S.P.C. Statistical Process Control: GMS-401 F2013

In GMS-401 we study 2 types:
1. Inspection for variables —there is typically one dimension most indicative of QUALITY or lack of Quality of an item being studied for compliance to a Quality Standard. Here it is a dimension such as the contents of a jar of fruit jam, the size of a pair of shoes etc. These are called X-bar and R charts. One calculates X-bar-bar and R-bar averages and these are the centre lines of the SPC run-charts that will be drawn. The charts MUST have these centre lines PLUS upper and lower control AND range limits. The points on these graphs MUST be joined so that a reader can follow the level of quality versus centre lines and control limits over time and look for trends and potential out-of-control conditions.

The data will be in a set of readings typically taken at say one-hour intervals. The number of readings taken each hour is the sample size–for example 4 jars of jam in the exercise book. The sample size of 4 is used in calculating the control limits and for determining the value of the statistical constants used in these calculations such as A2, D3,D4.
The “number of samples” is 10 but the “sample size” is 4.
The 10 samples will be plotted on a graph but the number 10 in this case is NOT used in the calculation of control limits when looking up the A2,D3, and D4 values.

In this type of SPC BOTH graphs must be drawn and examined. If a SINGLE POINT on either graph exceeds the upper or lower control or range limits, the process is said to be “out of control”. If NO points exceed the range or control limits, the process is said to be “in control”.

In addition the analyst will examine the graphs for patterns showing either expected random behaviour or the tendency towards an out-of-control condition. The QUALITY GURUS: Deming, Juran, Crosby, Taguchi, Feigenbaum were the originators and proponents of SPC. Their themes were:

1. A statistical sample can be taken and can provide great accuracy as to the quality and acceptability of a batch of production. One need not examine EVERY unit of production–it is too time consuming and too expensive AND would put a firm that used this approach at a competitive disadvantage.
2. Perhaps we cannot have ZERO DEFECTS in production but we can certainly minimize the defects (in many cases a total financial loss for the firm) but taking statistical samples at appropriate intervals (depends on the volatility of the process–how frequently will a factor affect quality–sharpness of tools etc.) and EMPOWERING the production line employees with the ability to shut down the production line if a trend towards OUT-OF-CONTROL is noted. We want employees to stop the process BEFORE it is out-of-control and producing substandard products that will not meet our customer’s needs–and they will probably return them at our expense and stop buying from us. Look at the one-page lime green sheet handed-out in class that discusses how to read and interpret a control chart. There you can see the trends that we would expect production line employees to note and act accordingly—caution if production is heading towards out-of-control and shutting down production before an out-of-control condition occurs and arranging to have the process problems corrected–either by themselves if they work in a TQM (Total Quality Management) factory or calling the Maintenance Department otherwise.

2. Inspection for Attributes:
These are p-bar and c-bar charts. p-bar charts are for fraction defective in a batch. (Product is either ok or defective–there is no middle ground). For example 12 coat hangers out of 200 are defective. c-bar charts are defects in a single unit of production–example the rubber sink stoppers in the exercise book.
Typically items here are not economically repairable–example standard incandescent light bulb–“a filament enclosed in a glass envelope with a ferrule on the other end–the threaded thing that screws into a light socket”. Firms such as GE and Westinghouse and other firms make these things and test them–they either work or they don’t work–such a light bulb is a 35 cent item in a hardware store. If the bulb does n’t work it is rejected–it is not economically feasible to repair a 35 cent item.

Other typical items–wire coat hangers 2 cent item, AA, AAA,B,C,D, 9V batteries etc are similar items. They are made in a mass-production setting and are inexpensive items. The buyer accepts that there will be a certain fraction defective. To supply 100% perfect would mean very expensive 100% inspection and the cost of such inspection would have to be recovered in the cost of goods and paid for by the customer. Remember Ch. 4S, the reliability chapter? I have a new stove exhaust hood with 2 lights. I installed it and one of the two light bulbs failed on day 2. Items can fail at any time–MTBF!

If you are calculating a fraction defective in the case of a p-bar chart: the fraction defective is a probability that a unit of production selected at random will be defective. Just like probability, the range is ZERO (no defectives) to 1 (100% defective). The p-bar is called FRACTION DEFECTIVE. For each sample the number of defectives will be used to calculate the fraction defective. If you have 7 defectives in a sample of 200, the fraction defective is .035 i.e. 7/200. Sample sizes will vary according to the type of product being produced and the volatility or changeability of the process. Fraction defective cannot exceed ONE or 1.0 (100% defectives) and it cannot be NEGATIVE–better than perfect?
Again the SAMPLE SIZE (in the case of the coat hangers = 200) is used in the calculation–the number of samples–25 in the case of the coat hangers is NOT used in the calculation of control limits–the 25 sample are used to plot 25 points on the run chart that will be plotted.
The c-bar charts are used for defectives in a single unit of production. When calculating the center line and control limits, the results are a range of acceptable defectives–blemishes in the case of the rubber sink stoppers. The lower limit cannot be negative. If your calculation returns a NEGATIVE number, set the lower range limit to ZERO.

Assignable Causes?
If a process does go OUT-OF-CONTROL there must be a reason. The reason(s) are called assignable causes. What happened to cause the out-of-control condition?
Jars of jam—what if the jam jars are supplied by a new supplier who provides thinner or thicker glass in their bottles and someone neglects the necessary recalibration of the measuring scales (scales are set such that the scale weight reads zero with an empty bottle on the scale–you are paying for 14 ounces of jam). Ever order a sandwich at Druxy’s Deli? How are you sure that you are getting the correct amount of corned beef or pastrami in your sandwich? They have a little scale to weigh it on to ensure that you are getting the correct weight. Employee judgment is not sufficiently accurate.

Manufacturer of blue jeans–sewn seams—done with professional sewing machines-what if the needles get dull or break? Missed or incorrectly spaced stitches.

Assignable causes could also be:
-new employees not sufficiently trained to provide the required level of quality.
-production machine goes out of adjustment.
-change in raw materials–jeans–new batch of denim cloth is thinner(tears) or thicker (sewing machines jam) than usual. Paper for your computer printer is thicker than usual–printer will jam.

Where do they start looking for assignable causes? The production expert is likely a Process Engineer ( a manufacturing expert–mechanical or chemical or aeronautical etc.) He/She knows what has caused problems in the past and will begin the search for assignable causes there and then begin to examine other possibilities until the problem source is determined and repaired.

Federal Government Department of Weights and Measures: A consumer protection branch of the Government to ensure that we are getting what the bottle or box says on it. Boxes of cereal are sold by weight, not volume—“contents will have settled in transit”. The Government inspectors buy products at regular stores and use SPC testing techniques the same as we are covering here.