Want a start - for UCL & LCL

  • Thread starter axnman
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Using the given information of $2 for rework and $6 for scrap, an equation can be derived to calculate the expected cost based on the X bar, R, and σ values. In summary, to minimize expected cost, the process mean should be located at the nominal value and an equation can be derived to calculate the expected cost based on given values.
  • #1
axnman
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Nominal value = 0.5; specification limits ± 0.5...find the % of non-conformance below LCL and above UCL produced by this process assuming normality? The data set given to me has 1 reading out of the limits given here? should i calc. like that? no right? or it has a generalized equation?

since it also says when msmnt. below LCL $2 to rework and when above UCL $6 to scrap and cost=0 when msmnt between spec. limits. Asking where should be the process mean located to minimize expected cost?

So my assumption is probably wrong that the data set values should be used in this case...can anyone give me a start to this question...just a brief idea? Have calc values of X bar , R and σ...maybe an eqn. based on that?
 
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  • #2
The % of non-conformance above/below the LCL/UCL cannot be determined from the data given. To minimize the expected cost, the process mean should be located at the nominal value (0.5). This will ensure that the majority of the measurements are within the specification limits and the cost associated with rework and scrap is minimized.
 

1. What is UCL and LCL in the scientific context?

UCL and LCL stand for Upper Control Limit and Lower Control Limit, respectively. They are statistical tools used in process control to determine the acceptable range of variation in a process. UCL and LCL are typically set at a certain number of standard deviations from the process mean and can help identify when a process is out of control.

2. How are UCL and LCL calculated?

UCL and LCL are calculated using statistical methods such as the standard deviation, mean, and sample size. The specific calculation may vary depending on the type of process being measured. However, a common method is to calculate the mean and standard deviation of a sample of data points and then set the UCL and LCL at a specific number of standard deviations from the mean.

3. What is the purpose of using UCL and LCL in scientific research?

The purpose of using UCL and LCL is to monitor and control the variation in a process. By setting limits, scientists can determine when a process is operating within acceptable parameters and when it may need adjustments or further investigation. UCL and LCL can also help identify trends and patterns in data that may be useful for improving the process.

4. Can UCL and LCL be adjusted during a research study?

Yes, UCL and LCL can be adjusted during a research study if new data or information suggests that the existing limits are not appropriate. It is important to regularly review and update UCL and LCL to ensure they accurately reflect the current state of the process being studied.

5. Are UCL and LCL the only methods for process control?

No, UCL and LCL are not the only methods for process control. Other statistical tools, such as control charts, can also be used for process monitoring and improvement. The specific method used may depend on the type of process and the goals of the research study.

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