Question

Refer to Table 56.1 - Factors for Computing Control Chart Limits (sigma) for this problem. Thirty-five samples of size 7 each were taken from a fertilizer-bag-filling machine at Panos Kouvels Lifelong Lawn Lid. The results were: Overal mean = 54.75 lb.: Average range R 164 b. a) For the given sample size, the control limits for 3-sigma x chart are Upper Control Limit (UCL) - D. (round your response to three decimal places). Lower Control Limit (LCL)-1. (round your response to three decimal places). b) The control limits for the 3-sigma R-chart are Upper Control Limit (UCL) -16. (round your response to three decimal places). Lower Control Limit (LCLR) Ib. (round your response to three decimal places)

Answer 1

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Answers::

Overall mean ($\bar{\bar{X}}$) = 54.75

Average Range ($\bar{R}$) = 1.64

Sample size (n) = 7

(A)

*Use mean factor table to find value of A2 at n=7

Value of A2 = 0.419

$UCL_{\bar{X}}=\bar{\bar{X}}+A_{2}\bar{R}$

UCL = 54.75 + (0.419 × 1.64)

UCL = 55.437

$LCL_{\bar{X}}=\bar{\bar{X}}-A_{2}\bar{R}$

LCL = 54.75 - (0.419 × 1.64)

LCL = 54.063

(B)

*Use mean factor table for find value of D3 and D4 at n=7

Value of D4 = 1.924

Value of D3 = 0.076

$UCL_{R}=D_{4}\bar{R}$

UCL = 1.924 × 1.64

UCL = 3.155

$LCL_{R}=D_{3}\bar{R}$

LCL = 0.076 × 1.64

LCL = 0.125