Two results and their uncertainties

The designer has specified that a hole should be 50 mm ± 0.005 mm (top and bottom

lines). The first operator measures the size with a traceable micrometer as 50.004 mm and states that the hole conforms to the drawing. However, the foreman, looking at this result examines the uncertainty of the micrometer. The measurement uncertainty of the micrometer is 0.003 mm and applying this uncertainty he realises that the actual size could lie between 50.001 mm and 50.007 mm. He gets the hole remeasured on a bore comparator that has a 0.001 mm uncertainty. The measurement comes out at 50.006 mm and conformance is not proven. As a general rule the measurement uncertainty of the equipment should be no greater than ten percent of the tolerance band.

Note that in this case both measurement results agree to within their uncertainties. For measurement 1, however, the measured value is less than the uncertainty away from the upper specification limit (USL) and no real information has been obtained about whether the true value is inside or outside the specification limits.

ISO 14253 recommends that the following rules be applied for the most important specifications controlling the function of the workpiece or the measuring equipment.

Uncertainty of measurement: the uncertainty range reduces the conformance and non-conformance zones (copyright BSI)

At the design stage the terms “in specification” and “out of specification” refer to the areas separated by the upper and lower tolerance (double sided) or either LSL or USL for a one sided specification (see areas 1 and 2, line C).

When dealing with the manufacturing or measurement stages of the process the LSL and USL are added to by the measurement uncertainty. The conformance or non-conformance ranges are reduced due by the uncertainty (see line D).

These rules are to be applied when no other rules are in existence between supplier and customer. ISO 14253 allows for other rules to be agreed between customer and supplier. These rules must be fully documented.

Conformance with a specification is proved when:

• The result of measurement, complete statement, falls within the tolerance zone or within the maximum permissible error of the specification for measuring equipment (for example, the maximum permissible error of a CMM).
• The measurement result falls within the tolerance zone reduced on either side by the expanded uncertainty.

The conformance zone is linked to the LSL, USL and actual expanded uncertainty.

Non-conformance with a specification is proved when: 

• The result of measurement, complete statement, falls outside the tolerance zone or outside the maximum permissible error of the specification for measuring equipment.
• The measurement result is outside the tolerance zone increased on either side by the expanded uncertainty.

The non-conformance zone (4) is linked to the USL, LSL and expanded uncertainty.

Neither conformance nor non-conformance with a specification can be proven when the result of measurement, complete statement, includes one of the specification limits (for example, measurement 1).

It is important that the principle behind these rules is applied to a supplier/customer relationship where the uncertainty of measurement always counts against the party who is providing the proof of conformance or non-conformance, i.e. the party making the measurement. That is to say the supplier will reduce the tolerance by their measurement uncertainty to prove conformance. The customer will increase the tolerance by their measurement uncertainty to prove non-conformance.

Conformance or non-conformance

Three items have been measured. The purple line shows the LSL, the blue line the USL.

Measurement of item 1 - neither conformance nor non-conformance with a specification can be proven

Measurement of item 2 – non-conformance is proven

Measurement of item 3 – conformance is proven

In the case of item 1 the result of measurement, complete statement straddles the USL and neither conformance nor non-conformance with a specification can be proven. In the case of item 2 the result of measurement, complete statement is above the USL and so non conformance is proven. In the case of item 3 the result of measurement, complete statement is above the LSL and below the USL and so conformance is proven.

The Inspector

The inspector, Sid, has been operating the CMM for the last five years and is responsible for quality assurance within the jobbing shop. He signs the measurement reports and passes off the good components for shipping to the customer. He also scraps those items that fail inspection – which doesn’t always make him popular with the machinists on the shop floor.

The Auditor

The auditor, Irene, is an experienced metrologist working under contract for an independent accreditation body. She has over twenty years measurement experience, has been conducting technical assessments for ten years, and has a reputation as a tenacious assessor.

Sid was waiting in the inspection department when the foreman and works manager walked in and introduced Irene.

'Irene will be conducting a technical assessment of your inspection department while we go through the company quality manual with the lead assessor,' said the works manager briskly.

'Right,' said Sid cautiously. 'Where would you like to start Irene?'

'I see that this room has air conditioning – do you have an environmental logger to record the air temperature and such like?' enquired Irene.

'Yes, we have a chart recorder on the wall behind the CMM, it records the air temperature and relative humidity on a circular chart and we change the chart once a week and file the old ones away in this filing cabinet,' replied Sid confidently.

'That’s a good start, now tell me, do you have a calibration certificate for the logger?' asked Irene.

'Certainly have – it’s over here in the filing cabinet with the old charts' replied Sid strolling over to the cabinet and pulling out the file. 'Here you go, a certificate from a UKAS laboratory for the calibration of the temperature and humidity sensors that was issued four months ago.'

