Question

4) Now that Continental can detect more defects before the Silver Box is shipped, I decided process Improvements in its circuit board fabrication department would further improve quality. So, for one process they collected the following data this morning to set up a mean control chart. Since the process mean is unknown, estimate the mean and find the UCL and LCL for a 3-sigma mean control chart using this morning's samples. Sample 1 - 24, 24, 25, 22, 21 Sample 2 -28, 26, 30, 26, 27 Sample 3 -26, 27, 26, 27, 28 Sample 4-23, 25, 22, 22, 24 Sample 5 -29, 27, 28, 24, 26 Sample 6-21, 23, 27, 20, 25 Estimate of process mean: UCL: In the afternoon, if the next samples' observations are sample 7): 28, 20, 29, 19, 27 and sample 8): 15, 34, 36, 14, 26, is the process in or out of control using the mean control chart they made and if out what sample mean? _ Is there any way to improve monitoring this process with SPC tools look at the afternoon samples), and if so what? 5) Another circuit board process is monitored with a pass-fail test. Given 5 samples of 100 observations each, use the data to find an estimate of the process proportion of defectives, UCL and LCL for a 3-sigma chart P-chart. Sample 1 - 4 defects Sample 2 - 12 defects Sample 3 - 10 defects Sample 4 - 15 defects Sample 5 - 7 defects Sample proportions of defectives: (1) (2) (3)__(4)___:(5) Estimate of process proportion of defectives: Estimate of the standard deviation of the sampling distribution: UCL: _ _;LCL:__

Answer 1

4.

Xbar of sample 1=AVERAGE(B4:F4)=23.2

(Drag this cell formula down for rest of the samples)

Process mean=Xbar bar=Average of all the Xbar values=AVERAGE(G4:G9)=25.10

Range of sample 1=MAX(B4:F4)-MIN(B4:F4)=4

(Drag this cell formula down for rest of the samples)

Rbar=Average of all the range values=AVERAGE(H4:H9)=4.17

From the control constants table ,for n=5 ,A2=0.577,D3=0 ,D4=2.115

In X chart ,

UCLx=X-bar bar +A2*Rbar=D12+H13*D11=27.50

LCLx=X-bar bar -A2*Rbar=D12-H13*D11=22.70

Xbar of sample 7=(28+20+29+19+27)/5=24.6

Xbar of sample 8=(15+34+36+14+26)/5=25

Since the xbar values of sample 7 and 8 lie within the control limits and hence the process is in control.

fx D17 A =D12+H13*011 D E B C F G H I 1 2 3 Sample 5 xbar Xbar 211 Range 23.2' 1 24 28 - 26 23 29 21 OWNED Observation 2 3 24 25 26 30 27 26 25 221 27 28 23 27 4 22 26 27 28 24 26 2 5 26.8° 23.2' 24 20 26.8 Rbar Xbar bar 4.17 25.10 For n= 0.577 2.114 UCLX LCLX 27.50 22.70 UCLr8.81 LCLIO

5.In P chart,

we first calculate p-bar i.e the center line

p-bar =Average of the fraction defectives =AVERAGE(E3:E7)=0.10

Next, we calculate Sp =sqrt(p-bar(1-p-bar)/n))

=sqrt(0.10*(1-0.10)/100))

=0.03

UCLp =p-bar+z *Sp=0.10+3*0.03=0.184

LCLp=p-bar-z*Sp=0.10-3*0.03=0.008

Calculations are as shown below:

for C12 AB =C10+(C16*011) D 1 Fraction defective(p) Sample 0.04 Number of defects 100 100 100 100 100 400 0.12 0.10 0.15 0.07 Total 1 p-bar Sp 0.10 0.03 0.184 0.008 UCL LCL