Question

In: Statistics and Probability

At one engineering firm, several call centers are maintained to track customer complaints. Unfortunately, very few...

At one engineering firm, several call centers are maintained to track customer complaints. Unfortunately, very few employees like this job and therefore there is a lot of employee turnover. This call center uses X-Bar and s charts to track voluntary quits over time. The averages compiled below are from three call centers. The average number is 25 minutes before an employee gets frustrated and quits. The sample size was n = 5 for each month. Use the data below to create one X-Bar chart and one s chart.

Month (Avg. Time) ((s))

January (27.0) ((2.0)) February (27.0) ((2.7)) March (26.5) ((3.0)) April (28.0) ((2.7)) May (25.5) ((2.0)) June (27.5) ((3.0)) July (25.0) ((1.5)) August (25.5) ((1.6)) September (28.0) ((0.5)) October (26.0) ((2.5)) November (26.0) ((4.7)) December (26.5) ((1.3)) January (25.5) ((2.5)) February (25.0) ((6.0)) March (26.5) ((5.5)) April (25.0) ((4.4)) May (28.5) ((2.0)) June (28.0) ((0.5)) July (26.5) ((2.5)) August (24.5) ((1.0))

Create X-Bar and s control charts from this data. Also, calculate the following: X-Double-Bar, s-Bar, UCLx, LCLx, UCLs, and LCLs

Note: single bracket represents “avg.time” and double bracket represents “s”

Solutions

Expert Solution

The X-bar and S chart are obtained in excel by following these steps,

X-bar chart:

Step 1: Write down the data value in excel for X-bar and S. The screenshot is shown below,

Step 2: The X-double bar is obtained by taking average of x-bar column. The screenshot is shown below,

The s bar value is obtained by taking average of S column. The screenshot is shown below,

Step 3: The Upper and lower control limits for the x-bar chart is obtained using the formula,

Where,

The screenshots are shown below,

Step 4: Now, Select the x-bar, UCL and LCL then INSERT > Recommended Charts > XY Scatter > OK. The screenshot for the chart is shown below,

s-chart:

The upper and lower control limits are obtained using the formula,

Where,

The screenshot is shown below,

The s-chart is shown below,

There two possible sample out of control limit in s chart.

The data values are,

Sample	X bar	s	x double bar	s bar	UCL X-bar	LCL X-bar	UCL s-bar	LCL s-bar
1	27	2	26.4	2.595	30.10307	22.69694	5.420955	0
2	27	2.7	26.4	2.595	30.10307	22.69694	5.420955	0
3	26.5	3	26.4	2.595	30.10307	22.69694	5.420955	0
4	28	2.7	26.4	2.595	30.10307	22.69694	5.420955	0
5	25.5	2	26.4	2.595	30.10307	22.69694	5.420955	0
6	27.5	3	26.4	2.595	30.10307	22.69694	5.420955	0
7	25	1.5	26.4	2.595	30.10307	22.69694	5.420955	0
8	25.5	1.6	26.4	2.595	30.10307	22.69694	5.420955	0
9	28	0.5	26.4	2.595	30.10307	22.69694	5.420955	0
10	26	2.5	26.4	2.595	30.10307	22.69694	5.420955	0
11	26	4.7	26.4	2.595	30.10307	22.69694	5.420955	0
12	26.5	1.3	26.4	2.595	30.10307	22.69694	5.420955	0
13	25.5	2.5	26.4	2.595	30.10307	22.69694	5.420955	0
14	25	6	26.4	2.595	30.10307	22.69694	5.420955	0
15	26.5	5.5	26.4	2.595	30.10307	22.69694	5.420955	0
16	25	4.4	26.4	2.595	30.10307	22.69694	5.420955	0
17	28.5	2	26.4	2.595	30.10307	22.69694	5.420955	0
18	28	0.5	26.4	2.595	30.10307	22.69694	5.420955	0
19	26.5	2.5	26.4	2.595	30.10307	22.69694	5.420955	0
20	24.5	1	26.4	2.595	30.10307	22.69694	5.420955	0

orchestra answered 1 year ago

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