Question

Observation	DiscThickness
1	54.2739
2	41.9414
3	39.9223
4	53.2279
5	34.0326
6	53.1034
7	39.848
8	52.9238
9	47.8287
10	42.7878
11	51.2813
12	36.6275
13	48.6066
14	39.7545
15	38.0288
16	63.2095
17	57.5585
18	55.9449
19	49.1416
20	66.8436
21	45.0807
22	64.537
23	38.154
24	41.5022
25	48.7585
26	46.1061
27	35.2494
28	57.0696
29	41.0096
30	40.1394

The Quality Management team has collected observations on brake disc thickness. The mean brake disc thickness is normally distributed with a mean of 47.48 mm ± 3 mm (based on a customer requirement). Observations by the quality management team were collected and recorded in the file, “AcmeBrakeCo.csv”.  There are concerns that too much material is being added to the production process and that this additional material results in brake discs that are thicker than they need to be. A disc ring that is produced above the specification limit costs the company about $85.25.

1. Calculate the probability that a brake disc will be manufactured with a thickness that is greater than the upper specification limit (show all your work).
2. Calculate the loss that occurs if the disc thickness shifts to 3mm above the target.

Answer 1

Disc Thickness
Mean	47.48310333
Standard Error	1.636703676
Median	46.9674
Mode	#N/A
Standard Deviation	8.964595233
Sample Variance	80.3639677
Kurtosis	-0.594054736
Skewness	0.503039351
Range	32.811
Minimum	34.0326
Maximum	66.8436
Sum	1424.4931
Count	30

Mean	47.48310333

Standard Error

1.636703676

The probability that disk thickness will be greater than 17.48+3 mm or 50.48mm is given by

The probability that one disk will have the thickness greater than 50.48 is 0.03355

The loss that occurs if the disc thickness shifts to 3mm above the target.

= $85.25* 0.03355=2.8601375