A company manufactures a product that has a design (nominal) target width of 5 inches with tolerances of + .05 inch. The process that produces the product has a mean of 4.995 inches and a standard deviation of 0.01 inch. According to the process capability ratio is the process capable of being within design specifications?

a. The process is capable of meeting design specifications because the index is greater than 1

Explanation:

Missing word "a. the index is greater than 1.0, b. the process is not capable of meeting design specifications because the index is less than 1.0, c. the process is capable of meeting design specifications because the index is twice the process capability ratio, d. none of the above"

Process capability ratio (Cp) = (USL - LSL) / 6σ

- USL = 5+0.05= 5.05

- LSL = 5 - 0.05 = 4.95

- Standard deviation σ = 0.01

Process capability ratio (Cp) = 5.05 - 4.95 / 6*0.01

Process capability ratio (Cp) = 0.1 / 0.06

Process capability ratio (Cp) = 1.666666666666667

Process capability ratio (Cp) = 1.67

Process capability ratio Cp > 1. So, the Process is capable of meeting design specification.

a manufacturer of printed circuit boards uses exponential smoothing with trend to forecast monthly demand of its product. at the end of december, the company wishes to forecast sales for january. the estimate of trend through november has been 200 additional boards sold per month. average sales have been around 1000 units per month. the demand for december was 1100 units. the company uses α = 0.20 and β = 0.10. make a forecast including trend for the month of january.