Complete Discussion Assignment 18.1 using the following dataset:

Discussion Assignment 18.1

Hi-Sport is a small company that manufactures logo sporting jackets. A key goal of the company has always been excellent quality. This has been achieved largely through rigorous inspection, a process that has come to be known as inspecting the quality in. As a result, the firm has always had a high reject rate at final inspection. This has necessarily resulted in too many jackets being scrapped or sold below cost as seconds. It has also resulted in a bothersome percentage of imperfect jackets slipping through inspection and ending up in the hands of customers. The impact has been a so-so reputation with customers, and prices that are too high to be competitive with the imports or major U.S. manufacturers.

Management tried and tried to get the production workers to do better, but it seemed that every effort to reduce defects came to nothing. Sometimes it appeared that good ideas and the best of intentions only made matters worse. A few weeks ago the managers retained a manufacturing consultant with statistics and process control credentials. He told them their first priority should be to get their processes under control.

With the consultants help, they started their program by identifying and eliminating several special causes of variation. These special causes had included machines that needed maintenance and calibration, some employees with insufficient training, and the absence of written work instructions for certain procedures. By the six-week mark, Hi-Sports quality had noticeably improved. Management decided it was time to attempt the development of a control chart.

Because rejects were based on pass/fail criteria for various characteristics, the managers needed a control chart that could respond to nonmeasurable attributes. Three common charts meet that requirement: the p-chart, np-chart, and c-chart. The p-chart could help control the percentage of defective jackets. The np-chart could help control the number of defective jackets. The c-chart could help control the number of defects in a jacket. They decided the c-chart would give them what they wantednamely, using one jacket as the sample and tracking the defects found in the sample.

For the initial chart-development data, one jacket was inspected each hour for 30 consecutive working hours. The data are listed in the accompanying table. The data were recorded in the five most common defect categories, with a sixth column collecting all other types of defects encountered. At the end of the 30th hour, 46 total defects had been recorded from the 30 jacket samples.

You are the consultant, and because this is Hi-Sports introduction to control charts, you will have to help it develop the chart. From the data table, compute c, UCL_(c) and LCL_(c).

Next, construct a control chart. Be sure to include some headroom above the upper control limit to allow for any out-of-limit events that may be encountered. Also make the chart long enough horizontally to include all the data points in the table, plus a few more days of real-time data points that will need to be plotted as SPC tracking begins.

Now plot the appropriate data from the table on the chart. Is the process in control, or is one or more special causes still lingering? Where do you go from here? Complete your task by (a) providing Hi-Sport with a control chart that reflects an in-control process or (b) abandoning the current data and starting over again by seeking out the special causes that prevented success the first time.

\begin{tabular}{|r|r|r|r|r|r|r|r|} \hline \multicolumn{7}{|c|}{ Hi-Sport Manufacturing Co. Inc. } \\ \hline & \multicolumn{7}{|c|}{ Defects by Type } \\ \hline \end{tabular}