A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the Irregularities (e.g.. loose threads and tears), the following data were collected from a sample provided by the supplier. SAMPLE IRREGULARITIES 1 2 4 3 C Sp UCL LCL 3 3 4 4 5 3 6 2 7 4 8 4 9 10 3 7 a. Determine the c. Sp UCL and LCL for a c-chart with z= 2. (Leave no cells blank. Round up any negative LCL value to "0". Round your answers to 2 decimal places.)

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Chapter2: Introduction To Spreadsheet Modeling
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**Problem 13-8 (Algo)**

A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier.

| SAMPLE          | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|-----------------|---|---|---|---|---|---|---|---|---|----|
| IRREGULARITIES  | 4 | 3 | 3 | 4 | 3 | 2 | 4 | 4 | 3 | 7  |

a. Determine the \(\bar{c}\), \(S_p\), UCL, and LCL for a c-chart with \(z = 2\). *(Leave no cells blank. Round up any negative LCL value to "0". Round your answers to 2 decimal places.)*

|        |        |
|--------|--------|
| c̄      |        |
| Sp     |        |
| UCL    |        |
| LCL    |        |

**Explanation:**

The table provided displays data regarding the number of irregularities observed in each of the ten samples of cloth. These observations will be used to calculate the average number of defects (\(\bar{c}\)), the standard deviation of defects (\(S_p\)), the Upper Control Limit (UCL), and the Lower Control Limit (LCL) for a c-chart. The c-chart is a type of control chart used to monitor the number of defects per unit in quality control settings.

The instruction at the bottom specifies that for calculating the control limits, a z-value of 2 should be used. Any negative values for the LCL should be rounded up to zero, and all final answers should be rounded to two decimal places.
Transcribed Image Text:**Problem 13-8 (Algo)** A shirt manufacturer buys cloth by the 100-yard roll from a supplier. For setting up a control chart to manage the irregularities (e.g., loose threads and tears), the following data were collected from a sample provided by the supplier. | SAMPLE | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |-----------------|---|---|---|---|---|---|---|---|---|----| | IRREGULARITIES | 4 | 3 | 3 | 4 | 3 | 2 | 4 | 4 | 3 | 7 | a. Determine the \(\bar{c}\), \(S_p\), UCL, and LCL for a c-chart with \(z = 2\). *(Leave no cells blank. Round up any negative LCL value to "0". Round your answers to 2 decimal places.)* | | | |--------|--------| | c̄ | | | Sp | | | UCL | | | LCL | | **Explanation:** The table provided displays data regarding the number of irregularities observed in each of the ten samples of cloth. These observations will be used to calculate the average number of defects (\(\bar{c}\)), the standard deviation of defects (\(S_p\)), the Upper Control Limit (UCL), and the Lower Control Limit (LCL) for a c-chart. The c-chart is a type of control chart used to monitor the number of defects per unit in quality control settings. The instruction at the bottom specifies that for calculating the control limits, a z-value of 2 should be used. Any negative values for the LCL should be rounded up to zero, and all final answers should be rounded to two decimal places.
**a.** Determine the \( \bar{c}, S_p, \) UCL, and LCL for a \( c \)-chart with \( z = 2 \). (**Leave no cells blank. Round up any negative LCL value to "0". Round your answers to 2 decimal places.**)

|   |   |
|---|---|
| \( c \) |   |
| \( S_p \) |   |
| UCL |   |
| LCL |   |

**b.** Suppose the next five rolls from the supplier had four, four, two, two, and eight irregularities. Is the supplier process under control?

- O No
- O Yes

**Explanation of Concepts:**

- \( \bar{c} \): The average number of defects or irregularities.
- \( S_p \): Standard deviation for the process.
- UCL (Upper Control Limit) and LCL (Lower Control Limit): Limits used to determine if a process is in control. If data points fall outside these limits, the process may be out of control.
Transcribed Image Text:**a.** Determine the \( \bar{c}, S_p, \) UCL, and LCL for a \( c \)-chart with \( z = 2 \). (**Leave no cells blank. Round up any negative LCL value to "0". Round your answers to 2 decimal places.**) | | | |---|---| | \( c \) | | | \( S_p \) | | | UCL | | | LCL | | **b.** Suppose the next five rolls from the supplier had four, four, two, two, and eight irregularities. Is the supplier process under control? - O No - O Yes **Explanation of Concepts:** - \( \bar{c} \): The average number of defects or irregularities. - \( S_p \): Standard deviation for the process. - UCL (Upper Control Limit) and LCL (Lower Control Limit): Limits used to determine if a process is in control. If data points fall outside these limits, the process may be out of control.
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