__QUETSION 1__

Rock and Smith, Inc. manufactures Oscar brand of pencils. A random sample of 100 pencils is inspected every day, looking specifically for 4 opportunities for defects in each inspected pencil – lead, wood, eraser, and grip. During a recent day, quality inspector, Denzel, found a total of 8 defects overall in a sample of 100 pencils.

Calculate and report the Defects per Million Opportunities (DPMO), rounded to two places after the decimal, for that sample.

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__QUESTION 2__

The pressure in a household water pipe averages 59 degrees PSI and has a standard deviation of 3 PSI. The lower and upper specifications for this water pressure from Licensing Inspector, Olivia Rodrigo, are 50 PSI and 70 PSI.

- Calculate and report the Process Capability Ratio (Cp), rounded to two places after the decimal.
- Calculate and report the Process Capability Index (Cpk), rounded to two places after the decimal.

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__QUESTION 3__

**The information in this paragraph applies to this question and the question that follows (so, questions 3-4).**

**Silk Sonic Pizza shop collects data on the number of errors (i.e., defects) in pizza orders. The errors are not defined beforehand, and can include a wide variety of issues such as incorrect toppings, incorrect address, discount coupon not applied, special seasoning packet missing, etc…. The data provided below (and provided in an Excel file: 2023 M7 Quality Management Problems 3 and 4.xlsx Download 2023 M7 Quality Management Problems 3 and 4.xlsx) gives the number (or count) of errors noted in samples of 100 orders each taken daily for 10 days. Shop owner, Finneas, has requested your help to make a Count (c) control chart to track the process.**

Day | Errors (Defects) |

1 | 16 |

2 | 11 |

3 | 10 |

4 | 18 |

5 | 27 |

6 | 17 |

7 | 15 |

8 | 19 |

9 | 15 |

10 | 12 |

Please help Finneas by calculating and reporting, the value for the __Center Line__ (rounded to the __nearest__ whole number) of the Count (c) control chart.

__QUESTION 4__

Refer to the information, data, and your response to the previous question (number 3).

Please calculate and report the value for the Upper Control Limit (UCL) (rounded to the __previous__ whole number) __and__ the Lower Control Limit (LCL) (rounded to the __next__ whole number) of the Count (c) control chart.

__QUESTION 5__

Management of the Agua Golf Pro Shop collects data on the number of dissatisfied customers for their visits using a survey of customers conducted soon after their golf rounds are completed. Customers respond to a single question indicating on a Yes/No scale whether they were satisfied or dissatisfied with their golf rounds. The data provided below (and provided in an Excel file: __2023 M7 Quality Management Problem 5.xlsx__ Download 2023 M7 Quality Management Problem 5.xlsx) gives the number of dissatisfied customers noted in 135 responses each week over 12 weeks. Pro Shop Manager Nile Rodgers, has requested your help in using a control chart to assess the process. Please calculate and report what is the value of the __Center Line (only)__ for the Proportion (p) control chart. (Nile Rodgers can complete the rest of the calculations for this p chart). Please round your final answer in proportion to 2 places after the decimal.

Week | Number Dissatisfied |

1 | 12 |

2 | 9 |

3 | 15 |

4 | 18 |

5 | 12 |

6 | 15 |

7 | 6 |

8 | 27 |

9 | 15 |

10 | 12 |

11 | 9 |

12 | 12 |

__QUESTION 6__

At the EXO Hotel, manager Kai collected extremely precise data in minutes on check-in times using a sample (sub-group) of 6 check-ins per day over a period of 30 days. An excerpt of that data, consisting of the first 5 days of data, are shown below (no Excel file for this question).

| Observations | |||||

1 | 2 | 3 | 4 | 5 | 6 | |

Day 1 | 6.00 | 4.33 | 7.33 | 7.00 | 6.00 | 5.00 |

Day 2 | 5.75 | 8.25 | 2.33 | 4.25 | 5.75 | 7.50 |

Day 3 | 7.00 | 7.75 | 6.75 | 6.25 | 7.00 | 6.50 |

Day 4 | 5.67 | 8.25 | 7.25 | 6.75 | 6.00 | 7.50 |

Day 5 | 7.00 | 5.00 | 4.75 | 6.25 | 5.50 | 6.50 |

Kai would like your help in identifying what control chart(s) to use.

- Please identify and report the type of control chart(s) that would be appropriate if only this data is available, and provide a one-sentence justification for the same.
- Describe in words how you would go about calculating the Center Line(s) for the control chart(s) including what you would need to get from each sample individually and from all samples together.