Question

SPC MODELING

Create a Control Limit chart for the following:  You are a manager at RadioTag Inc., a maker of RFID tags for US military and private use (e.g., Wal Mart).  Your process assembles radio id tags to certain specifications – 95.5 confidence intervals, however as they come off the assembly line a test is run on each tag to determine whether the frequency works or does not (hint the data are dichotomous distributed binary).  Below are the data you collected over a 2-week period:                                                                                                                                                                                                                                                                                                                                    GRAPH GOES UNDER THIS

Day sample size         non-working tags

1                    100                       15

2                    100                       13

3                    100                       12

4                    100                       11

5                    100                       16

6                    100                       19

7                    100                       5

8                    100                       8

9                    100                       19

10                  100                       15

11                  100                       2

12                  100                       6

13                  100                       9   

14 100                       10

P bar =

SD of P bar =

UCLP Bar =

LCLP bar =

B) Graph and Plot the data.  Round answers to three places.

Clearly identify the P bar, s.d. of Pbar, UCL, LCL (make sure the graph elements are labeled) and identified in A above. Place a box around these final answers.  Failure to place a box will result in failure to earn points.

C) Compare p value to a.  What is the result?

Answer 1

Day	n	np	p = np / n
1	100	15	0.1500
2	100	13	0.1300
3	100	12	0.1200
4	100	11	0.1100
5	100	16	0.1600
6	100	19	0.1900
7	100	5	0.0500
8	100	8	0.0800
9	100	19	0.1900
10	100	15	0.1500
11	100	2	0.0200
12	100	6	0.0600
13	100	9	0.0900
14	100	10	0.1000
		Average	0.1143
			p_bar

p_bar = 0.1143
SD of p_bar, S_p = [p_bar * (1 - p_bar) / n]^1/2 = sqrt(0.1143*(1 - 0.1143) / 100) = 0.0318

Confidence level = 95.5%, so, α = 0.045 and α/2 = 0.0225
So, z_α/2 = Normsinv(1 - 0.0225) = 2.00

UCL_p = p_bar + z_α/2 * S_p = 0.1143 + 2*0.0318 = 0.1779
LCL_p = Max(0, p_bar - z_α/2 * S_p)= Max(0, 0.1143 - 2*0.0318) = 0.0507