Apple is interested in using your patented sapphire crystal on their i-phone 7s

Question

Apple is interested in using your patented sapphire crystal on their i-phone 7s which are due for release in October Your patented method sliced the crystal thin enough that the assembly was able to fit within the dimensions of the smartphone. Youre creating 500 sheets per hour on the robotic lasers and as you're in the development stage, you sample 100 pieces each hour for defects in clarity, thickness and strength. Apple's specification calls for a failure rate of less than 3% You're analyzing the following data: (round to 3 decimal places) Sample Defects 10 12 13 14 15 16 17 18 20 21 23 24 25 Calculate the p-bar anld determine the UCLp and LCLp using 3 standard deviations above and below the mean b. Based on your samples, are your results in controlt If the answer is no, specifically which samplets) are out of control? Are you eeting Apple's Performance Standard

Explanation / Answer

a. Total sum of all defects = 66

so average number of defects persample = 66/25 = 2.64

p - bar (p*) = 2.64/100 = 0.0264

n-bar (n*)= 100 * 25/25 = 100

LCL = p* - 3 * sqrt [p*(1-p*)/ n*]

LCL = 0.0264 - 3 * sqrt [ 0.0264 * 0.9736/ 100]

LCL = 0.0264 - 3 * 0.016

LCL = -0.0126 = 0

UCL = p* + 3 * sqrt [p*(1-p*)/ n*]

UCL = 0.0264 +- 3 * sqrt [0.0264 * 0.9736/ 100]

UCL = 0.0745

so LCL, UCL = ( 0, 0.0745)

(b) So, based on our results we can see that our results of sample are not in control. as there are 2 sample out of 25 which are not under control which are sample no. 15 and sample no. 22.

(c) Here Failure rate of apple = 3%

so here mean failure rate = 2.64% so we are meeting the apple's standard.

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