Probability of System Malfunction & Defective Tubes Selection

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SUMMARY

The discussion focuses on calculating the probability of system malfunction in mechanical systems using binomial probability distribution functions (PDF). Specifically, it addresses a scenario with 5 bulbs where the system operates if at least 3 are functioning, given a 15% defect rate. The calculations yield probabilities for various outcomes, including the likelihood of selecting defective tubes from a population of 5, with the same defect rate applied. The results provide clear insights into system reliability and defect management.

PREREQUISITES
  • Understanding of binomial probability distribution functions (PDF)
  • Basic knowledge of probability theory
  • Familiarity with mechanical systems and their operational thresholds
  • Ability to perform statistical calculations
NEXT STEPS
  • Study binomial probability distribution calculations in detail
  • Learn about reliability engineering principles
  • Explore statistical software tools for probability analysis, such as R or Python's SciPy library
  • Investigate methods for improving system reliability and reducing defect rates
USEFUL FOR

Engineers, statisticians, and quality control professionals involved in reliability analysis and defect management in mechanical systems.

axnman
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Que. 1 : In a mech. sys. 5 bulbs are used and system will operate if any 3 are functioning. Given that 15% of bulbs are defective , with aid of binomial PDF determine what are the chances that the system will malfunction?

Que. 2 : Suppose 15% of total population of tubes is defective and that 5 tubes are randomly selected. Determine the probability that there will be among those selected:
1) no defectives
2) only 2 defectives
3) no more than 2 defectives
4) only 3 defectives
5) no more than 3 defectives
 
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