State whether the following statements are True or False. Give reason in support of your answer. 
a) If the average number of defects in an item is 4, the upper control limit of the c-chart will be 12.
b) The specification limits and natural tolerance limits are same in statistical quality control.
c) If the probability of making a decision about acceptance or rejection of a lot on the first sample is 0.80 and the sizes of the first and second samples are 10 and 15, respectively, then
the average sample number for the double sampling plan will be 25.
d) Two independent components of a system are connected in series configuration. If the reliabilities of these components are 0.1 and 0.30, respectively then the reliability of the system will be 0.65.
e) A point in the pictorial representation of a decision tree having states of nature as immediate sub-branches is known as decision point. 

a) False. The upper control limit (UCL) of a c-chart is not fixed and is calculated using a formula based on the average number of defects. The formula for the UCL is usually UCL = avg + 3 * sqrt(avg), where avg is the average number of defects. So, if the average number of defects is 4, the UCL will not be 12.

b) False. The specification limits and natural tolerance limits are not the same in statistical quality control. Specification limits are the predetermined upper and lower limits set by _____ _______ _____ ____ ________ __________ _______ _________ ____ ____ ____.
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