It is known from Phase I data that we have 40 defects per 10

It is known from Phase I data that we have 40 defects per 1000 board.

(a) One engineer suggests to make a quality check every hour by selecting 100 boards, how to construct a monitoring chart (CL = ? UCL = ? LCL = ?)?

(b) How many boards should be checked at each sampling hour in order to obtain a positive lower control limit?

(c) One month later, this engineer decides to check 400 boards at each sampling hour. Under this new sampling strategy, how do you suggest for continuously monitoring such a process (using a c chart or u chart?)

(d) For (c), if a u chart is suggested, what is a convenient inspection unit that you like to suggest? What is the sample size? What are the control limits (CL, UCL, and LCL)? What are c0 and u0?

(e) If a c chart is still used for (c), what are the control limits (CL, UCL, and LCL)? (f) If at time t, it is found that a sample of 400 boards has 22 defects, what are the monitoring statistics to be plotted in above charts of (d) and (e)?

Solution

p = no fo defects proportion = 0.04

100 board to be selected

For 100 board mean = np = 4

Hence CL =4

and it varies both sides from higher to lower.

Variance = npq = 0.24

std dev = 0.49

If confidence interval 95% is taken

then LCL = 4-0.29(0.49)/10 = 3.986

UCL = 4.0142

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b) If the margin of error is fixed as 0.005 say

0.005 = 2.58(0.49)/rtn

then no of boards to be checked = 25.84^2 = 63928

Sample size >63928

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For 400 charts we first draw a chart using 99% confidence with mean np = 16

Then check whether this lies within this range every hour continuously.

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d) If only u chart is suggestsed then size should be double of 63928

= 127856.

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If 400 has 22 defects then mean = 22.