For this purpose, there are a number of statistical methods that can be employed that provide a means of measuring how controlled a process is.
A new material, "super plastic", has recently been employed as the material used in production. With the introduction of this new material, it is important to have a measure on its consistency in producing quality products. Particularly, defects in the form of uneven edges, cracks, scratches, air bubbles, and thickness variations are analyzed to reveal any problems with the new process. Tables 1 and 2 present the number of defects for the new material, "super plastic", as well as the standard material.
Since only raw defect data are available, the c-chart would be the best statistical tool to aid in the analysis of the new process. Since we are interested in identifying the reliability of the new manufacturing process, we take all the defects in a day as one figure. Taking the mean of this, the upper control limit (UCL) and the lower control limit (LCL) may be determined using the following formulas.
The two charts show that the total defects for both materials are within the computed limits. For the standard material, the number of defects fluctuates around the mean, but there is no apparent trend and there appears to be nothing suspicious with regards to the defect rate. For the new material, however, there appears to be a slightly increasing trend in the daily defect values. During the earlier days, the values were generally below the mean, and in the later days, the values have become generally greater than the mean. This suggests the possibility of the defect count exceeding the limit in the future. This may be due to the equipment used on the new material, or it could be because of the new material itself.
It therefore becomes necessary to construct individual control charts for each defect type to attempt to isolate the problem to a particular process. Calculating the means of each defect type, the upper and lower control limits presented in Tables 3 and 4 may be obtained.
Table 3. The Upper and Lower Control Limits for the Standard