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ular interval can be computed if the sample means have a distribution that is close to nor- mal Acceptance intervals can also be computed for nonnormal probability distributions Acceptance intervals find wide application for monitoring manufacturing processes to determine if product standards continue to be achieved. For example, in a manufactur ing process the manufacturing engineer carefully sets and tests a new process so that it will produce products that all meet the guaranteed specifications for size, weight, or other measured properties. Thus, the mean and standard deviation for the units produced are specified so that the desired product quality will be obtained. In addition, these inter vals are also used for monitoring various business activities that involve customer service, Acceptance standards are established that meet stated marketing goals and customer ser vice-level capability. These standards, in turn, are used to develop means, variances, and acceptance intervals to be used for process monitoring (Deming, 1956) However, it is possible that the process could come out of adjustment and produce defective product items Changes in either the mean or variance of the critical measure ment result from a process that is out of adjustment Therefore, the process is monitored regularly by obtaining random samples and measuring the important properties, such as the sample mean and variance. If the measured values are within the acceptance interval, then the process is allowed to continue If the values are not, then the process is stopped and necessary adjustments are made Acceptance intervals based on the normal distribution are defined by the distribution mean and variance from the central limit theorem we know that the sampling distribu tion of sample means is often approximately normal, and thus, acceptance intervals based on the normal distribution have wide applications. Assuming that we know the popula tion mean and Varance then we can construct a symmetric acceptance interval provided that has a normal distribution and is the standard normal when the upper tail probability is a 2 The probability that the sample mean its included in the interval As noted, acceptance intervals are widely used for quality control monitoring of vari ous production and service processes the interval 62 plotted over time the result is called an X-bar chart) and provides limits for the sample mean T. given that the population mean is typically, a is very small (a <.01 and standard practice in us industries is to use="3" this the source for term sex sigma tised various quality assurance programs if sample mean outside acceptance interval then we suspect that population not a typical project engineers will take steps achieve small variance important prod- uct measurements are directly related product quality. once process has been adjusted so an mean-called control merealis established form of chart periodic random samples obtained compared interval. within it concluded operating properly no action taken but correct example monitoring health insurance claims charlotte king vice president financial underwriting large company wishes monitor daily claim payments determine aver- age dollar value subscriber stable increasing or decreasing individual varies up down from one day next would be naive draw conclusions change operations based on these variations at some point changes become substantial should noted. she asked you de- velop procedure>