Question

3. Suppose we collect the following set of data for five subgroups of four observations each: Subgroup 1 Subgroup 2 Subgroup 3 Subgroup 4 Subgroup 5 2 9 (a) For each subgroup, calculate the mean and standard deviation Subye, : Me 112 111 1 9 10.25 16.2 Sulyos: .: Hran: 1 0: 19-26-)+(225)+(23-26.5 .177-355) : 2.99 Sulgwea: Min2 *17 10 +/ cd: 12-23)+117-23) 23 12- ' (21-23) Dubroup: Meer: 22 411 4111974 2-1) 23.5 01-133) 1.1.5) 2197 Subyre : Ms 2+ 1 at 1 2 0.25 td 2.01 (b) Contruct the x-bar and R charts for the data. Are there any out-of-control sub- groups?

Answer 1

We know that,

Mean=Sum of the observation / Number of observation

Standard deviation (σ) = sqrt[ Σ ( X_i – Mean)² / n-1]

a)

For subgroup 1,

Mean=(29+22+27+27)/4   

=26.25

σ = sqrt [ ( 29-26.25)² +( 22-26.25)² +( 27-26.25)² +( 27-26.25)² / 4-1 ]

=2.99

For subgroup 2,

Mean=(20+27+20+25)/4   

=23

σ = sqrt [ ( 30-23)² +( 27-23)² +( 20-23)² +( 25-23)² / 4-1 ]

=3.56

For subgroup 3,

Mean=(22+22+21+29)/4   

=23.5

σ = sqrt [ ( 22-23.5)² +( 22-23.5)² +( 21-23.5)² +( 29-23.5)² / 4-1 ]

=3.697

For subgroup 4,

Mean=(26+27+31+25)/4   

=27.25

σ = sqrt [ ( 26-27.25)² +( 27-27.25)² +( 31-27.25)² +( 25-27.25)² / 4-1 ]

=2.63

For subgroup 5,

Mean=(32+36+32+34)/4   

=33.5

σ = sqrt [ ( 32-33.5)² +( 36-33.5)² +( 32-33.5)² +( 34-33.5)² / 4-1 ]

=1.914

b)

X-bar abd R chart,

Xbar Chart of S1, ..., 55 UCL=32.93 Sample Mean X=26.2 - LCL=19.47 Sample

R Chart of S1, ..., 55 UCL=24.85 Sample Range R=11.75 LCl=0 Sample

Conclusion: There are no any out-of control subgroup.