The quality manager of a computer services company wants to create a specification for the amount of time it takes the company to respond to problems reported by customers. The goal time limits is 10 hours (i.e., 600 minutes) at most. To determine how well the company meets the specification, data are collected on the response times over recent weeks, based on three customers chosen at random in each week. The data consist of the response time (in minutes) for three customers each over 32 weeks. The data are shown below and included on the course Blackboard site. Use control chart(s) to determine if the process is stable. Eliminate all subgroups that constitute Shewhart rule violations assuming that a root cause is found and eliminated.
| Week | Response Time (Min.) | ||
| 1 | 450 | 522 | 522 |
| 2 | 300 | 570 | 426 |
| 3 | 534 | 486 | 540 |
| 4 | 462 | 606 | 354 |
| 5 | 474 | 582 | 354 |
| 6 | 444 | 462 | 528 |
| 7 | 426 | 282 | 600 |
| 8 | 438 | 456 | 528 |
| 9 | 492 | 576 | 558 |
| 10 | 402 | 546 | 504 |
| 11 | 510 | 426 | 336 |
| 12 | 510 | 342 | 444 |
| 13 | 402 | 474 | 546 |
| 14 | 366 | 438 | 444 |
| 15 | 510 | 510 | 522 |
| 16 | 492 | 510 | 504 |
| 17 | 480 | 576 | 420 |
| 18 | 630 | 474 | 462 |
| 19 | 546 | 342 | 408 |
| 20 | 612 | 600 | 570 |
| 21 | 564 | 558 | 486 |
| 22 | 486 | 588 | 432 |
| 23 | 468 | 390 | 492 |
| 24 | 366 | 462 | 372 |
| 25 | 498 | 534 | 582 |
| 26 | 420 | 408 | 426 |
| 27 | 432 | 558 | 510 |
| 28 | 504 | 630 | 456 |
| 29 | 462 | 396 | 510 |
| 30 | 336 | 426 | 528 |
| 31 | 480 | 402 | 462 |
| 32 | 498 | 480 | |
The quality manager of a computer services company has initiated a project to assess and improve the company’s responsiveness to customer-reported problems. The primary objective is to establish a specification for response times, with a goal of not exceeding 10 hours (600 minutes). To determine the stability of the current process and identify areas for improvement, data has been collected over 32 weeks, with response times (in minutes) recorded for three randomly selected customers each week. In this analysis, we will employ control charts to assess process stability and eliminate subgroups that violate Shewhart rules.
Control charts are valuable tools in statistical process control (SPC) for monitoring and maintaining the stability of a process. They help identify variations that may arise from common causes (inherent to the process) and special causes (unexpected events). In this case, we will create control charts to visualize the response time data and identify any trends, shifts, or outliers.
To begin, we will create a control chart (commonly referred to as an Individual/Moving Range or I-MR chart) for the response time data. The I-MR chart consists of two plots: one for individual values and another for the moving ranges between consecutive data points within each subgroup.
For simplicity, we will use software tools like Excel, Minitab, or specialized statistical software to create the control chart. These tools automatically calculate control limits and detect any out-of-control points based on defined criteria.
The control chart will display the following elements:
Individual Values Plot: This plot shows individual response times for each subgroup (week).
Moving Range Plot: The moving range plot displays the variation between consecutive data points within each subgroup.
Control Limits: Upper and lower control limits are calculated based on the data. Points falling outside these limits may indicate special causes of variation.
Centerline: The centerline represents the average response time across all subgroups.
Shewhart Rules: Shewhart rules are used to identify out-of-control points. These rules include criteria such as points outside control limits, runs above or below the centerline, and other patterns.
When a subgroup exhibits a violation of Shewhart rules, it suggests a special cause of variation. To improve process stability, the root cause of such violations should be identified and eliminated. This may involve investigating specific issues in the weeks where violations occurred and implementing corrective actions.
In summary, the quality manager of the computer services company has collected response time data over 32 weeks to assess process stability. Control charts, including Individual/Moving Range charts, are powerful tools for this purpose. By identifying and eliminating subgroups that violate Shewhart rules, the company can work towards achieving its goal of responding to customer-reported problems within 10 hours. Process stability is crucial for delivering consistent and efficient customer service, and this analysis is a critical step in the quality improvement journey.
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