Variable processes are those in which direct measurements can be made of the quality characteristic in a periodic or daily sample. The daily samples are then compared with a historical record to see if the manufacturing process for the part is in control. In X, R charts, the sample measurements taken today are expected to fall within three standard deviations 3 s of the distribution of sample averages taken in the past. In moving range (MR) charts, the sample is compared with the 3 <r of the population standard deviation derived from an R estimator of cr. When the sample taken falls outside of the 3 s limits, the process is declared not in control, and a corrective action process is initiated.
Another type of charting for quality in production is the precontrol chart. These charts directly compare the daily measurements to the part specifications. They require operators to make periodic measurements, before the start of each shift, and then at selected time intervals afterward. They require the operator to adjust the production machines if the measurements fall outside a green zone halfway between the nominal and specification limits.
Precontrol charts ignore the natural distribution of process or machine variability. Instead, they require a higher level of operator training and intervention in manufacturing to ensure that production distribution is within halfway of the specification limits, on a daily basis. This is in direct opposition to six sigma concepts of analyzing and matching the process distribution to he specification limits only in the design phase, and thus removing the need to do so every time parts are produced.
Moving range charts (MR) are used in low-volume applications. They take advantage of statistical methodology to reduce the sample size. They will be discussed further in the Chapter 5. In high-volume manufacturing, where several measurements can be taken each day for production samples, X and R control charts are used to monitor the average and the standard deviation of production. It is important to note that 叉 control charts are derived from the sample average distribution, which is always normal, regardless of the parent distribution of the population σ, which is used for six sigma calculations of the defect rate, and is not always normal, as discussed in the previous chapter.
The X chart shows whether the manufacturing process is centered around or shifted from the historical average. If there is a trend in the plotted data, then the process value, as indicated by the sample average X, is moving up or down. The causes of X chart movements include faulty machine or process settings, improper operator training, and defective materials.
The R chart shows the uniformity or consistency of the manufacturing process. If the R chart is narrow, then the product is uniform. If the R chart is wide or out of control, then there is a nonuniform effect on the process, such as a poor repair or maintenance record, untrained operators, and nonuniform materials.
The variable control charts are generated by taking a historical record of the manufacturing process over a period of time. Shewhart, the father of control charts, recommends that “statistical control can not be reached until under the same conditions, not less than 25 samples of four each have been taken to satisfy the required criterion. ” These observations form the historical record of the process. All observations from now on are compared to this baseline.
From these observations, the sample average X and the sample range R, which is the absolute value of highest value minus the lowest value in the sample, are recorded. At the end of the observation period (25 samples), the average ofXs, designated as^ and the average of R% designated as R, are recorded.