Question

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 1

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