Question

Could you please assist with this question? If possible could you illustrate in Excel? The Langley tire company measures their tire stems to see if they hold air.
They produce 300 tires a month and record the defective rate for each day's production.
Below are the results of this month's tests.
a. Determine the 3 sigma UCL and LCL
b. Does the tire stem process appear to be in statisical control?
Day	Fraction Defective	Day	Fraction Defective	Day	Fraction Defective
1	0.01	11	0.02	21	0.02
2	0.01	12	0.03	22	0
3	0	13	0	23	0.01
4	0.03	14	0.06	24	0.02
5	0	15	0.01	25	0.01
6	0.01	16	0.03	26	0.03
7	0.03	17	0	27	0
8	0	18	0	28	0.02
9	0	19	0.01	29	0.01
10	0.02	20	0.03	30	0

Answer 1

a. Determine the 3 sigma UCL and LCL

Creating X -bar and S chart for variables in excel

Step - by step procedure

1. first bring data in to excel sheet.

find the control chart table of contents (Biasing Constraints) from internet. This will help to calculate Lower and upper control limit.

3. Our sample size is 10 . so A3 = 0.975, B3 = 0.284, B4 = 1.716 (Refer the biasing table)

4. Now we need to calcluate X-bar,St.dev,UCL's,LCLx,X bar-bar, and UCLx

5.X-bar is an average of week (calculation in row wise) "formula = "=IF(C5="","",AVERAGE(C5:N5))"

6. st.dev = =IF(C5="","",STDEV(C5:N5))

7.S-bar = average(st.dev)

8. LCLs = B3* S-bar

9.UCLs = B4* St.dev

10. LCLx = (X bar-bar) - (A3 * S-bar)

11 X bar-bar = Average (S-bar)

12 UCLx = (X bar-bar) + (A3 * S-bar)

b. Does the tire stem process appear to be in statisical control?

As per the data, stem process appear to be out of control.

In the above X bar and S chart clearly explains that both X and R bar are aboe the upper control limits.