Imperfect preventive maintenance for numerical control machine tools with log-linear virtual age process

Abstract

Based on the log-linear virtual age process, an imperfect preventive maintenance policy for numerical control (NC) machine tools with random maintenance quality is proposed. The proposed model is a combination of the Kijima type virtual age model and the failure intensity adjustment model. Maintenance intervals of the proposed hybrid model are derived when the failure intensity increase factor and the restoration factor are both random variables with uniform distribution. The optimal maintenance policy in infinite time horizon is presented. A numerical example is given when the failures of NC machine tools are described by the log-linear process. Finally, a discussion is presented to show how the optimal results depend on the different cost parameters.

Keywords

reliability / imperfect preventive maintenance / virtual age / log-linear process / failure intensity

References

[1] WangY-q, JiaY-z, JiangW-wei. Early failure analysis of machining centers: A case study [J]. Reliability Engineering and System Safety, 2001, 72(1): 91-97

[2] PhamH, WangH. Imperfect Repair [J]. European Journal of Operational Research, 1996, 94(3): 425-438

[3] WangZ-m, YangJ-guo. Numerical method for Weibull generalized renewal process and its applications in reliability analysis of NC machine tools [J]. Computers & Industrial Engineering, 2012, 63(4): 1122-1128

[4] LiuF-m, ZhuH-p, LiuB-xing. Maintenance decision-making method for manufacturing system based on cost and arithmetic reduction of intensity model [J]. Journal of Central South University, 2013, 20(6): 1559-1571

[5] NguyenD G, MurthyD N P. Optimal preventive maintenance policies for repairable systems [J]. Operations Research, 1981, 29(6): 1181-1194

[6] NakagawaT. Periodic and sequential preventive maintenance policies [J]. Journal of Applied Probability, 1986, 23(2): 536-542

[7] NakagawaT. Sequential imperfect preventive maintenance policies [J]. IEEE Transactions on Reliability, 1988, 37(3): 295-298

[8] LinD, ZuoM J, YamR C M. General sequential imperfect preventive maintenance models [J]. International Journal of Reliability Quality and Safety Engineering, 2000, 7(3): 253-266

[9] LinD, ZuoM J, YamR C M. Sequential imperfect preventive maintenance models with two categories of failure modes [J]. Naval Research Logistics, 2001, 48(2): 172-182

[10] KijimaM, MorimuraH, SuzukiY. Periodical replacement problem without assuming minimal repair [J]. European Journal of Operational Research, 1988, 37(2): 194-203

[11] KijimaM. Some results for repairable systems with general repair [J]. Journal of Applied Probability, 1989, 26(1): 89-102

[12] GuoR, AscherH, LoveC E. Generalized models of repairable systems-A survey via stochastic processes formalism [J]. ORiON, 2000, 16(2): 87-128

[13] DoyenL, GaudoinO. Classes of imperfect repair models based on reduction of failure intensity or virtual age [J]. Reliability Engineering and System Safety, 2004, 84(1): 45-56

[14] WuS, Clements-CroomeD. Preventive maintenance models with random maintenance quality [J]. Reliability Engineering and System Safety, 2005, 90(1): 99-105

[15] WangZ-m, YangJ-g, WangG-q, ZhangG-bao. Sequential imperfect preventive maintenance policy with random maintenance quality under reliability limit [J]. Journal of Mechanical Engineering Science, 2011, 225(8): 1926-1935

[16] PanjaS C, RayP K. Reliability analysis of a “point-and-point machine” of the Indian railway signaling system [J]. Quality and Reliability Engineering International, 2007, 23(1): 833-848

[17] MarshallS E, ChukovaS. On analysing warranty data from repairable items [J]. Quality and Reliability Engineering International, 2010, 26(1): 43-52

[18] AscherH E, KobbacyK A H. Modelling preventive maintenance for repairable systems [J]. IMA Journal of Mathematics Applied in Business and Industry, 1995, 6(1): 85-100

[19] BakerR D. Some new tests of the power law process [J]. Technometrics, 1996, 38(3): 256-265

[20] SaldanhaP L C, DesimoneE A, FrutosoP F. An application of non-homogeneous Poisson point processes to the reliability analysis of service water pumps [J]. Nuclear Engineering and Design, 2001, 210(1): 125-133

[21] WangZ-m, YuXia. Log-linear process modeling for repairable systems with time trends and its applications in reliability assessment of NC machine tools [J]. Journal of Risk and Reliability, 2013, 227(1): 55-65