A comparison of time-based maintenance and condition-based maintenance
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1 A comparison of time-based maintenance and condition-based maintenance Bram de Jonge Ruud Teunter Warse Klingenberg Tiedo Tinga University of Groningen The Netherlands COPE congres 2013 November 1, 2013
2 Introduction
3 Introduction We consider the following setting:
4 Introduction We consider the following setting: A single unit.
5 Introduction We consider the following setting: A single unit. Gradual deterioration, condition monitoring is possible.
6 Introduction We consider the following setting: A single unit. Gradual deterioration, condition monitoring is possible. The cost of a breakdown is 1, after which a new unit is putting into use.
7 Introduction We consider the following setting: A single unit. Gradual deterioration, condition monitoring is possible. The cost of a breakdown is 1, after which a new unit is putting into use. Preventive maintenance can be performed at cost c < 1 and makes the unit as good as new.
8 Maintenance policies
9 Maintenance policies Time-based maintenance (TBM)
10 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed.
11 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age).
12 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age). Maintenance is performed when the unit reaches age T.
13 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age). Maintenance is performed when the unit reaches age T. Condition-based maintenance (CBM)
14 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age). Maintenance is performed when the unit reaches age T. Condition-based maintenance (CBM) Condition monitoring required, more appropriate scheduling.
15 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age). Maintenance is performed when the unit reaches age T. Condition-based maintenance (CBM) Condition monitoring required, more appropriate scheduling. Decision variable: M (threshold deterioration level).
16 Maintenance policies Time-based maintenance (TBM) Easy to implement, no condition monitoring needed. Decision variable: T (maintenance age). Maintenance is performed when the unit reaches age T. Condition-based maintenance (CBM) Condition monitoring required, more appropriate scheduling. Decision variable: M (threshold deterioration level). Maintenance is performed when the deterioration level M is reached.
17 Gamma deterioration process
18 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t).
19 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties:
20 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties: Continuous-time process.
21 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties: Continuous-time process. X (0) = 0 with probability 1.
22 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties: Continuous-time process. X (0) = 0 with probability 1. X (τ) X (t) f a(τ t),b for τ > t 0 (f is the gamma density function).
23 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties: Continuous-time process. X (0) = 0 with probability 1. X (τ) X (t) f a(τ t),b for τ > t 0 (f is the gamma density function). X (t) has independent increments.
24 Gamma deterioration process The state of the unit is assumed to deteriorate gradually according to a stationary/homogeneous gamma process X (t). Properties: Continuous-time process. X (0) = 0 with probability 1. X (τ) X (t) f a(τ t),b for τ > t 0 (f is the gamma density function). X (t) has independent increments. Jump process with infinitely many jumps in any time interval.
25 Gamma deterioration process
26 Gamma deterioration process The stationary gamma process has two parameters:
27 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a.
28 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a. Scale parameter b.
29 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a. Scale parameter b. Properties:
30 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a. Scale parameter b. Properties: E(X (t)) = abt.
31 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a. Scale parameter b. Properties: E(X (t)) = abt. Var(X (t)) = ab 2 t.
32 Gamma deterioration process The stationary gamma process has two parameters: Shape parameter a. Scale parameter b. Properties: E(X (t)) = abt. Var(X (t)) = ab 2 t. A breakdown is assumed to occur if the level of deterioration exceeds 1. We choose a and b such that the mean time to failure equals 1 (this does not imply ab = 1).
33 Gamma deterioration process X(t) t
34 Gamma deterioration process X(t) 1 Low a, high b t
35 Gamma deterioration process X(t) 1 High a, low b Low a, high b t
36 Gamma deterioration process X(t) 1 In between High a, low b Low a, high b t
37 Research methodology
38 Research methodology Simulation:
39 Research methodology Simulation: Exact calculations are practically impossible.
40 Research methodology Simulation: Exact calculations are practically impossible. If the number of iterations is sufficiently high, the outcomes are very accurate.
41 Research methodology Simulation: Exact calculations are practically impossible. If the number of iterations is sufficiently high, the outcomes are very accurate. Simulation details: Time step: = Number of iterations: n = 100,000.
