Please help with this. 1. A company was experiencing high rejections in their pu

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Please help with this.

1. A company was experiencing high rejections in their pumps departments. "" charts were introduced as part of a program to reduce defectives. Control limits were based on data history. In the chart below, "pl" is the historical value of percent defective for each department; and the respective %-defective for a period of 6 weeks (w1 thru w6) are also shown: Dept p1 w1 w2 w3 w4 w5 w6 104 9 8 11 6 13 12 10 105 16 13 19 20 12 15 17 106 15 18 19 16 11 13 16 1000 pieces were inspected each week in each department. Which department(s) exhibited a point, o tenth of a % point). Show calculations, please r points, out of control during this period (round off calculations to the nearest

Explanation / Answer

Here for Department 104

pbar = 9/1000 = 0.0009

the control limits are = p+- 3 * sqrt [p * (1-p)/N] = 0.009 +- 3 * sqrt [0.009 * 0.991/1000]

= 0.009 +- 0.00896 = (0.00004 , 0.01796)

so, as we see that for no week from w1 to w6, the proportion of defectives are out of control limits. So, no point is outside the control limits in department 104.

Here for Department 105

pbar = 16/1000 = 0.016

the control limits are = p+- 3 * sqrt [p * (1-p)/N] = 0.016 +- 3 * sqrt [0.016 * 0.984/1000]

= 0.016 + 0.0119 = (0.0041 , 0.0279)

so, as we see that for no week from w1 to w6, the proportion of defectives are out of control limits. So, no point is outside the control limits in department 105.

Here for Department 106

pbar = 15/1000 = 0.016

the control limits are = p+- 3 * sqrt [p * (1-p)/N] = 0.015 +- 3 * sqrt [0.015 * 0.985/1000]

= 0.015 - 0.0115 = (0.0035 , 0.0265)

so, as we see that for no week from w1 to w6, the proportion of defectives are out of control limits. So, no point is outside the control limits in department 106.

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