Jamison Kovach Supply Company manufactures paper clips and other office products

Question

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).

Explanation / Answer

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

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