Answered

Welcome to Westonci.ca, the place where your questions are answered by a community of knowledgeable contributors. Discover comprehensive answers to your questions from knowledgeable professionals on our user-friendly platform. Get precise and detailed answers to your questions from a knowledgeable community of experts on our Q&A platform.

The following data was collected from the manufacturing of an auto component. It represents the diameter (in mm) of that component. What is the UCL for a control chart using this data (z=3)? show working please
Sample Obs 1 Obs 2 Obs 3 Obs 4
1 10 12 12 14
2 12 11 13 16
3 11 13 14 14
4 11 10 7 8
5 13 12 14 13

Sagot :

Answer:

UCL = 14.624

Explanation:

Data Given:

z= 3

And beside the value of z, we are given:

Number of samples = 5

And observations.

First of all, we have to calculate the mean of all the samples.

Sample 1 Mean = [tex]\frac{10+12+12+14}{4}[/tex] = 12

Sample 2 Mean = [tex]\frac{12+11+13+16}{4}[/tex]  = 13

Sample 3 Mean = [tex]\frac{11+13+14+14}{4}[/tex] = 13

Sample 4 Mean = [tex]\frac{11+10+7+8}{4}[/tex] = 9

Sample 5 Mean = [tex]\frac{13+12+14+13}{4}[/tex] = 13

Now, add all the means and find out the mean of the sample size.

Mean of the sample size = [tex]\frac{12+13+9+13+13}{5}[/tex] = [tex]\frac{60}{5}[/tex] = 12

Secondly, we have to find out the maximum and minimum of the observations in each sample.

Sample 1 (max, min) = (14,10)

Sample 2 (max, min) = (16,11)

Sample 3 (max, min) = (14,11)

Sample 4 (max, min) = (11,7)

Sample 5 (max, min) = (14,12)

Thirdly, we need to calculate the Range of each sample.

Range = Max - Min

Range 1 = 14-10 = 4

Range 2 = 16-11 = 5

Range 3 = 14-11 = 3

Range 4 = 11-7 = 4

Range 5 = 14-12 = 2

ΣRange = 18

Now, sum all the ranges and divide it by the number of samples n.

(Range-bar) = ΣRange/n

Range-bar = 18/5

Range-bar = 3.6

Now, we need value of A2 for the sample size of 4. So, it can find out from the table of control chart constants which is attached for your reference.

A2 = 0.729

Now, we have all the data required to calculate the UCL.

UCL = (Mean of the sample size) + (A2 * Range-bar)

UCL = (5) + (0.729x 3.6)

UCL = 14.624

View image adnansoomro2019
Thanks for using our service. We aim to provide the most accurate answers for all your queries. Visit us again for more insights. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.