The below data is for questions 1-3 problems below

26.7 |
24 |
25.8 |
29.2 |
28.6 |

23.1 |
27.7 |
26.6 |
28.9 |
30.7 |

29 |
27.2 |
24.6 |
28.5 |
27.8 |

28 |
24 |
30.9 |
31.7 |
24.2 |

23.1 |
29.8 |
30.3 |
22.2 |
27.1 |

1) What proportion of the population do we expect to fall outside the specifications if the specifications are LSL=20 and USL=32? (assume a Normal distribution and use the standard normal table)

2) We wish to test if there is sufficient evidence at the 95% confidence level that the process may be off the target of 26 in H2O. What is the appropriate Null Hypothesis?

3) From the data collected, is there sufficient evidence at the 95% confidence level that the process may be off the target of 26 in H2O? (i.e. Is the process mean significantly different from 26?)

4) A production process is operating at 5% nonconforming. If we select 20 pieces at random from the production process, what is the probability that more than 2 of the 20 are nonconforming.

Note: ensure probabilities are between 0 ≤ p ≤ 1

5) The billing department of a major credit card company tracks the number of errors on customer’s bills. Suppose that errors occur according to a Poisson distribution with parameter l=.07. What is the probability that a customer’s bill selected at random contains at least one error?

Note: ensure probabilities are between 0 ≤ p ≤ 1

6) A chemical manufacturing process is monitored by X-bar and S charts. Twenty five subgroups of size 4 are collected to establish the control limits.

X-bar-bar =200

S-bar = 4.5

A. Calculate the control limits for both charts.

Ai) What is the LCL for the X-bar chart?

7) A chemical manufacturing process is monitored by X-bar and S charts. Twenty five subgroups of size 4 are collected to establish the control limits.

X-bar-bar =200

S-bar = 4.5

A. Calculate the control limits for both charts.

Aii) What is the UCL for the S chart?

8) A chemical manufacturing process is monitored by X-bar and S charts. Twenty five subgroups of size 4 are collected to establish the control limits.

X-bar-bar =200

S-bar = 4.5

B. Estimate the process standard deviation

9) Six Sigma methodology allows for process shifts of up to a 1.5 sigma from batch to batch. If the process is being monitored by X-bar and R charts with a subgroup size n=4 and shifts 1.5 sigma, what would be the ARL of the X-bar chart? (ie how long will it take us on average to detect a shift of that magnitude)

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