2. (16 points) A company is going to introduce a new cell phone. ABC Cell Servic

Question

2. (16 points) A company is going to introduce a new cell phone. ABC Cell Services is going to sell the phones and expects the phones to weigh between 5.0 and 5.5 ounces (referred to as the spec limits). The company currently believes that its phones currently weigh 5.3 ounces.

a) If the company wants to have a six sigma process, what must the standard deviation (o) be so that the Cpk of the process indicates that the company can provide the six sigma process (CpJt of 2.0 or greater)?

b) Suppose that the company can maintain an average weight of 5.3 ounces and a standard deviation (ct) of 0.04 ounces. If the minimum acceptable process capability is 2.0, can the company meet the specification requirements at this time? If it cannot, explain if it is due to a drifting of the mean or too much variability. Explain.

Explanation / Answer

a)

USL = 5.5 oz

LSL = 5.0 oz

Average weight, = 5.3 oz

For a six sigma process, Cpk value must be at least 2

Cpu = (USL-)/3

Cpl = (-LSL)/3

Cpk = MIN(Cpu, Cpl)

Denominator of Cpu & Cpl is same. So, Cpk is determined by the minimum of the numberator. (USL-) = 5.5-5.3 = 0.2, (-LSL) = 5.3-5.0 = 0.3

Numerator of Cpu is less. So, (USL-)/3 = 2 , = (USL-)/6 = (5.5-5.3)/6 = 0.033

Standard deviation () = 0.033 oz

b) As we have determined in part a, maximum std deviation for six sigma capability is 0.033, therefore, with std dev of 0.04, company cannot meet the specification requirements at six sigma level.

However, Cp = (USL-LSL)/6 = (5.5-5.0)/(6*0.04) = 2.083

Process capability ratio (Cp) is greater than 2, which means if the mean is shifted to exactly midway between the specification limits, then Cpk will also be equal to 2.083. Therefore, the reason of process not meeting specification requirement is because of drifting of mean, rather than variability.

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