How to Estimate Loss in Production with Given Design Specifications
a) Estimate the loss for a production if the characteristic under study takes on a value of 10.04 and 100 parts are produced
Based on the Taguchi loss function, how can we calculate the estimated loss for this scenario?
b) What action, if any, is needed when the production process reveals a sample mean of 9.789 after recalibration?
How does the sample mean value impact the production process and what steps can be taken to address the situation?
Estimation of Loss in Production
a) The estimated loss for producing 100 parts with a characteristic value of 10.04 is 2.24.
Action Needed in Production Process
b) Action is needed as the sample mean of 9.789 is below the lower limit of the design specification, indicating the production process does not meet requirements.
a) To estimate the loss for a production if the characteristic takes on a value of 10.04, we can substitute the given values into the Taguchi loss function.
Given:
Design specification: $10.00 \pm 0.10$ cm
Taguchi loss function: $L(x) = 1,400(x-T)^2$
Substituting the values:
$x = 10.04$
$T = 10.00$
Loss = $L(x) = 1,400(10.04 - 10.00)^2$
Loss = $L(x) = 1,400(0.04)^2$
Loss = $L(x) = 1,400(0.0016)$
Loss = $L(x) = 2.24$
Therefore, the estimated loss for the production with a characteristic value of 10.04 would be 2.24.
b) In this situation, we are given the sample mean ($x$-bar) after recalibrations as 9.789. To determine if any action is needed, we can compare this value with the design specification range of $10.00 \pm 0.10$ cm.
The lower limit of the design specification is $10.00 - 0.10 = 9.90$ cm, and the upper limit is $10.00 + 0.10 = 10.10$ cm.
Since the sample mean ($x$-bar) of 9.789 is below the lower limit of the design specification, it indicates that the production process is not meeting the specified requirements. In this situation, an action is needed to address the issue.
Possible actions could include recalibrating the production process to bring the mean value closer to the target (T = 10.00 cm), identifying and correcting any process issues, or investigating the sources of variation to improve the quality of the cylinders being produced.