Quality - 2

ATTRIBUTE CHARTING

In Quality-1 we took a look at Average and Range Charts that are used to monitor process variables that we are able to measure, record and plot such as length, width and diameter etc.  If possible it is preferable to use direct measurement and monitor using X-bar & R charts but there are occasions where we would use go/no-go gauges or visual assessment, instead of direct measurement. In this case we would monitor the process by assessment of how many defectives (or defects) have been seen.  An example would be the visual inspection of plastic lenses for the presents of scratches.  There would either be a scratch, multiple scratches or no scratches.  The inspection process is not measuring the size of any scratches present only detecting scratches.  This is called Control by Attributes.  There are a number of Attribute charts that we can use but before we take a look lets hear from Mr Stat.

There are two attribute control charts for DEFECTIVES 

‘np’ CHART that monitors the number of defectives obtained from fixed sized samples.

‘p’ CHART that monitors the % defective from samples that vary in size.  (if there is a large variation in sample size then it is not possible to set control limits).

There are two attribute charts for DEFECTS

‘C-CHART’ that plots the number of defects in an inspection sample.

‘U-CHART’ that plots the average number of defects per unit in an inspection sample. (e.g. if you were inspecting 5 assemblies and found 2 defects in assembly 1 and 3 and 1 defect in assembly 5 the average number of defects per unit would be (2 + 2 + 1) / 5 assemblies = 1 defect / assembly.

Example ‘np’ charts look like-

This chart is typical of all four charts mentioned above.  To use this chart we would select a sample of, say, 50 parts from a machines output container at 9:00 am and inspect each with a go/no-go gauge.  If there were 4 defective parts we would record 4 against the sample number and time sample was taken.  A plot on the chart corresponding to 4 defects would be made.  At 9:30 am another sample of 50 parts would be examined and the number of defectives would be plotted.  The chart would contain an upper control limit that would warn us that the process had altered if the number of defectives in the sample checked were to exceed the control limit.  It would be telling us that it was not “just bad luck that we picked 50 parts at random that contained an above average number of defectives.

These charts are ok to use when the process is in trouble, but there are limitations.  One is that with even relatively high levels of defectives being produced you have to take large sized samples (50 to 200 parts per sample) to be able to obtain sufficient data of defectives.  Another is if your quality is at a level of 200 parts per million the average will only yield one defective in 5,000.  In this case you will be repeatedly plotting zeros on the control charts and the information will be virtually worthless.  The modern alternative is to use computer controlled vision systems that detect defectives and reject them.

Where it is not practical to use np charts or where you cannot install a vision system but still wish to use some form of limited gauging/visual inspection the following could be adopted –

1. Increase the sampling frequency but decrease the sample size.
2. If the part is OK continue to run the process.
3. If the part is BAD check the following 5 parts, if any are BAD, STOP THE PROCESS.
4. Instead of plotting the number of defectives, tick or cross the time at which the check was carried out.

This suggestion will not spot the slight drift from the normal performance but it will highlight a major deviation.

Another form of monitoring when quality is very high and occurrence of defectives is very low is to record the elapsed time between one defective being found and the next.

Whatever system of process monitoring you put in place, modern quality standards will not tolerate large numbers of defectives reaching the customer.  Attribute charting allows defectives to be released through the system.  Finally, on the question of visual defects, remember what I said on the start of quality, if a part looks bad it is bad, if it looks good it may be good.

CALCULATION OF CONTROL LIMITS  

Calculation of control limits for the ‘np’ chart uses results from previous data.

Before we look at the calculations lets look at a few of the symbols –

NP-bar (usually written as a P with a minus sign above it) = average of a number of defectives                        P-bar (usually written as p with a minus sign above it) = Sum of defectives / Total parts inspected in study  UCL = Upper Control Limit used on the chart.                                                                                                 LCL = Lower Control Limit used on the chart. 

First we need to calculate the average no of defectives (NP-bar) –

NP-bar = (1+2+1+1+2+0+1+0+3+1+2+5+1+0+2+1+4+0+0+2) / 20 samples = 1.45

Next we need to calculate P-bar 

P-bar = 29 / (20 x 50) = 0.029

Next we need to calculate the control limits 

UCL = NP-bar + 3 x Sq Root of [NP-bar x (1 - P-bar)]

UCL = 1.45 + 3 x sq Root of [1.45 x (1 – 0.029)]

UCL = 5     Note Mr Stat has rounded the number to the nearest whole number.

LCL = NP-bar - 3 x Sq Root of [NP-bar x (1 - P-bar)]

LCL = 1.45 - 3 x sq Root of [1.45 x (1 – 0.029)]

UCL = 0     Note Mr Stat has set the number to zero because the calculated value was a negative.

The use of both control limits is to indicate when the process has drifted, but if it drifts down below the LCL something has altered to improve the process. Clearly you cannot get less than 0 defectives as calculated in our example, however in other cases it is possible to calculate a LCL that is greater than zero.