A chocolatier, Alain, in Belgium conducted extensive market research and focus groups, to understand the perfect chocolate for a distinct group of consumers. The perfect piece of chocolate would have a target weight of 60 grams. The voice of the specific consumers prefers a specification of +/- 2 grams. Alain has targeted a selling price of 15 Euros a piece. A box of dozen would be 150 Euros, gift wrapped for special occasions. Alain searched for a depositor that would give the most accurate fill weight, with a tight tolerance, a machine that would not only make elegant shapes of chocolate with precise caramel filling and clean impression. A confectionery machinery maker, Mod d’Art has several models. Model A. costs $5,000 and could produce fill weights at average of 60.50 grams, and standard deviation of 1.5 grams. Model B. costs $15,000, but with a standard deviation of 0.95 grams, with 59.95 grams average fill weight. Model C. runs $25,000; this deluxe model has standard deviation of 0.60 grams, average fill weight of 60.15 grams.

Answer :

Voice of consumer = 4

Cpk of Model A= 0.333

Cpk of Model B= 0.7017

Cpk of Model C= 1.1388

Explanation :

As per the data given in the question,

Voice of consumer = Upper limit - Lower limit

= 62 - 58

= 4

Cp of Model A = Voice of consumer ÷ (6 × Standard deviation)

= 4 ÷ (6 × 1.5)

= 0.4444

Cpk of Model A = Min(Cpl, Cpu)

and Cpl = (Mean-lower limit) ÷ (3 × standard deviation)

Cpu = (Upper limit- Mean) ÷ (3 ×  standard deviation)

So, Cpk of Model A = Min((60.5 - 58) ÷ (3 × 1.5), (62 - 60.5) ÷ (3 × 15))

= Min(0.555, 0.333)

Hence, , Cpk of Model A = 0.333

Cp of Model B = (62-58) ÷ (6 × 0.95)

= 0.7017

Cpk of Model B = Min((59.95 - 58) ÷ (3 × 0.95), (62 - 59.95) ÷ (3 ×0.95))

Cpk of Model B = 0.6842

Cp of Model C = (62 - 58) ÷ (6 × 0.60)

= 1.111

Cpk of Model C = Min((60.15 - 58) ÷ (3 × 0.60), (62 - 59.95) ÷ (3 ×0.60))

= 1.1388

steering wheels are always situated on the left side of the car.

always drive on the right side of the road.

white lines separate lanes of traffic traveling the same direction.

hashed or broken lines means you may change lanes when it is safe.

solid white lines mean stay in your lane.

yellow lines separate traffic moving in opposing directions.

hashed or broken yellow lines mean you can carefully pass, paying attention to oncoming traffic.

never cross a solid yellow line (or double yellow line).

when turning left at an intersection, pass in front of any cars that are turning left from the opposing direction (do not try to pass behind them).

use the left lane to pass other cars traveling your direction.

do not pass in the right lane unless absolutely necessary.

if you are driving in the far left hand lane and someone would like to pass you, move over to the right lane when it is safe to do so and allow them to pass.

you must always yield to pedestrians.

come to a complete stop whenever you see pedestrians trying to cross the street.

never pass a school bus if it has flashing red lights. wait until the lights have stopped.

be aware of bicyclists. often they share the road with cars and are supposed to also follow general traffic laws.

be particularly careful about driving in cities with bike lanes -- always check before turning that a bike is not coming.

it is mandatory to pull over or stop at an intersection to allow an emergency vehicle to pass you if you see one traveling with lights flashing and/or a siren running.

do not overuse your car horn. horns are used almost exclusively for emergency situations or for when you feel unsafe.

explanation:

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