March 28, 2010
Week 5 – Statistical Process Controls
Statistical Process Control
Total Quality Management is a philosophy that stresses three principles for achieving high levels of process performance and quality: Customer Satisfaction, Employee Involvement, and Continuous Improvement in Performance. This paper will address a practical type of continuous improvement - the use of statistical process control.
One definition of statistical process control (SPC) is “the application of statistical techniques to determine whether a process is delivering what the customer wants” (Goetsch & Davis, 2006). SPC primarily involves using control charts to ...view middle of the document...
Typically, the elimination process includes development of standard work, error-proofing and training, however, additional measures can also be used.
Detecting Special Causes
According to Shewart, since control is not defined as the complete absence of variation, we do want to identify and eliminate special causes of variation (Pyzdek, 1980). The following is a list of special causes:
1. A special cause is indicated when a single point falls outside a control limit.
2. A special cause is indicated when two out of three successive values are: a) on the same side of the centerline, and b) more than two standard deviations from the centerline.
3. A special cause is indicated when eight or more successive values fall on the same side of the centerline.
4. A special cause is indicated by a trend of six or more values in a row steadily increasing or decreasing.
Control Charts for Variables
There are different types of control charts for use. They include:
I chart. Used to construct a confidence interval that moves through time, then by tracking how each new period’s data falls within that range to help in making judgment about how a process is performing. Used when individual data is unknown.
X-Bar and S-Chart. Used when each subgroup has more than one observation to account for the sample variations. In the example below, we have the average caloric intake using a sample of 5 days for 5 consecutive weeks.
| |Wk 1 |Wk 2 |Wk 3 |Wk 4 |Wk 5 |
|count |5 |5 |5 |5 |5 |
|Xbar |1,182.80 |1,100.60 |1,114.60 |1,082.20 |1,184.80 |
|variance |2,627.70 |10,111.30 |3,804.80 |11,694.70 |1,279.70 |
|sdev |51.26 |100.55 |61.68 |108.14 |35.77 |
|minimum |1121 |1000 |1021 |900 |1143 |
|maximum |1250 |1250 |1189 |1189 |1232 |
|range |129 |250 |168 |289 |89 |
| | | | | | |
|confidence interval 95.% lower |1,119.15 |975.74 |1,038.01 |947.92 |1,140.38 |
|confidence interval 95.% upper |1,246.45 |1,225.46 |1,191.19 |1,216.48 |1,229.22 |
Xbar is the average for each day, sdev is the standard deviation for each day. If we take the average of the average (Xbarbar) we get 1133, and if we take the standard deviation of all the sample means (Sbar) we get 190.0. Now we...