'I see on the chart here that there was a dip in the temperature over the weekend – the temperature dropped below 15 °C and didn’t rise to 20 °C until Monday afternoon.

What happened here?' asked Irene.

'We had a problem with the air conditioning plant when the power tripped over the weekend. The air re-heaters didn’t reset properly and when the chiller and air handler came back on line they over cooled the room. When I came in on Monday morning I reset the circuit breaker and as you can see the room temperature was back to normal by the afternoon' explained Sid.

'Did you perform any measurements on Monday morning?' asked Irene expectantly.

'Oh no, I couldn’t – not with everything as cold as that – we can only do accurate measurements when we’re working between 19 and 21 °C as the components are made of aluminium alloys and their thermal expansion coefficients are around 23 ppm. It wasn’t until after lunch that I could even check out the CMM,' said Sid.

'What do you mean by 'check out' the CMM?' asked Irene.

'Well every Monday I run a quick verification of the CMM performance by measuring this master component – that one with the red label in the corner. It’s actually a scrap part that I saved as a representative part. I put it in the same place on the CMM and run the same measurement programme and record a few of the key dimensions on that statistical process control chart over on the wall so I get a bit of confidence that everything is alright with the machine.'

'And did it check out alright on Monday afternoon?' asked Irene.

'Funnily enough it didn’t initially, so I ran the measurement programme again and got the same results – way out of the tramlines on the SPC chart. Something was wrong with the y axis of the machine – it was measuring longer than it should have by about

0.020 mm. So I moved the master part and put a good ring gauge in the same place and measured the roundness – sure enough it came out as an oval, so I knew I had a scale factor problem. I checked the scale temperatures for the x, y and z axes and got a hint of the problem – the y and z axes which are both on the top of the CMM were at about 21 °C while the x-axis which is down here under the bed of the CMM was sitting down at 16 °C.'

'It looked like the x axis was still cold from the weekend while the y and z axes being less massive and closer to the air vents had warmed up more quickly. At the end of the day I told the Foreman that I couldn’t make any measurements at all on Monday and it would be better to wait for the machine to stabilise overnight and to try again on Tuesday morning – which is what we did. I’ve noted the air conditioning failure in my notebook and recorded the testing and results that I got that day. I sent a memo to the Works Manager with the suggestion that we replace the re-heater circuit breakers with something that will recover properly from a power failure.'

'So you are confident in the results from this CMM are you?' enquires Irene.

'Actually I am' said Sid 'we've had this machine for five years now and it was installed and calibrated by the manufacturer. Then we did a performance verification test to the ISO 10360–2 standard using a calibrated step gauge that we measured in seven different orientations within the working volume of the machine. That test was successful and verified the performance of the CMM as being within the manufacturer’s specification so we were happy and they got paid! We’ve had the machine serviced annually since then and each time the service engineer brings in a step gauge and we check out the performance, if it’s not in specification he has to adjust the machine and redo the check.'

'Do you have any traceable length standards of your own, or do you rely on the service engineer’s step gauge?' asked Irene.

'Well the service engineer’s step gauge is calibrated annually by the NPL so that is traceable. We’ve got a fairly new set of grade 0 gauge blocks that came with a UKAS accredited laboratory certificate and I use those to calibrate my working sets of grade 1 gauge blocks by mechanical comparison and I used those working sets for checking some of the critical jigs and fixtures and calibrating our micrometers and verniers. We’ve also got an old set of length bars that I’ve got a lot of calibration history on over the last twenty years. We don’t use them that often so there’s not much wear and tear on them, so I’ve extended the calibration interval. I only get them calibrated every five years now but they are handy when I want to be sure about my measurements on a big job,' explained Sid at length.

'Well you seem to have the equipment and the standards sorted out, perhaps we should look at a recent measurement report. Tell me about this job' said Irene walking over to a stack of components with their inspection reports waiting to return to production and pointing at one of them.

'Right you are then,' said Sid. 'This is a batch of differential casings and that one you pointed at has a serial number stamped on the side which ties up with the measurement report that it’s sitting on.'

Sid went through the measurement report with Irene. The report refers to a measurement procedure QA CMM 0003 GEN that covers:

• the verification checks
• probe qualification, check for dirt too
• clamping fixtures
• part alignment
• measurement program name and location of results files
• comparison to known artefacts, etc.
• measurement results, statistical analysis and uncertainty budget,
• name of operator, date of measurement, etc.

Irene went through all the documentation checking things such as authorisation and document control.

Later that day, Sid had an appointment in his diary for the closing meeting. He stepped through the door to the boardroom. He could see Irene at the head of the table alongside the Company Director, his Team Leader and the Company Quality Manager.

'Let’s start,' she said. Irene then went through all she had seen. She mentioned a small number of minor issues that needed addressing and agreed timescales for their resolution.

'And to close,' she said, 'can I say how professional, helpful and organised all the staff I met were. I look forward to my next visit in a years time.'