Question

Rachel loves to bake cookies, but she has an old oven that has trouble maintaining a constant temperature. Assume the acceptable temperature range for making the cookies is 350 plus or minus 5 degrees. Six Sigma quality (3.4 defects per million units produced) is probably a bit much to ask of Rachel’s old oven.

a. What would the standard deviation in the temperature of her oven need to be if she settled for a “Three Sigma” level of quality? (Round your answer to 2 decimal places.)

b. If her oven exactly meets this quality level, what percentage of the time would her oven be operating at a temperature outside the acceptable range? Use Table 6-5. (Round your answer to 2 decimal places.)

Answer 1

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Standard deviation refers to the variability of a process. It is denoted by the symbol .

Known data corresponding to Person R’s old oven is given below:

• The mean temperature of the oven is 350 degrees

• The standard deviation is 5 degrees

(a)

Calculate the standard deviation in the temperature for 3 sigma control limits as shown below:

For three sigma controls limits the specification width is shown below in figure-1:

Figure-1: Specification width

For three sigma control limits all deviations must fall between the 6 standard deviations. Range of the process would be 10, as the standard deviation is 5 degrees above and below the mean value.

The standard deviation would be calculated using the following formula:

The standard deviation in the temperature for 3 sigma control limits is 1.67 degrees.

(b)

From “how quality relates to Sigma” table, determine the corresponding defects per million units for Sigma level For 3-sigma control limits there exists 66,807 defects per million units.

Therefore, the percentage of time the oven is operating at a temperature outside the acceptable range is calculated using given formula:

Hence, it is concluded that 6.68% of the time oven is operating outside the acceptable range.

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