## Related questions with answers

**Reliability of a manufacturing network**. A team of industrial management university professors investigated the reliability of a manufacturing system that involves multiple production lines (Journal of Systems Sciences & Systems Engineering, March 2013). An example of such a network is a system for producing integrated circuit (IC) cards with two production lines set up in sequence. Items (IC cards) first pass through Line 1 , then are processed by Line 2. The probability distribution of the maximum capacity level $(x)$ of each line is shown below. Assume the lines operate independently. Find the mean maximum capacity for each line. Interpret the results practically.

Line | Maximum Capacity, $x$ | $p(x)$ |
---|---|---|

1 | 0 | $.01$ |

12 | $.02$ | |

24 | $.02$ | |

36 | $.95$ | |

2 | 0 | $.002$ |

35 | $.002$ | |

70 | $.996$ |

Solution

VerifiedWe need to determine the expected value for each line.

The expected value (or mean) is the sum of the product of each possibility $x$ with its probability $P(x)$:

$\begin{aligned} \mu &=\sum xP(x) \end{aligned}$

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