SETTING RANGE LIMITS USING TABLE VALUES. Roy Clinton’s mail-ordering business wants to measure the response time of its operators in taking customer orders over the phone. Clinton lists below the time recorded (in minutes) from five different samples of the ordering process with four customer order

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SETTING RANGE LIMITS USING TABLE VALUES. Roy Clinton’s mail-ordering business wants to measure the response time of its operators in taking customer orders over the phone. Clinton lists below the time recorded (in minutes) from five different samples of the ordering process with four customer orders per sample. He wants to determine the upper and lower range control chart limits.
APPROACH [latex]\blacktriangleright[/latex] Looking in Table S6.1 for a sample size of 4, he finds that [latex]D_4 = 2.282 and D_3 = 0[/latex].

TABLE S6.1	Factors for Computing Control Chart Limits (3 sigma)
SAMPLE SIZE, n	MEAN FACTOR, [latex]A_2[/latex]	UPPER RANGE, [latex]D_4[/latex]	LOWER RANGE, [latex]D_3[/latex]
2	1.880	3.268	0
3	1.023	2.574	0
4	.729	2.282	0
5	.577	2.115	0
6	.483	2.004	0
7	.419	1.924	0.076
8	.373	1.864	0.136
9	.337	1.816	0.184
10	.308	1.777	0.223
12	.266	1.716	0.284

Accepted Answer

SOLUTION [latex]\blacktriangleright[/latex]

SAMPLE	OBSERVATIONS (MINUTES)	SAMPLE RANGE ([latex]R_i[/latex])
1	5, 3, 6, 10	10 – 3 = 7
2	7, 5, 3, 5	7 – 3 = 4
3	1, 8, 3, 12	12 – 1 = 11
4	7, 6, 2, 1	7 – 1 = 6
5	3, 15, 6, 12	15 – 3 = 12
		Σ[latex]R_i[/latex] = 40

[latex]\bar{R} = \frac{40}{5} = 8[/latex]

[latex]UCL_R[/latex] = 2.282(8) = 18.256 minutes

[latex]LCL_R[/latex] = 0(8) = 0 minutes

INSIGHT [latex]\blacktriangleright[/latex] Computing ranges with Table S6.1 is straightforward and an easy way to evaluate dispersion. No sample ranges are out of control.

LEARNING EXERCISE [latex]\blacktriangleright[/latex] Clinton decides to increase the sample size to n = 6 (with no change in average range, [latex]\bar{R}[/latex]). What are the new [latex]UCL_R and LCL_R[/latex] values? [Answer: 16.032, 0.]

RELATED PROBLEMS [latex]\blacktriangleright[/latex] S6.3b, S6.5, S6.6, S6.7, S6.9, S6.10c, S6.11, S6.12, S6.26 (S6.29b, S6.30b, S6.31b, S6.32b, S6.33b are available in MyOMLab)

Question 6.S3: SETTING RANGE LIMITS USING TABLE VALUES. Roy Clinton’s mail-...

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