Question

A process that is considered to be in control measures an ingredient in ounces. Below are the last 10 samples​ (each of size n ​= 5) taken. The population process standard deviation is 1.36. Samples 1 2 3 4 5 6 7 8 9 10 9 13 13 11 11 10 9 13 7 9 8 11 9 11 10 10 12 11 7 12 9 12 9 12 10 7 11 7 13 10 10 14 11 10 10 13 9 9 12 7 13 12 10 10 9 9 10 8 10 13 ​a) Standard deviation of the sampling means​ = . 608 ounces ​(round your response to three decimal​ places). ​b) With z​ = 3​, the control limits for the mean chart​ are: UCL Subscript x overbar ​= 12.124 ounces ​(round your response to three decimal​ places). LCL Subscript x overbar ​= 8.476 ounces ​(round your response to three decimal​ places). ​c) The control limits for the​ R-chart are: UCL Subscript Upper R ​= nothing ounces ​(round your response to three decimal​ places).

Answer 1

Kindly check explanation

Explanation:

Given the data:

Population standard deviation (σ) = 1.36

Sample size (n) = 5

A.)Standard deviation of sampling mean (σx) = (σ/√n)

(1.36/√5)

1.36 / 2.236

= 0.608

B.) With z​ = 3​, the control limits for the mean

chart​ :

Control limit = m ± zσx

Using calculator ; mean (m) of the data = 10.40

Lower control limit : 10.4 - 3(0.608) = 8.576

Upper Control limit : 10.4 + 3(0.608) = 12.224

The control limit for the range :

Average value of range(R) in the sample = 3.6

Lower Control limit : R*D3

Upper control limit: R*D4

From the range chart table :

D3 = 0 ; D4 = 2.114

Lower Control limit : R*D3 = 3.6(0) = 0

Upper control limit: R*D4 = 3.6(2.114) = 7.61