Q2-Reliability

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Apr 3, 2024

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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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Slipper Example A company is concerned about the reliability of the stitching and glue that are both needed to hold a slipper together. The lifetime of a slipper should be 5 years. The reliability of the glue for 5 years is 0.98, and the reliability of the stitching is 0.80. To increase the reliability of the slipper, the company is adding two extra rows of stitching. This makes a total of three rows of stitching (each with a reliability of 0.80), even though only one row is needed to hold the slipper together. What is the probability that a slipper will last (glue and stitching) for 5 years? Workstation 2 Example There is a 43% chance that the equipment at workstation 2 will function correctly through an entire 8-hour shift. The company keeps 5 extra units at the workstation in case of failure. If the first unit fails, the next unit will immediately take its place. Each of the 6 units has the same reliability. A new set of 6 units can be available for the next shift in the event of a failure. The company operates 30 of these 8-hour shifts each month and loses an average of $12,000 each time the production line experiences downtime. How much does the company expect to lose over the next 6 months due to downtime caused by workstation 2 failure? Copyright 2023 LL Clark Referenced Material : Operations & Supply Chain Management, 10 th Ed. by Russell & Taylor p. 4

Q2-Reliability

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