![]() ![]() To find out the area between two values, you use the fact that the area under the standard normal curve is 1. The area in red represents the product that is below the lower specification limit. From the z tables, the fraction of data below 1.7 is 0.0446 or 4.46%. This means that 83 is 1.7 standard deviations below the average. You want to find out what percent of the product will be out of specification on the low side. To make matters worse, the customer has now set the lower specification as 83. So, you must use 1 – NORMSDIST(z) if you want the fraction of data above z. This function in Excel returns the fraction of results less than a value. You can also use the NORMSDIST function in Excel to find the above result. The area in red represents material that is out of specifications on the high side. This means that 11.51% of the data will be above the upper specification limit of 112. To find out how much product is more than 1.2 standard deviations above the average, you can use what is called the “z table.” The z table gives the fraction of process output that is beyond some value x that is z standard deviations from the average. If z is negative, it means that the value is below the average. So, 112 is 1.2 standard deviations above the average. Z represents the number of standard deviations some value is away from the average. This is where the z value becomes important. The question is how much will be out of specification. You can easily see from the histogram and the normal distribution that some of your product will be out of specification. Now suppose a customer has decided that the upper specification limit for your process should be 112. Life is good – everything has been within specifications. The specifications for the process have been 65 to 140. Thus, 68% of the data lies between 90 and 110 95% of the data between 80 and 120 and 99.7% of the data between 70 and 130.
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