Competitive pressures have forced many U.S. firms to improve the quality of their products. One quality improvement method being introduced in the production process by Cherry Textron is statistical process control (SPC). The objective of SPC is to manufacture all parts to specifications the first time, eliminating costly rework, scrap, and unnecessary 100 percent inspection. This is accomplished by having each machine operator regularly measure parts they are producing against statistically pre-established quality standards and charting their results. den parts fall outside of the statistically acceptable range, production is immediately stopped and the problem is identified and corrected. Such an approach prevents discovery of faulty components after completion of an entire production run. Responsibility rests with the machine operators for producing acceptable parts only, thus they become in essence their own inspectors.
Cherry Textron (Cherry) produces and sells blind rivet fasteners to the aerospace and automotive industries. Frequently, customers within these industries demand that vendors implement and maintain evidence that their manufacturing processes are within statistical control. In response, Cherry started an extensive program to train 350 employees in SPC methods. SPC will give production personnel the tools to measure their own quality, and when out of the control, a means to systematically analyze the causes.
The concept of x-bar and R control charts is based on statistical hypothesis testing including computation of mean and standard deviation under a normal distribution curve. Upper and lower control limits are typically calculated +/- 3 standard deviations, thus providing a 99.7 percent assurance that a type 1 error will not occur (rejection of a null hypothesis that is true).
The prime use of the control chart is to detect "assignable causes of process variation. Process variations are attributable to two kinds of causes: random -- due solely to chance, and assignable -- due to specific "findable" causes. Ideally, only random causes should be present; therefore, they represent the minimum possible variation. A process which is operating without assignable causes of variation is said to be "in a state of statistical control." This occurs when samples selected and charted on the x-bar and R control charts fall within the control limits. Assignable causes exist when the actual variation exceeds the control limits. After giving consideration to cost/benefit analysis, the process is investigated, causes are identified and corrected, and finally the process is remeasured to determine if it is now in control.
The x-bar and R control chart concepts are used repeatedly to control quality in the following order:
Gauge Capability Study. Cherry determines that the gauges used for measuring critical part specifications are in control.
Process Capability Study. Production processes are measured for control to pre-established tolerances.
Process Control Procedures. These constitute the day-to-day surveillance to ensure that the production process remains in control. After a short explanation of x-bar and R control charts, we discuss each of the above functions.
An example of a typical x-bar and R control chart data sheet is Figure 1 (next page).
Twenty-five subgroups of five samples each were selected. For each subgroup, Cherry calculated the average (x-bar), the range (R) (the difference between the highest and lowest measure), and a grand total average (shown in Figure 1 as an x with a double-bar above) and range (shown in Figure 1 as an "R" with a single bar above) for the 25 averages (x-bar) and ranges (R). Upper and lower control limits were also computed for x-bar and R. The mean and range for each subgroup are plotted on graphs. Since all plot points in Figure 1 fall within the upper and lower limits, the process is in statistical control.
The chart of x-bar values tells when a change has occurred in central tendency. …