(i) Determine the upper and lower control limits for an X-Bar chart and R-chart with a sample size of four. (ii) After the control chart was established a sample of four observations had the following times in seconds: 193, 259, 197, and 149. Is corrective action needed?

Practical Management Science
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ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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Please answer both i and ii in the problem provided.!?
**Study on Bed-Making Time at a Motel**

*Objective:*  
The time required for maids to make beds at a motel should be within a predefined range to ensure efficiency. This study observes the time taken by four maids to make a bed over three separate occasions.

*Data:*

The table below shows the service time (in seconds) recorded for each maid on three different occasions:

| Maid   | Sample 1 | Sample 2 | Sample 3 |
|--------|----------|----------|----------|
| Alex   | 122      | 90       | 152      |
| Marie  | 130      | 111      | 140      |
| Linda  | 200      | 180      | 175      |
| Ann    | 163      | 155      | 141      |

*Analysis:*

- **Alex:** Times vary significantly from 90 to 152 seconds, indicating inconsistency.
- **Marie:** Moderate consistency, with times ranging from 111 to 140 seconds.
- **Linda:** Consistently the slowest, with times between 175 and 200 seconds.
- **Ann:** Shows some variation but generally faster than Linda, with times from 141 to 163 seconds.

This data can be used for analyzing efficiency, consistency, and training needs among the staff.
Transcribed Image Text:**Study on Bed-Making Time at a Motel** *Objective:* The time required for maids to make beds at a motel should be within a predefined range to ensure efficiency. This study observes the time taken by four maids to make a bed over three separate occasions. *Data:* The table below shows the service time (in seconds) recorded for each maid on three different occasions: | Maid | Sample 1 | Sample 2 | Sample 3 | |--------|----------|----------|----------| | Alex | 122 | 90 | 152 | | Marie | 130 | 111 | 140 | | Linda | 200 | 180 | 175 | | Ann | 163 | 155 | 141 | *Analysis:* - **Alex:** Times vary significantly from 90 to 152 seconds, indicating inconsistency. - **Marie:** Moderate consistency, with times ranging from 111 to 140 seconds. - **Linda:** Consistently the slowest, with times between 175 and 200 seconds. - **Ann:** Shows some variation but generally faster than Linda, with times from 141 to 163 seconds. This data can be used for analyzing efficiency, consistency, and training needs among the staff.
The text in the image reads:

(i) Determine the upper and lower control limits for an X-Bar chart and R-chart with a sample size of four.

(ii) After the control chart was established a sample of four observations had the following times in seconds: 193, 259, 197, and 149. Is corrective action needed?

There are no graphs or diagrams present in the image.
Transcribed Image Text:The text in the image reads: (i) Determine the upper and lower control limits for an X-Bar chart and R-chart with a sample size of four. (ii) After the control chart was established a sample of four observations had the following times in seconds: 193, 259, 197, and 149. Is corrective action needed? There are no graphs or diagrams present in the image.
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