Jamison Kovach Supply Company manufactures paper clips and o

Jamison Kovach Supply Company manufactures paper clips and other office products. Although inexpensive, paper clips have provided the firm with a high margin profitability. Sample size is 50. Results are given for the last 10 samples. Sample 23 4 5 678 9 10 Defectives 5 The type of control chart that is best to monitor this process is p-chart a) Establish the control limits to include 99.73% of the random variation in defectives. UCL 0.261 (enter your response as a number between 0 and 1, rounded to three decimal places) LCLp0.000 (enter your response as a number between 0 and 1, rounded to three decimal places). b) Has the process been in control? Based on the developed control limits, the number of defectives has been IN-CONTROL c) If the sample size were 25 instead, how would your limits and conclusions change? UCL(enter your response as a number between 0 and 1, rounded to three decimal places).

Solution

We are dealing with \'defectives\'. So, the appropriate chart is a \'p-chart\'.

(a)

Std. Error (Sp) = SQRT(p_bar*(1 - p_bar)/N) = SQRT(0.122*(1-0.122)/50) = 0.046

UCLp = p_bar + 3*Sp = 0.122 + 3*0.046 = 0.261

LCLp = max(0, p_bar - 3*Sp) = max(0, 0.122 - 3*0.046)) = max(0, -0.017) = 0

(b)

IN-CONTROL because all the above p values are less than UCLp

(c)

N=25

p_bar = 0.244
Sp = SQRT(0.244*(1-0.244)/25) = 0.086

UCLp = p_bar + 3*Sp = 0.244 + 3*0.086 = 0.502

LCLp = max(0, p_bar - 3*Sp) = max(0, 0.244 - 3*0.086)) = max(0, -0.014) = 0

Sample	1	2	3	4	5	6	7	8	9	10	Average
Defectives (N.p)	5	7	3	6	12	5	5	5	1	12
p = N.p / N	0.1	0.14	0.06	0.12	0.24	0.1	0.1	0.1	0.02	0.24	0.122