# GMS 401 Lecture Notes - Statistical Process Control, Ferrari F2012, Incandescent Light Bulb

1S.P.C. Statistical Process Control: GMS-401 F2012

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

## Document Summary

In gms-401 we study 2 types: 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. 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.