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Maintenance Policies

Maintenance Policies. Corrective maintenance: It is usually referred to as repair. Its purpose is to bring the component back to functioning state as soon as possible. In some cases, it involves replacement of one or more components.

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Maintenance Policies

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  1. Maintenance Policies • Corrective maintenance: It is usually referred to as repair. Its purpose is to bring the component back to functioning state as soon as possible. In some cases, it involves replacement of one or more components. • Preventive maintenance: Its purpose is toreduce the probability ofcomponent failure. It may involve lubrication, small adjustment, or replacing components or parts of components that are beginning to wear out. Periodic testing and maintenance based on condition monitoring are also regarded aspreventive maintenance.

  2. Maintainability The ability of an item, under stated conditions of use, to be retained in, or restored to, a state in which it can perform its required functions, when maintenance is performed under stated conditions and using prescribed procedures and resources (BS 4778).

  3. Availability The ability of an item (under combined aspects of its reliability, maintainability, and maintenance support) to perform its required function at a stated instant of time or over a stated period of time (BS 4778). When considering a production system, the average availability of the production is sometimes called the production regularity.

  4. Corrective Maintenance Replacement/repair after failure

  5. Transition of Component States Normal state continues Component fails Failed state continues N F Component is repaired

  6. The Failure-to-Repair Process

  7. Repair Probability - G(t) • The probability that repair is completed before time t, given that the component failed at time zero. • If the component is non-repairable

  8. Repair Density - g(t)

  9. Repair Rate - m(t) • The probability that the component is repaired per unit time at time t, given that the component failed at time zero and has been failed to time t. • If the component is non-repairable

  10. Mean Time to Repair - MTTR

  11. The Whole Process

  12. Availability - A(t) • The probability that the component is normal at time t, i.e., A(t)=Pr{X(t)=1}. • For non-repairable components • For repairable components

  13. Unavailability - Q(t) • The probability that the component fails at time t, i.e., • For non-repairable components • For repairable components

  14. Unconditional Failure Density, w(t) The probability that a component fails per unit time at time t, given that it jumped into the normal state at time zero. Note, for non-repairable components.

  15. Unconditional Repair Density, v(t) The probability that the component is repaired per unit time at time t, give that it jumped into the normal state at time zero.

  16. Conditional Failure Intensity λ(t) The probability that the component fails per unit time, given that it is in the normal state at time zero and normal at time t. In general , λ(t)≠r(t). For non-repairable components, λ(t) = r(t). However, if the failure rate is constant (λ) , then λ(t) = r(t) = λ for both repairable and non-repairable components.

  17. Conditional Repair Intensity, µ(t) The probability that a component is repaired per unit time at time t, given that it is jumped into the normal state at time zero and is failed at time t, For non-repairable component, µ(t)=m(t)=0. For a constant repair rate m, µ(t)=m.

  18. The Average Availability The average availability in a time interval is defined as This definition can be interpreted as the average proportion of interval where the component is able to function.

  19. The Limiting Availability It can be shown that In the reliability literature, the symbol A is often used as notation both for the limiting availability and the average availability.

  20. Expected Number of Failures (ENF)

  21. ENF over an interval, W(t1,t2 ) Expected number of failures during (t1,t2) given that the component jumped into the normal state at time zero. For non-repairable components

  22. ENR over an interval, Expected number of repairs during , given that the component jumped into the normal state at time zero. For non-repairable components

  23. Mean Time Between Repairs, MTBR Expected length of time between two consecutive repairs. MTBR = MTTF + MTTR Mean Time Between Fails, MTBF Expected length of time between two consecutive failures. MTBF = MTBR

  24. Let where

  25. RELATIONS AMONG PROBABILISTIC PARAMETERS FOR REPAIR-TO-FAILURE PROCESS (THE FIRST FAILURE) General r(t) Failure Rate r(t) Const. r(t)= ●

  26. RELATIONS AMONG PROBABILISTIC PARAMETERS FOR FAILURE-TO-REPAIR PROCESS Repair Rate m(t) General m(t) Const. m(t)=u ●

  27. RELATIONS AMONG PROBABILISTIC PARAMETERS FOR THE WHOLE PROCESS Repairable Non-repairable ※ ※ ※ Fundamental Relations ◎ ( Next )

  28. Stationary Values Remark

  29. CALCULATION OF w(t) and v(t) (given f (t) and g (t)) Two types of components fail during [t, t+dt] : Type I F N F N Type II time u u+du t t+dt Probability of Type I : ( v (u) du ) ( f (t-u) dt ) Probability of Type II : f (t) dt OR

  30. One type of components which is repaired during [t, t+dt] F N time u u+du t t+dt OR

  31. [ EXAMPLE ]

  32. 0 1 2 3 4 5 6 7 8 9 18 18 15 5 4 2 1 1 0 0 1 1 0.8333 0.2778 0.2222 0.1111 0.0556 0.0556 0 0 0 0 0.1667 0.7222 0.7778 0.8889 0.9444 0.9444 1 1 0 3 10 1 2 1 0 1 0 0 0 0.1667 0.5556 0.0556 0.1111 0.0556 0 0.0556 0 0 0 0.1667 0.6667 0.2001 0.5000 0.5005 0 1.0000 - -

  33. TTF data assumption Exponential Weibull Normal Log-normal Histogram polynomial approximation parameter identification f (t) MTTF r (t) F (t) R (t)

  34. TTR data assumption Exponential Weibull Normal Log-normal Histogram Polynomial approximation parameter identification MTTR g (t) m (t) G (t)

  35. f (t), g (t) or w(0) = f(0), v(0) = 0 w (t), v (t) Q (t) A (t) = 1 - Q (t) A (t)

  36. Constant-Rate Models • Repair-to-Failure

  37. NON-REPAIRABLE 1 Good Failed P (t) = probability that the component is good at time t = R(t) good at t and remained good failed at t and was repaired Initial Condition :

  38. Constant-Rate Models • Failure-to-Repair

  39. Constant-Rate Models • Dynamic Behavior of Whole Process (1) • also

  40. REPAIRABLE 1-λΔt 1-μΔt μΔt λΔt Good Failed good and remained good failed and repaired

  41. Initial Condition: P(0)=1

  42. Constant-Rate Models • Dynamic Behavior of Whole Process (2)

  43. Constant-Rate Models • Stationary Values of the Whole Process

  44. Proof (1) • From • Laplace Transform

  45. Proof (2) • Rearrangement and Inversion

  46. System Availability

  47. Approximate Average (Limiting) System Unavailability

  48. Preventive Maintenance Periodic Testing and/or Replacement

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