Homework # 7

Problems: 9.4, 9.8, 9.18

Problem No.4

The process in a state of statistical control is studied. The reported loss associated with the key quality characteristic is x = 30, L = 40; x = 36, L = 30; x = 40, L = 42

1. Calculate the values for L₀, k, and m in the quadratic loss function.

2. What is the loss when x=34?

3. If the replacement cost of a part is $46, calculate the specifications so that they are set at the point where the loss and the replacement costs are equal.

4. Find the expected loss if the process has a mean of 41 and a standard deviation of 3.

5. What is the expected loss if the process mean is shifted to the target/nominal value?

Graduate Credit

A company that is poorly schooled in the principles and methods associated with the modern quality movement, is undertaking a process capability study. Their approach is to take thirty parts, calculate a sample mean and sample standard deviation. These statistics are then used in conjunction with the part specifications to calculate Cpk. The company is failing to recognize that Cpk, for such a situation, will be subject to considerable uncertainty and in fact is a random variable that can be described by a statistical distribution.

A normal population with a mean of 20 and a standard deviation of 1 is of interest. Assume specifications of 17 and 23. What is the true Cpk value? Draw 1000 samples of size 30 from the normal population. For each sample, calculate the sample mean, sample standard deviation, and Cpk value. Make a histogram for the Cpk values. Interpret the results. Compare the result with the true Cpk value. Comment on the advisability on using this sampling method to calculate Cpk.

Hint : Use excel to generate the data

Due date : Nov, 16 2005

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Problems?? contact psshirod@mtu.edu