A manufacturer of an automotive speed sensor subjects 10 sensors to a reliabilit

Question

A manufacturer of an automotive speed sensor subjects 10 sensors to a reliability test that simulates the environmental conditions (such as temperature and speed) at which the sensors normally operate. A sensor is regarded as failed when its output falls outside 5% tolerance. The miles accumulated before the failures of the sensors are (in thousands) 110 130 150 155 159 163 166 68 169 170 Assuming that the miles to failure follow a Rayleigh distribution determine the value of the parameter of the distribution and the corresponding estimate of the mean. Solution. The value of the parameter used is the m.l.e. of the above sample of 10 values of mileage. Applying formula (1.40) lambda = 2n/sigma we have lambda_10 = 2 middot 10/240616 middot 8.31199 middot 10^-11 Using (1.46) we find, , mu_10 = 137, 470 miles.

Explanation / Answer

240616x106 is the sum of squares of the list of 10 numbers given

Its given that the numbers given are in thousands.

So,

1110002 + 1300002 + 1500002 + 1550002 + 1590002 + 1630002 + 1660002 + 1680002+ 1690002 + 1700002

= 240616x106

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