1. Pengantar Reliabity and Maintainability
Pertemuan Ke-1
Pengantar Reliabity and Maintainability

2. Pokok Bahasan Pengantar Reliabiality dan Maintainability.
Failure Distribution
Constant Failure Rate
Time Dependent Failure Models
Reliability of System
State Dependent System
Physical Models
Realiability Design
Maintainability
Maintainability Design
Availability
Empirical Methods
Reliability Testing
Growth Testing
Software Reliability

3. Referensi
E.Ebeling, Charles.” Introduction to Relaibility and Maintainability Engineering”. 2nd Edition, McGrawHill Internasional,
Xie, Min et al. “Computing Reliability System”. Kluwer Academic Publisher, 2004.
Etc

4. Introduction

5. Study of Reliability and Maintainability
System Complexity
Public Awareness
Insistence on ptoduct quality
Product Liability
others

6. Why Reliability and Maintainability ?
Life cycle costing
Cost benefit analysis
Operational capability study
Refair and facility resourcing
Inventory and spare parts requirement determinations
Replacement decisions
others

7. Random vs Deterministic
“Deterministic is complete information or under certainty condition” “Random is uncomplete information or under uncertainty cinditon”

8. Term and Defintion
Reliability is defined to be the probability that a component or system will perform a required function for a given period of time when used under stated operating conditions.
Design Load
Environment
Operating Conditions

9. Maintenance resources
Term and Definition
Maintainability is defined to be the probability that a failed component or system will be restored or repaired to a specified condition within a period of time when maintenance is performed in accordance with prescribed procedures.
Skill level
Maintenance program
Maintenance resources

10. Term and Definition
Availability is defined as the probability that a component or system is performing its required function at a given point in time when used under stated operating conditions.

11. Reliability vs Quality
Reliability is closely associated with the quality of a product and is often considered a subset of quality.
Quality can be defined qualitatively as th amount by which the product satifies the user’s requirements.
Product quality is in part a function of design and conformance to design specifications.
On the other hand, reliability is concerned with how long the product continues to function once it becomes operational.

12. Statistical And Mathematic Overview

13. Random Event
In relaibility engineering a failure can be described as a random event.
A random event E will occur with some probability denoted by P(E).
The collection of all possible outcomes (events) relative to a random process is called space S, where S = {E1, E2,….EK}
P (E) + P(Ec) =1

14. Random Event
Example : Let the event A = the failure of component 1 and B = the failure of component 2. Then: 𝐴∩𝐵=… 𝐴𝑐∩𝐵=… 𝐴𝑐∪𝐵=…

15. Random Event
Two events A and B mutually exclusive if the occurrence of one precludes the occurrence of the other.
𝑃 𝐴∪𝐵 =𝑃 𝐴 +𝑃 𝐵
𝑃 𝐴∩𝐵 =∅
Two events A and B independent if and only if
𝑃 𝐴∩𝐵 =𝑃 𝐴 𝑃(𝐵)
If two events are not independent, the probability of their intersection must be defined using conditional probability.
𝑃 𝐴 𝐵 = 𝑃(𝐴∩𝐵) 𝑃(𝐵)

16. Random Event Bayes’ Formula
𝑃 𝐴 𝐵 = 𝑃(𝐴∩𝐵) 𝑃(𝐵) = 𝑃 (𝐵∩𝐴) 𝑃[ 𝐵∩𝐴 ∪ 𝐵∩ 𝐴 𝑐 ]
Where B∩𝐴 𝑑𝑎𝑛 𝐵∩ 𝐴 𝑐 are mutually exclusive

17. Random Variables
Random variable is a variable that takes on numerical values in accordance with some probability distribution.
Random variable may be either continuous or discrete.
The probability distribution that assigns a probability to each value of a discrete random variable or assign a probability to an interval of values of a continous random variable can be describe in term of PMF in discrete case and PDF in continous case.

18. Thank you......
For your attention