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

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

Referensi E.Ebeling, Charles.” Introduction to Relaibility and Maintainability Engineering”. 2nd Edition, 2009. McGrawHill Internasional, Xie, Min et al. “Computing Reliability System”. Kluwer Academic Publisher, 2004. Etc

Introduction

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

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

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

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

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

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.

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.

Statistical And Mathematic Overview

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

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=…

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)

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

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.

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