# Quality management & operating characteristics

QUALITY MANAGEMENT & OPERATING CHARACTERISTICS CURVES

Operating Characteristics Curve is a tool to show the strength of a given sampling plan. It graphically presents fraction defective or percent defective in a lot against the probability of acceptance.

Every acceptance sampling plan has an â€˜operating characteristicsâ€™ (OC) curve that shows how it works or how effective it is in discriminating between a good lot and a bad lot.

First set up a plan and then look at its OC curve. Weâ€™ll start by deciding the producerâ€™s risk. This is the risk that the producer takes that a very good lot might, by chance, be rejected. It is called the acceptable quality level (AQL) and is, generally, set at 5 percent. AQL is defined as the maximum percent defective or the maximum number of defects per 100 units. For sampling inspection, this can be considered as a process average. This means that quite good lots will pass 95 percent of the time.

Next we will set the consumerâ€™s risk or the lot tolerance percent defective (LTPD). This is sometimes called the lot tolerance fraction defective LTFD. The consumerâ€™s risk is generally set at 10 percent, which means that the consumer wants a plan which will reject lots the maximum proportion of defectives ( the LTPD) 90 times out of every 100 such lots.

The plan that will accomplish the objectives we want is an instruction to the inspector guiding him how many to include in his sample and also the maximum number of defectives that will let the lot pass. If the lot is 10,000 or more than he should inspect a sample of 400 and reject all lots whose sample contains eight to more rejects. With seven or fewer defectives he accepts the lot. But if the lot is only 1,000 we get the same quality assurance by having him inspect a sample of only 275 and accepting the lot if he finds no more than five defects. If the whole lot is 200, he should inspect 125 and accept if he finds two or fewer rejects. Our â€˜planâ€™, therefore, for each size lot, tells the inspector how big a sample to take and how good it has to be.

Size of required acceptable.

Universe——-Sample——–Defectives
âˆž—————400————7
10,000———-400———–7
1,000————275———–5
200————–125———–2

On this chart, the horizontal line at the bottom is an â€˜Ifâ€™ line. â€˜Ifâ€™ a lot submitted has 1,2,3,4, etc., percent defectives, then we can read up to the curve and across to the left to see what the chances are that we will accept such a lot. Lots which actually contain 1 percent defectives will pass about 95 percent of the time. Lots with 2 percent defectives will pass 40 percent of the time. Lots containing 3 percent defectives will get by only 10 percent of the time and poorer lots have very little chance of getting by.

Every acceptance inspection plan has its own operating characteristics curve. The shape of the line depends on the quality we want and the extent to which we want to be certain that we will get this quality. The slope of the curve depends upon the size of the sample and on its proportion of the parent lot. For any given size lot, the larger the sample, the steeper the curve.

Degrees of Defects in Acceptance Sampling

Many products can have major or minor defects or both at the same time. If so, we might like our receiving inspectors to be using two or more inspection plans at the same time and on the same sample. We might, for instance, allow no defects at all in the sample for critical or major defects. The curvature of a spring for an automobile door lathe might be critical. If it curves too much and puts on too much pressure, it might break and let the car door swing open. So if one finds even one defective in the sample one would reject the lot.

We would also want to have very few or no major defects even when danger isnâ€™t involved. If an automatic seat adjuster in an automobile doesnâ€™t have enough pull, the seat wonâ€™t adjust. Sometimes we need to watch for defects because they will jam machinery. The head diameter on a driver installed by automatic assembly machine, if it is too big, will jam the machine. The defect is unimportant functionally, yet it is important in keeping production moving. Again, we might use an inspection plan that allows for no defects in the sample.

But minor defects which wonâ€™t affect the productâ€™s operation arenâ€™t so serious. We could accept lots with a few minor defects. Probably youâ€™d use a plan that would accept the lot even if the sample had 10 percent minor defectives. Our inspectors could be applying two or three inspection plans when they inspect a sample. The rejection number would be low for serious defects and high for minor or trivial defects.