Log-linear process modeling for repairable systems with time trends and its applications in reliability assessment of numerically controlled machine tools

Abstract

Two non-homogeneous Poisson processes including the power law process and the log-linear process with reliability improvement or deterioration are analyzed. Based on Akaike information criterion and Bayesian information criterion, the best model of failure data is presented. The point maximum likelihood and interval estimators of the parameters, as well as seven reliability indices of the log-linear process model, such as cumulative mean time between failures, cumulative number of failures, reliability at a given time, and warranty time given reliability are given. In tests for failure time trends, both the graphical methods, including the cumulative failures versus time plot and the total-time-on-test plot, and the analytical methods including the Laplace, the Military Handbook, and the Lewis–Robinson tests are used. Three real cases for failure data with failure truncation and time truncation of multiple numerically controlled machine tools are given to illustrate the use of the proposed models.

Keywords

Power law process log-linear process repairable systems reliability assessment

Get full access to this article

View all access options for this article.

References

Ascher

Feingold

. Repairable systems reliability: Modeling, inference, misconceptions and their causes. New York: Marcel Dekker, 1984.

Calabria

Pulcini

. Inference and test in modeling the failure/repair process of repairable mechanical equipments. Reliab Eng Syst Saf 2000; 67: 41–53.

Saldanha

PLC

de Simone

Frutuoso e Melo

. An application of non-homogeneous Poisson point processes to the reliability analysis of service water pumps. Nucl Eng Des 2001; 210: 125–133.

Weckman

Shell

Marvel

. Modeling the reliability of repairable systems in the aviation industry. Comput Ind Eng 2001; 40: 51–63.

Ascher

Kobbacy

KAH

. Modelling preventive maintenance for repairable systems. IMA J Mgmt Math 1995; 6: 85–100.

Baker

. Some new tests of the power law process. Technometrics 1996; 38: 256–265.

Coetzee

. The role of NHPP models in the practical analysis of maintenance failure data. Reliab Eng Syst Saf 1997; 56:161–168.

Panja

Ray

. Reliability analysis of a ‘point-and-point machine’ of the Indian railway signaling system. Qual Reliab Eng Int 2007; 23: 833–848.

Marshall

Chukova

. On analysing warranty data from repairable items. Qual Reliab Eng Int 2010; 26: 43–52.

10.

Lawless

Thiagarajah

. A point-process model incorporating renewals and time trends, with application to repairable systems. Technometrics 1996; 38(2): 131–138.

11.

Muralidharan

. A review of repairable systems and point process models. ProbStat Forum 2008; 1: 26–49.

12.

Lawless

Nadeau

. Some simple robust methods for the analysis of recurrent events. Technometrics 1995; 37(2): 158–168.

13.

Nelson

. An application of graphical analysis of repair data. Qual Reliab Eng Int 1998; 14(1): 49–52.

14.

Kvaloy

Lindqvist

. TTT-based tests for trend in repairable systems data. Reliab Eng Syst Saf 1998; 60: 13–28.

15.

Park

Kim

. Goodness-of-fit tests for the power-law process. IEEE Trans Reliab 1992; 41(1): 107–111.

16.

Lee

. Testing adequacy of the Weibull and log linear rate models for a Poisson process. Technometrics 1980; 22(2): 195–199.

17.

Louit

Pascual

Jardine

AKS

. A practical procedure for the selection of time-to-failure models based on the assessment of trends in maintenance data. Reliab Eng Syst Saf 2009; 94(10): 1618–1628.

18.

Viertava

Vaurio

. Testing statistical significance of trends in learning, ageing and safety indicators. Reliab Eng Syst Saf 2009; 94: 1128–1132.

19.

Crowder

Kimber

Smith

. Statistical analysis of reliability data. London: Chapman & Hall, 1994.

20.

Akaike

. A new look at statistical model identification. IEEE Trans Automat Control 1974; 19: 716–723.

21.

Schwarz

. Estimating the dimension of a model. Ann Stat 1978; 6: 461–464.

22.

Nelson

. Accelerated testing: statistical methods, test plans, and data analysis. New York: John Wiley & Sons, 1990.

23.

Meeker

Escobar

. Statistical methods for reliability data. New York: John Wiley & Sons, 1998.

24.

Walls

. A graphical approach to identification of dependent failures. J R Stat Soc Ser D Stat 1996; 45(2): 185–196.

25.

Guo

Liao

Zhao

. A new stochastic model for systems under general repairs. IEEE Trans Reliab 2007; 56(1): 40–49.

26.

Zhang

Shen

. Three-parameter Weibull distribution for random truncated NC machine tool fault data. J Jilin Univ Eng Technol Ed 2009; 39(2): 378–381 (in Chinese).

27.

Jia

Zhao

Zhang

. Lifetime distribution and failure analysis for VDL series vertical machining center. Modular Machine Tool Automatic Mfg Technique 2011; 7: 42–47 (in Chinese).

28.

Wang

Jia

Jiang

. Early failure analysis of machining centers: a case study. Reliab Eng Syst Saf 2001; 72: 91–97.

29.

Wang

Yang

Wang

. Sequential imperfect preventive maintenance policy with random maintenance quality under reliability limit. Proc IMechE, Part C: J Mechanical Engineering Science 2011; 225: 1926–1935.