**Calculation of UCL and LCL for a Range Chart**Given:- **Sample size ($ n $)** = 9- **Average of the sample ranges ($ \bar{R} $)** = 4To calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) of the range chart, use the following values from the table:| $ n $ | A2 | D3 | D4 ||---------|------|------|------|| 2 | 1.880| 0.000| 3.267|| 3 | 1.023| 0.000| 2.575|| 4 | 0.729| 0.000| 2.282|| 5 | 0.577| 0.000| 2.114|| 6 | 0.483| 0.000| 2.004|| 7 | 0.419| 0.076| 1.924|| 8 | 0.373| 0.136| 1.864|| 9 | 0.337| 0.184| 1.816|| 10 | 0.308| 0.223| 1.777|**Calculation:**For $ n = 9 $:- **D3**: 0.184- **D4**: 1.816Formulas:- **UCL** = $ D4 \times \bar{R} $ = $ 1.816 \times 4 = 7.26 $- **LCL** = $ D3 \times \bar{R} $ = $ 0.184 \times 4 = 0.736 $**Answer:**- Correct option: **UCL=7.26, LCL=0.74** This guide shows how control limits are determined using the constants $ D3 $ and $ D4 $ from the table for a given sample size.

Given, Sample size (n)=9Sample ranges (R)=4 The range chart for this process is given as-

Sample size (n) is 9, average of the sample ranges (R )is 4. Calculate the UCL and LCL of the range chart for this process. n A2 D3 D4 2 1.880 0.000 3.267 3 1.023 0.000 2.575 4 0.729 0.000 2.282 0.577 0.000 2.114 6 0.483 0.000 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864

Sample size (n) is 9, average of the sample ranges (R )is 4. Calculate the UCL and LCL of the range chart for this process. n A2 D3 D4 2 1.880 0.000 3.267 3 1.023 0.000 2.575 4 0.729 0.000 2.282 0.577 0.000 2.114 6 0.483 0.000 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Estimation

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Question

**Calculation of UCL and LCL for a Range Chart**

Given:
- **Sample size ($ n $)** = 9
- **Average of the sample ranges ($ \bar{R} $)** = 4

To calculate the Upper Control Limit (UCL) and Lower Control Limit (LCL) of the range chart, use the following values from the table:

| $ n $ | A2 | D3 | D4 |
|---------|------|------|------|
| 2 | 1.880| 0.000| 3.267|
| 3 | 1.023| 0.000| 2.575|
| 4 | 0.729| 0.000| 2.282|
| 5 | 0.577| 0.000| 2.114|
| 6 | 0.483| 0.000| 2.004|
| 7 | 0.419| 0.076| 1.924|
| 8 | 0.373| 0.136| 1.864|
| 9 | 0.337| 0.184| 1.816|
| 10 | 0.308| 0.223| 1.777|

**Calculation:**

For $ n = 9 $:
- **D3**: 0.184
- **D4**: 1.816

Formulas:
- **UCL** = $ D4 \times \bar{R} $ = $ 1.816 \times 4 = 7.26 $
- **LCL** = $ D3 \times \bar{R} $ = $ 0.184 \times 4 = 0.736 $

**Answer:**
- Correct option: **UCL=7.26, LCL=0.74**

This guide shows how control limits are determined using the constants $ D3 $ and $ D4 $ from the table for a given sample size.

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