Question

In: Operations Management

A quality control inspector has taken four samples with five observations each at the Beautiful Shampoo...

A quality control inspector has taken four samples with five observations each at the Beautiful Shampoo Company, measuring the volume of shampoo per bottle. If the average range for the four samples is 0.4 ounces and the average mean of the observations is 20.0 ounces, develop 3-sigma control limits for the bottling operation. (Round answers to 2 decimal places, e.g. 15.25.)

CL
UCL
LCL

Expert Solution

3 Sigma control limits for example :

Upper Control Limit ( UCL) ,
Lower control Limit ( LCL) and
focal Line ( CL)

must be created for Xbar graph and Range outline

Given ,

Xbar = Average mean of perceptions = 20 ounce

Rbar = Average Range of perceptions = 0.4 ounce

Control Limits for Xbar graph :

Given an incentive for A2( for test size = 5) as got from standard table for control graph constants is = 0.577

Upper Control Limit = UCL = Xbar + A2.Rbar

= 20 + 0.577 x 0.4

= 20 + 0.2308 = 20.2308 Ounce

((23 .28 adjusted to 2 decimal spots)

Lower Control Limit = LCL = Xbar – A2.Rbar

= 20 - 0.577 x 0.4

= 20 – 0.2308= 19.7692 Ounce ( 19.77 adjusted to 2 decimal spots)

Focus line = Xbar = 20 Ounce

Control outline for Range graph :

Following are the given estimations of D3, D4 got from standard table for control outline constants for

test size = n = 5:

D3 = 0

D4 = 2.114

Lower Control Limit = LCL = D3 X Rbar

= 0 x 0.4

= 0 Ounce

Upper Control Limit = UCL = D4 X Rbar
= 2.114 x 0.4

= 0.8456

( 0.85 adjusting to 2 decimal spots)

keosha answered 4 months ago

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