Setting a target value and lower and upper bounds in response optimization

Lower bound

Minitab automatically sets the Lower value to the smallest value or the smallest proportion in the data. You may want to change that value depending on your response goal.

• If your goal is to maximize the response, set the lower value to the smallest acceptable value.
• If your goal is to target a specific value, you should set the lower value above your lower specification limit to ensure that individual observations are within this limit. Because the bounds are for the predictions of the mean response, if the mean response is close to a bound, some individual data will likely be outside the bounds. If you do not have specification limits, you may want to use a lower point of diminishing returns. This is the point at which going below a certain value does not make much difference.
• If the goal is minimize, the lower bound does not exist. You do not specify a lower value.

The bounds affect the desirability values. If the goal is maximize or target, the desirability is 0 for any mean response value at or below the lower bound. The closer the lower bound is to the target, the faster the desirability decreases as the response deviates from the target.

For example, you have a response with a target of 100. If the lower bound is 0 and the weight is 1, then the desirability of a response of 90 is 0.90. If the lower bound is 50 and the weight is 1, then the desirability of a response of 90 is 0.80.

Target

Minitab automatically sets the Target value as the target value that you input in the main dialog. You may want to change that value depending on your response goal.

• If your goal is to meet a target, then the target value should be the most desirable response value.
• If your goal is to minimize the response, you may want to set the target value at the point of diminishing returns. When you want to minimize the response, this is the point at which going below a certain value does not make much difference. If there is no point of diminishing returns, use a very small target value, one that is probably not achievable. All responses that are less than the target have a desirability of 1.
• If your goal is to maximize the response, you may want to set the target value at the point of diminishing returns. When you want to maximize the response, this is the point at which going above a certain value does not make much difference. If there is no point of diminishing returns, use a very high target value, one that is probably not achievable. All responses that are greater than the target have a desirability of 1.

Upper bound

Minitab automatically sets the Upper value to the largest value or largest proportion in the data. You may want to change that value depending on your response goal.

• If your goal is to minimize the response, set the upper value to the largest acceptable value
• If your goal is to target a specific value, then you should set the upper value below the upper specification limit to ensure that individual observations are below this limit. Because the bounds are for the predictions of the mean response, if the mean response is close to a bound, some individual data will likely be outside the bounds. If you do not have specification limits, you may want to use an upper point of diminishing returns. This is the point at which going above a certain value does not make much difference.
• If the goal is to maximize the response, the upper bound does not exist. You do not specify a lower value.

The bounds affect the desirability values. If the goal is minimize or target, the desirability is 0 for any mean response value at or above the upper bound. The closer the upper parameter is to the target, the faster the desirability decreases as the response deviates from the target.

For example, you have a response with a target of 100. If the upper bound is 200 and the weight is 1, then the desirability of a response of 110 is 0.90. If the upper bound is 150 and the weight is 1, then the desirability of a response of 110 is 0.80.