$($a$)$ What do you understand by the societal loss proposed by Taguchi? How is it different from Goal post philosophy? The cost of repair of a failed television set in a factory is $40$ dollars per unit. Let color concentration be used as the performance characteristics, $y,$ and let the customers consider the television set to be defective if $y$ varies over the range $+-10,$ where $$ is the target value of $y.$ Find the quality loss of a customer whose television set has a color concentration of $(-6).$ What kind of quality characteristics is it$?[3$ Marks$]$

$($b$)$ Discuss the essential steps used for Benchmarking. Elaborate how a process in your organization can be improved using benchmarking concept. $[3$ Marks$]$

$($c$)$ List the core concepts of Six Sigma philosophy. How is it different from the usual $3$ Sigma processes used earlier? $[3$ Marks$]$