Question

Aspen Plastics produces plastic bottles to customer order. To monitor the process, statistical process control charts...

Aspen Plastics produces plastic bottles to customer order. To monitor the
process, statistical process control charts are used. The central line of the chart for
the sample means is set at 8.50 and the range at 0.31in. Assume that the sample
size is 6 and the specification for the bottle neck diameter is 8.50 ± 0.25.
a. Calculate the control limits for the mean and range charts. (3 points)
b. Suppose that the standard deviation of the process distribution is 0.13 in.
If the firm is seeking three-sigma performance, is the process capable of
producing the bottle? (4 points)
c. If the process is not capable, what percent of the output will fall outside the
specification limits? (3 points

Homework Answers

Answer #1

Solution:

Let,

(X=) = Overall Mean = 8.50

R- = Range Bar = 0.31

A2 = Constant value derived from the control chart constant value table = 0.483

D3 = Constant value derived from the control chart constant value table = 0

D4 = Constant value derived from the control chart constant value table = 2.004

U = Upper Specification Limit = 8.50 + 0.25 = 8.75

L = Lower Specification Limit = 8.50 - 0.25 = 8.25

Answer a:

Control Limits for Mean Chart:

CL = Average Mean (X=) = 8.50

UCL = (X=) + (A2 * R-)

= 8.50 + (0.483 * 0.31)

= 8.6497 (Rounded to 4 decimal places)

LCL = (X=) - (A2 * R-)

= 8.50 - (0.483 * 0.31)

= 8.3503 (Rounded to 4 decimal places)

Control Limits for Range Chart:

CL = Average Range (R-) = 0.31

UCL = D4 X R- = 2.004 X 0.31 = 0.6212 (Rounded to 4 decimal places)

LCL = D3 X R- = 0 X 0.31 = 0

Answer b:

σ = Std Dev. = 0.13

Here, we will calculate Cp and Cpk as mentioned below:

Where,

So,

Cpk = Min (0.641,0.641) = 0.641

As Cpk < 1, The process is not capable of meeting the desired specifications.

Answer c:

i) % of output falling outside the Upper Specification Limit:

= (8.75 - 8.50) / 0.13

= 1.9231

So,

% of units above USL = Probability value derived from the standard normal table for Z_USL = 0.0272 or 2.72%

ii) % of output falling outside the Lower Specification Limit:

= (8.50 - 8.25) / 0.13

= 1.9231

% of units below LSL = Probability value derived from the standard normal table for Z_LSL = 0.0272 or 2.72%

Thus, % of total units out of the desired specification limits = 2.72 + 2.72 = 5.44 % (Rounded to the two decimal places)

(Kindly raise an upvote for this answer, if you found it useful)

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Broody Plastics produces plastic bottles for the customer orders. Statistical process control charts is being used...
Broody Plastics produces plastic bottles for the customer orders. Statistical process control charts is being used to monitor all the process. assume that the sample size is 4 and the specification for the bottle neck diameter is 6.00+-0.35. (Note that the central line of chart for the sample means is set at 6.00 and the range at 0.4 in.) (a) Calculate control limits for the mean and range charts. (b) If the firm is looking for the three-sigma performance, is...
Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from...
Aspen Plastics produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle​ neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions​ (in.) from the last six samples are Bottle Sample 1 2 3 4 1 0.617    0.582 0.602 0.610 2 0.596 0.606 0.615 0.574 3 0.591 0.594 0.580 0.593 4 0.613 0.616 0.613 0.591 5 0.622 00.596...
Process in statistical control has a mean of 100.0 and standard deviation of 3.0. ?_bar and...
Process in statistical control has a mean of 100.0 and standard deviation of 3.0. ?_bar and ? charts with subgroups of size 7 are used to monitor the process. If the process center shifts downward to 96.0, what is the probability of first point falling outside ?_bar chart control limits is on the third sample taken after the shift?
In order to determine if a process that produces housings for wireless speakers is in control,...
In order to determine if a process that produces housings for wireless speakers is in control, the following data is collected to construct a control chart. Ten samples of 200 wireless speakers each have been taken and the number of defective housing is: Sample1:3; Sample2:10; Sample3:8; Sample4:2; Sample5:6 Sample6:7; Sample7:4; Sample8:5; Sample9:6;Sample10:7. Based on this data, is the process in control if 2 sigma limits are employed? a. it is out of control b. it is in control because the...
Statistical Process Control T. Crews, Inc. has been contracted to make Foolio. The recipe calls for...
Statistical Process Control T. Crews, Inc. has been contracted to make Foolio. The recipe calls for 100 milligrams of taurine in each 16-ounce bottle. To make sure that they are in compliance, T. Crews has pulled eight bottles of Foolio from its last eleven batches and tested them for taurine content. The data from these tests is below. Use this data for questions 8 – 14. Mg taurine per bottle Batch Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle...
1) What are some indicators that there are assignable causes for variation in a process? I.Process...
1) What are some indicators that there are assignable causes for variation in a process? I.Process capability. II. Data patters outside of the control limits. III. Data patters within the control limits. IV. Points randomly falling above and below the control chart center line. a. II and III b. II, III, IV c. I, II, IV d. I, II, III, IV 2) The best quantitative tool to determine the cause for variation in a process is: a. ANOVA b. Correllation...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT