\"The Geometric Distribution and Shorts in NiCad Batteries\" In their article \"

Question

  "The Geometric Distribution and Shorts in NiCad Batteries"  In their article "A Case Study of the Use of an Experimental Design in Preventing Shorts in Nickel-Cadmium Cells"; Ophir, El-Gad, and Snyder describe a series of experiments conducted in order to reduce the proportion of cells being scrapped by a battery plant because of  internal shorts.  The experimental program was successful in reducing the proportion of manufactured cells with internal shorts to around 0.03.   The following procedure is being developed in order to monitor the process for increases in the true proportion of manufactured cells  with internal shorts.   Suppose that testing of batteries for internal shorts begins  on a production run in this plant for monitoring/control purposes,  let B = the number of batteries required until          the first internal short is discovered.  [a] What is the distribution and expected value of B,  if the proportion of manufactured cells with internal shorts  remains at 0.03?   What is the distribution and expected value of B,  if the proportion of manufactured cells with internal shorts  increases to 0.10?   What happens, in general, to the expected value of B  as the proportion of manufactured cells with internal shorts  increases? Choose one: [Larger or Smaller] 

Explanation / Answer

a) fot this is geommetric distribution with parameter p=0.03

expected value =1/p=1/0.03 =33.333

b)

fot this is geommetric distribution with parameter p=0.1

expected value =1/p=1/0.1 =10

c)

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