Question

In: Operations Management

Problem 2: Number of defective tires produced in 20 batches of 100 units each is given...

Problem 2: Number of defective tires produced in 20 batches of 100 units each is given below.

2, 5, 7, 1, 3, 5, 9, 12, 16, 5, 9, 12, 2, 14, 4, 7, 6, 8, 9, 11

What control charts will be appropriate? Develop upper and lower control limits for such charts. The next batch of 100 units showed 12 defectives. Is the process in control?

Problem 3: Inspection of 12 car panels in a Mercury plant showed the following number of defects on each panel:

9, 4, 3, 17, 24, 12, 10, 25, 12, 34, 10, 10

What control charts will be appropriate? Develop upper and lower control limits for such charts. Suppose the next three panels showed no defect at all. Is this process out of control? Why or why not?

Expert Solution

1. P-CHART WOULD BE APPROPRIATE HERE.

Z = 3
SAMPLE SIZE = 100
NUMBER OF SAMPLES TAKEN = 20

P-BAR = TOTAL NUMBER OF DEFECTS / (SAMPLE SIZE * NUMBER OF SAMPLES = 147 / (100 * 20) = 0.0735
STDEV = SQRT((PBAR * (1 - PBAR)) / SAMPLE SIZE = SQRT((0.0735 * (1 - 0.0735)) / 100 = 0.0261

UCL = PBAR + (Z * STDEV) = 0.0735 + (3 * 0.0261) = 0.1518
LCL = PBAR - (Z * STDEV) = 0.0735 - (3 * 0.0261) = -0.0048, SINCE LCL IS NEGATIVE, LCL = 0

2. NO, SINCE 1 POINT IS OUTSIDE THE CONTROL LIMIT(OBSERVATION 9), THE PROCESS IS NOT IN STATISTICAL CONTROL.

2. C CHART IS APPROPRIATE HERE

Z = 3
TOTAL NUMBER OF DEFECTS = 170
NUMBER OF SAMPLES = 12

C-BAR = TOTAL NUMBER OF OBSERVATIONS / NUMBER OF SAMPLES = 170 / 12 = 14.1667

UCL = C-BAR + (Z * SQRT(C-BAR)) = 14.1667 + (3 * SQRT(14.1667)) = 25.46
LCL = C-BAR - (Z * SQRT(C-BAR)) = 14.1667 - (3 * SQRT(14.1667)) = 2.88

2. THE CHART IS OUT OF CONTROL BECAUSE OBSERVATION 10 IS OUTSIDE THE CONTROL LIMITS.

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keosha answered 4 months ago

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