull Test Plans , 1976, IEEE Transactions on Reliability.

[25]  Andrew K. S. Jardine,et al.  Maintenance, Replacement, and Reliability: Theory and Applications, Second Edition , 2013 .

[26]  C. J. Wang.  Concept of durability index in product assurance planning , 1990, Annual Proceedings on Reliability and Maintainability Symposium.

[27]  Timothy M. Young,et al.  Statistical reliability analyses of two wood plastic composite extrusion processes , 2011, Reliab. Eng. Syst. Saf..

[28]  Ashraf Labib,et al.  World‐class maintenance using a computerised maintenance management system , 1998 .

[29]  Timo Pukkala,et al.  Comparison of beta, Johnson’s SB, Weibull and truncated Weibull functions for modeling the diameter distribution of forest stands in Catalonia (north-east of Spain) , 2007, European Journal of Forest Research.

[30]  R. Barlow,et al.  Optimum Preventive Maintenance Policies , 1960 .