Tensile strength of a new product is tested by taking 5 unit samples. This table

Question

Tensile strength of a new product is tested by taking 5 unit samples. This table below contains data from five samples. Strength of all units in each sample recorded in the same column.

Develop control charts for the data, subgroup by Sample. Is the process in control? You should show your reasoning

A.) Process is in control

B.) Process is not in control. At least one observation is beyond UCL for average chart.

C.) Process is not in control. At least one observation is beyond LCL for average chart.

D.)Proces s is not in control. At least one observation is beyond UCL for range chart.

Q2-3-4.jmp Sample Sample 2 Sample 3 Sample 4 Sample 5 1 99.23 2 96.26 94.5 95.99 5 95.58 8 2 96.29 96.56 98.74 96.02 96.15 97.47 98.69 97.07 94.91 95.45 100.1 98.87 98.46 100.91 99.96 95.85 97.47 98.96 99.36 95.99 8 Columns (50) Sample1 A Sample2 Sample3 Sample4 Sample Rows All rows Selected Excluded Hidden Labelled

Explanation / Answer

for above sample size n=5 ; factor d2 =2.326

hence lower limit =Xbar-d2*Rbar =97.39-2.326*3.44 =89.40

upper control limit =Xbar+d2*Rbar =97.39+2.326*3.44 =105.39

as all observations are within limit ; option A is correct

A.) Process is in control

sample 1 sample 2 sample 3 sample 4 sample 5 1 99.23 96.29 97.47 100.1 95.85 2 96.26 96.56 98.69 98.87 97.47 3 94.5 98.74 97.07 98.46 98.96 4 95.99 96.02 94.91 100.91 99.36 5 95.58 96.15 95.45 99.96 95.99 overall average average 96.312 96.752 96.718 99.66 97.526 97.39 range 4.73 2.72 3.78 2.45 3.51 3.44

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