Question

In: Math

A company that makes car accessories. The company control its production process by periodically taking a...

A company that makes car accessories. The company control its production process by periodically taking a sample of 99 units from the production line. Each product is inspected for defective features. Control limits are developed using three standard deviations from the mean as the limit. During the last 12 samples taken, the proportion of defective items per sample was recorded as follows:

0.01	0.03	0.0	0.04	0.01	0.01
0.00	0.01	0.02	0.02	0.03	0.03

a. Determine the mean proportion defective, the UCL, and the LCL? (Marks 1) (word count maximum:150)

b. Draw a control chart and plot each of the sample measurements on it? (Marks 1) (word count maximum:100)

c. Does it appear that the process for making tees is in statistical control? (Marks 0.5) (word count maximum:100)

Expert Solution

solution:

Mean proportion defective is roughly the average of all proportions. that is (0.01+0.03+0.0+0.04+0.01+0.01+0.00+0.01+0.02+0.02+0.03+0.03)/12=0.0175

The mean proportion defective is ( p_bar) is 0.0175

The UCL and LCL is

UCL = p_bar + 3*sqrt(p_bar*(1-p_bar)/n_bar) = 0.0175 + 3*sqrt(0.0175*(1-0.0175)/99) = 0.0570

LCL = p_bar - 3*sqrt(p_bar*(1-p_bar)/n_bar) = 0.0175 - 3*sqrt(0.0175*(1-0.0175)/99) = -0.0220. Since defectives cannot be in negative, LCL = 0.

b.

The control chart is shown below

C.

It appears that the process is in control since there is no breach of the UCL value.

please give me thumb up

milcah answered 1 month ago

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