Answer Happy

Problem 10 The table below shows a hypothetical solar array design. In this design the solar array is composed of a number of independent "strings", i.e. several solar cells connected in series (see attached diagram). The number of cells per string is determined by the array voltage requirement and therefore is not an array designer's option. Assume that there are 30 cells per string. The designer is using metallic interconnects welded to the solar cells and reverse-voltage-blocking diodes connected to the ends of the cell strings by wires. The items that contribute to the reliability of the arrays are the diodes, the interconnects, and the interconnect-to-cell welds. Experiments found that resistance in the weld joints was sufficient to require at least two welds per connection. Accelerated life testing resulted in 5 out of 1000 joints failed, suggesting a 0.5% failure probability per weld. Other testing data gave a similar reliability for the standard diodes, and 0.01% for the interconnects. To get the satellite's required power, multiple strings are mounted on the panel and connected in parallel. The minimum number of strings is not up to the designer. However, since the string outputs are additive, the designer can use extra strings to introduce additional redundancy. In this case assume that there are a total of 50 strings and that the minimum required number of operational strings is 48. Determine the reliability of the solar array panel, i.e. the probability that no more than 2 strings fail over the course of the mission. Item Weld Interconnect Braze to cell Braze to diodes Solar cell Diode Number of items per unit 4 1 1 1 1 2 Items required for unit operation 2 1 1 1 1 1 Units per string 60 31 2 2 30 1 Probability of failure of one item 0.005 0.0001 0 0 0 0.005