外文翻譯--當檢驗檢測失敗時基于恒基區(qū)間風險的一個多級層次時間延遲來預防維修檢查模型【中英文文獻譯文】,中英文文獻譯文,外文,翻譯,檢驗,檢修,檢測,失敗,基于,區(qū)間,風險,一個,多級,層次,時間,延遲,預防,維修,檢查,模型,中英文,文獻,譯文 ~ Pergamon Int. J. Math. Tools Manufact. Vol. 37, No. 6. pp. 823....836, 1997 ? 1997 Elsevier Science Lid All fights r-~erved. Printed in Great Britain 0890-6955/97517.00 + .00 PII: S0890-6955(96)00026-0 A DELAY TIME MULTI-LEVEL ON-CONDITION PREVENTIVE MAINTENANCE INSPECTION MODEL BASED ON CONSTANT BASE INTERVAL RISK--WHEN INSPECTION DETECTS PENDING FAILURE G. B. WILLIAMS and R. S. HIRANIt (Received 17 November 1995) Abstract--The model described in this paper is one of a series, which determines the optimal multi-level inspection-maintenance policy for a stochastically deteriorating multi-state sub-system, using the delay-time concept. The sub-system deterioration is assumed to be a non-decreasing semi-Markov process, where states are self-announced and inspection detects the sign of pending failure. Emphasis is placed on constant availability and reduction of production losses, deterioration rate and subsequent sub-system failure. In this respect, inspection is scheduled in such a way that the risk of failure is a constant for each inspection interval. Two pairs of mathematical models and softwares have been developed, and the policy decisions taken have been based on two criteria for optimisation. These decisions have then been validated by carrying out a simulation exercise using the ProModel simulation package. ? 1997 Elsevier Science Ltd. 1. INTRODUCTION Production systems can be viewed as multi-state stochastically deteriorating complex sys- tems. Their parts, from a maintenance point of view, can be grouped into five characteristi- cally different sub-systems. Thus, separate optimum multi-level pseudo-control limit main- tenance policies have been proposed \[1-5\]. This paper deals with a gradually deteriorating sub-system, whose present state is self-announced and inspection detects the sign of pend- ing failure, the transition state, its status and the time of transition. A delay-time concept, first introduced by Christer \[6\], regards the failure mechanism as a two-stage process. A fault initiates in a sub-system and becomes prominent at time y. This can be identified if inspection is carded out at the time. If the fault is not attended to, the faulty sub-system subsequently changes its state after some further interval h, which Christer called the failure delay time. Research has been carded out \[7-10, 6, 11-18\] using this concept in maintenance mod- elling for two-state single- or multi-component \[7, 8, 18\] systems, where inspection inter- vals for perfect and/or imperfect inspections are taken as constant or variable \[11\], and repair restores the system, taking into account subjective and objective \[7, 8, 18\] data. It would seem practically unreasonable to consider repair as a renewal of a system to its original condition \[19\] and constant inspection intervals may not have a constant risk of failure, which results in inconsistent availability, and hence a variable production rate and high inventory, labour and production costs \[5\]. Thus, the concept of delay time is here extended to multi-level maintenance of a multi-state sub-system, where inspections are scheduled in such a way that the risk of failure is constant for each inspection interval \[20, 21\]. 2. MATHEMATICAL MODEL Let the deterioration process of a sub-system be a semi-Markov process with state space ~={ 1, 2 .... ,L}, where states are described by the level of deterioration and the nature of the process limits the occurrence of transitions to higher states. The present state of the sub-system is self-announcing, whereas inspection detects the sign of pending failure. The tSchool of Manufacturing and Mechanical Engineering, University of Birmingham, Birmingham B 15 2Tl', U.K. 823 824 G.B. Williams and R. S. Hirani maintenance policy selected is a pseudo-control limit policy 6(°), where maintenance action is determined by the control state/3. Let N={ 1, 2 ..... /3- 1 } be a set of states which asks for no repair action if they are functional, and minimal repair when they are non- functional. Its complementary set R￠={/3, /3+1 ..... L} is the set of states which calls for repair or replacement of a sub-system to some better state in set pCN. Whenever inspection detects pending failure before the next inspection, on-condition preventive maintenance (OCPM) is performed instantaneously. This OCPM does not change the present and tran- sition states and their transition time, but reduces the probability of transition to a non- functional state. Mathematically, such a pseudo-control limit policy 6(k.) (where k. rep- resents either functional state kf or non-functional state knf) can be expressed as: I i = k for k. n- i, i e Ig and i n-I, i~}~ and i n- 1, illV~ and i E E 0 2 3 4 5 6 7 Control states /DExpeet0d data (n =2)IISimulatod data (n =2) 1 (n=3) msimlateu Uata (n =3) Lj The optimum policy selected by main programme and simulation was same within reasonable accuracy, where n = 2, 13 = 4, and policy no. 96 (which recommends purchase state 1, and replacement to state 1 for each transition state _> 13 Fig. 5. Optimum system availability. t._ 0 0 0 > .Q cO .O 0 t,.,. Q. E _1 v 3 4 5 6 7 Transition states _> 13 IIExpected data(n = 3) IBSimulated data (n = 3) 11 V Fig. 6. The probability of transition to various states. A delay time multi-level on-condition preventive maintenance inspection model 835 A 1 U) 1 (9 ~. 1 (9 .Q t~ (9 E F- - 1 2 3 4 5 Initial states 6 ~otecl~ta(n_- 2)msim~lated data(n ~ 21~ Fig. 7. Time available for a production cycle. and the supporting software, (iii) the main program determined the optimum results within a few minutes whereas simulation runs took longer, and (iv) different policies were selec- ted for different criteria because these decisions were data dependent (Figs 4 and 5). An industrial setup was modelled using the ProModel simulation package. To facilitate decision making, user-defined sub-routines were written in Turbo Pascal. The ProModel simulation was then run and identical results were obtained; this confirms the validity of the model and the supporting software. Capital recovery for a production system is taken to be equal to the drop in value considering inflation or deflation, which enables mature as well as premature replacement by the same or its alternative without additional investment. REFERENCES \[ 1 \] G. B. Williams and R. S. Hirani, Multi-level maintenance model for parts of a production system with a self-announcing present state. Proceedings of ProModel Corporation Third An