Question 10.12: Refer to Example 10.11. Assume that it is possible to adjust......

ISE Principles of Statistics for Engineers and Scientists [987713]

Refer to Example 10.11. Assume that it is possible to adjust the process mean to any desired value. To what value should it be set to maximize the value of $C_{pk}$ ? What will the value of $C_{pk}$ be?

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

The specification limits are LSL = 71.4 and USL = 72.8. The value of $C_{pk}$ will be maximized if the process mean is adjusted to the midpoint between the specification limits; that is, if 𝜇 = 72.1. The process standard deviation is estimated with 𝜎̂ = 0.2128. Therefore the maximum value of $C_{pk}$ is (72.1 − 71.4) ∕ (3)(0.2128) = 1.0965. The process capability would be acceptable.

Related Answered Questions

Question: 10.11

The design specifications for a piston rod used in an automatic transmission call for the rod length to be between 71.4 and 72.8 mm. The process is monitored with an X chart and an S chart, using samples of size n = 5. These show the process to be in control. The values of X and s are X = 71.8 mm ...

Verified Answer:

We estimate 𝜇̂ =

\overset{=}{X} = 71.8[/lat...

Question: 10.8

Compute the 3𝜎 X chart upper and lower control limits for the moisture data in Table 10.1. ...

Verified Answer:

With sample 6 deleted, the value of

\overli...

Question: 10.7

Compute the center line and the 3𝜎 S chart upper and lower control limits for the moisture data in Table 10.1. ...

Verified Answer:

The value of

\overline{s}

is 0.2445...

Question: 10.2

Compute the 3𝜎 X chart upper and lower control limits for the moisture data in Table 10.1. ...

Verified Answer:

With sample 6 deleted, the value of

\overse...

Question: 10.1

Compute the 3𝜎 R chart upper and lower control limits for the moisture data in Table 10.1. ...

Verified Answer:

The value of

\overline{R}

is 0.6066...

Question: 10.14

Refer to Example 10.13. To what value must the process standard deviation be reduced in order for the process to attain six-sigma quality? ...

Verified Answer:

To attain six-sigma quality, the value of

C...

Question: 10.13

Specifications for the output voltage of a certain electric circuit are 48 to 52 V. The process is in control with σ = 0.482 V. Compute the process capability index Cp. ...

Verified Answer:

C_{p} = \frac{USL\ −\ LSL}{6\hat{\sigma}} =...

Question: 10.10

Rolls of sheet aluminum, used to manufacture cans, are examined for surface flaws. Table 10.3 presents the numbers of flaws in 40 samples of 100 m² each. Compute the center line and 3𝜎 control limits for the c chart. Plot the chart. Does the process appear to be in control? ...

Verified Answer:

The average of the 40 counts is

\overline{c...

Question: 10.9

In the production of silicon wafers, 30 lots of size 500 are sampled, and the proportion of defective wafers is calculated for each sample. Table 10.2 presents the results. Compute the center line and 3𝜎 control limits for the p chart. Plot the chart. Does the process appear to be in control? ...

Verified Answer:

The average of the 30 sample proportions is [latex...

Question: 10.6

Refer to Example 10.4. If the sample size remains at n = 4, what must the value of the process standard deviation 𝜎 be to produce an ARL of 10 when the process mean shifts to 3.5? ...

Verified Answer:

Let 𝜎 denote the new process standard deviation. T...