Question

A product has three quality characteristics. The nominal values of these quality characteristics and their sample covariance matrix have been determined from the analysis of 30 preliminary samples of size n=10 as it is show in the Excel file. The sample means for each quality characteristic for 15 additional samples of size n=10 are shown in table. Is the process in statistical control?

X2 Tz Sample number 1 2 [1.40 1.021.05] S = 1.02 1.350.98 11.05 0.98 1.20) 3.1 3.3 3.7 3.9 3 3 3.1 2.4 2.5 2.6 2.8 3.5 3.3 4.6 4.2 3.3 7 3.8 3 2.7 2.2 10 1.8 2 3.2 2.6 3.9 4.1 - 3.2 3.8 3.2 4.7 4 3.6

Answer 1

ANSWER::

• Here, I have used Minitab to prepare the graph and to draw the associated results,

  steps are - Go to Stat > control Charts > Variable charts for subgroups > X bar R Charts

  charts for given data:

  

  Xbar-R Chart of X bar 1, ..., X bar 3 UCL-4.095 8.3.216 Sample Mean | | iCl=2 336 i 2 3 4 5 6 7 9 10 11 12 13 14 15 8 Sample UCL=2.214 Sample Range R=0.86 iCl=0 - 15 3 4 5 6 7 8 Sample 9 10 11 12 13 14

  Result:

  TEST 1. One point more than 3.00 standard deviations from center line.
  Test Failed at points: 10

  TEST 5. 2 out of 3 points more than 2 standard deviations from center line (on one side of
  CL).
  Test Failed at points: 10

  hence, we can conclude that process is out of control,

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