Question

Refer to Table 56.1 - Factors for Computing Control Chart Limits (3 sigma) for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filing machine at Panos Kouvelis Lifelong Lawn Ltd. The results were: Overall mean = 54.75 16.; Average range R = 1.84 6. a) For the given sample size, the control limits for 3-sigma x chart are: Upper Control Limit (UCL) - b. (round your response to three decimal places). Lower Control Limit (LL)-11. round your response to three decimal places). b) The controllimits for the 3-sigma R-chart are: Upper Control Limit (UCI) -1. (round your response to three decimal pieces). Lower Control Limit (LCLM) 16. (round your response to three decimal plocos).

Answer 1

Answer :

given data

Smples (N ) = 35

Size (n) = 7

overall mean (x double bar )= 54.75 lb

average range ( R - bar ) = 1.64 lb

(a)

by the table of 3-sigma control chart factors (x - chart )

for n=7 A₂ = 0.419

now

*( upper control limit )

* UCL_X = (X- Double bar ) + ( A₂ * R -Bar )

= 54.75 + ( 0.419 * 1.64 )

= 54.75 + (0.687 )

= 55 .43 lb

* ( lower control limit )

* LCL_X = (X- Double bar ) -  ( A₂ * R -Bar )

= 54.75 - ( 0.687 )

= 54.06

( B)

by the table of 3-sigma control chart factors (R - chart )

for n= 7

we have D3 = 0.08 , D4 = 1.92

now

Upper control limit (UCL_R ) = R * D4

= 1.64 *1.92

= 3.148

Lower control limit( LCR_R) = R * D3

= 1.64 * 0.08

= 0.1312

ABOVE D3 , D4 , A2 values are from the control chart for your clarification i have given the chat below

3-Sigma Control Chart Factors Sample size X-chart n A2 2 3 4 R-chart Dz D4 0 3.27 0 2.57 0 2.28 0 2.11 0 2.00 0.08 1.92 0.14 1.86 1.88 1.02 0.73 0.58 0.48 0.42 0.37 5 6 7 8

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