42 Base case
43 Base case Gamma deterioration process: a = 5, b
44 Base case Gamma deterioration process: a = 5, b Relative cost preventive maintenance: c = 0.2.
45 Cost analysis
46 Cost analysis Cost saving TBM Cost saving CBM Failure cost = 1 Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
47 Cost analysis Cost T or M
48 Cost analysis Cost saving TBM Cost saving CBM Failure cost = 1 Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
49 Cost analysis Cost T or M
50 Cost analysis Cost 1 TBM T or M
51 Cost analysis Cost saving TBM Cost saving CBM Failure cost = 1 Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
52 Cost analysis Cost 1 TBM T or M
53 Cost analysis Cost 1 TBM CBM T or M
54 Cost analysis Cost saving TBM Failure cost = 1 Cost due to uncertain failure level Cost saving CBM Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
55 Cost analysis Cost saving TBM Failure cost = 1 Cost due saving to CBM uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
56 Effect of deterioration process Cost σ
57 Effect of deterioration process Cost 1 TBM σ
58 Effect of deterioration process Cost 1 TBM CBM σ
59 Cost benefit CBM compared with TBM Cost σ
60 Cost analysis Cost saving TBM Failure cost = 1 Cost due saving to CBM uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
61 Planning time
62 Planning time Preventive maintenance needs to be planned s time units in advance.
63 Planning time Preventive maintenance needs to be planned s time units in advance. The cost c of preventive maintenance does not have to be paid if failure occurs between the moment that maintenance is planned and the moment that maintenance would have been performed.
64 Planning time Preventive maintenance needs to be planned s time units in advance. The cost c of preventive maintenance does not have to be paid if failure occurs between the moment that maintenance is planned and the moment that maintenance would have been performed. Under the CBM policy, maintenance is performed at time t(m) + s, with t(m) the time at which deterioration level M is reached.
65 Planning time Preventive maintenance needs to be planned s time units in advance. The cost c of preventive maintenance does not have to be paid if failure occurs between the moment that maintenance is planned and the moment that maintenance would have been performed. Under the CBM policy, maintenance is performed at time t(m) + s, with t(m) the time at which deterioration level M is reached. The planning time s has no influence on the TBM policy.
66 Planning time Cost 1 TBM CBM (s=0) T or M
67 Planning time Cost 1 TBM CBM (s=0.1) CBM (s=0) T or M
68 Planning time Cost s
69 Planning time Cost 0.6 TBM s
70 Planning time Cost 0.6 TBM CBM s
71 Cost analysis Cost saving TBM Failure cost = 1 Cost due saving to CBM uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
72 Cost analysis Cost saving TBM Failure cost = 1 Cost saving CBM Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
73 Imperfect condition monitoring
74 Imperfect condition monitoring The difference between the true level of deterioration and the observed level of deterioration is modelled by σ p W (t).
75 Imperfect condition monitoring The difference between the true level of deterioration and the observed level of deterioration is modelled by σ p W (t). W (t) is a standard Brownian motion.
76 Imperfect condition monitoring Prognostic error t Low σ p 0.4
77 Imperfect condition monitoring Prognostic error 0.4 High σ p t 0.4
78 Imperfect condition monitoring Cost σ p
79 Imperfect condition monitoring Cost 0.6 TBM σ p
80 Imperfect condition monitoring Cost 0.6 TBM CBM σ p
81 Cost analysis Cost saving TBM Failure cost = 1 Cost saving CBM Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
82 Cost analysis Cost saving TBM Failure cost = 1 Cost saving CBM Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
83 Uncertainty deterioration level failure
84 Uncertainty deterioration level failure The deterioration level at which failure occurs is normally distributed with mean 1 and standard deviation σ f.
85 Uncertainty deterioration level failure The deterioration level at which failure occurs is normally distributed with mean 1 and standard deviation σ f. The normal distribution is left truncated at 0 and right truncated at 2.
86 Uncertainty deterioration level failure Cost σ f
87 Uncertainty deterioration level failure Cost 0.8 TBM σ f
88 Uncertainty deterioration level failure Cost 0.8 TBM CBM σ f
89 Cost analysis Cost saving TBM Failure cost = 1 Cost saving CBM Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
90 Cost analysis Cost saving TBM Cost saving CBM Failure cost = 1 Cost due to uncertain failure level Cost due to imperfect condition monitoring Cost due to maintenance planning Cost due to noncontinuous deterioration information Cost due to deterioration process with jumps Minimal cost (PM just before failure) = c
91 Questions?
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