Q2-Reliability

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Virginia Tech *

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3414

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Industrial Engineering

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Apr 3, 2024

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docx

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Quality of Design -- Reliability Quality of Conformance vs. Quality of Design Reliability The probability that a product will perform its intended function for a specified length of time A producer must be able to estimate the Reliability of a product (or system) to make appropriate design decisions for quality, accurately forecast costs, and establish policies. Light Bulb Example The BrighterWorld company is producing a new light bulb with an expected life of 850 hours. A random sample of 1000 bulbs is selected from a preliminary production run and tested for 850 hours. After 850 hours of use: R(t) + Q(t) = 1 Components in series Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 1 R(t) = # surviving to time t # products total Q(t) = # that have failed before time t # products total 950 bulbs still work 50 bulbs have failed Reliability = Probability of Failure = R system = R A R B
Glen’s Prototype Example Glen is building a new prototype for a product. The prototype will only function correctly if all 3 of the required components function correctly. Based on information provided by suppliers, the reliabilities of the 3 components vary as follows: 0.9752, 0.9522, and 0.9641. What is the reliability of the prototype? Set of Tires Example Gary purchases a new set of tires for his car. Each of the 4 tires has a 3-year warranty. The probability that a tire will last for 3 years is 0.9900. What is the probability that the company will have to pay for at least one warranty claim from Gary? Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 2 0.85 0.90 B A all components must function for the system (product) to function Event A: component A survives to time t Event B: component B survives to time t
Components in parallel only one of the components in parallel must be functioning for the system (product) to function Multi-level Parallel Component Example Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 3 0.95 0.85 0.60 0.95 0.85 A B R system = R A + (1 – R A )R B
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