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## Process Capability

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**Process Capability**• Process capability is the ability of a process to consistently meet specified customer-driven requirements • Specification limits are set by management in response to customers’ expectations • The upper specification limit (USL) is the largest value that can be obtained and still conform to customers’ expectations • The lower specification limit (LSL) is the smallest value that is still conforming**Estimating Process Capability**• Must first have an in-control process • Estimate the percentage of product or service within specification • Assume the population of Xvalues is approximately normally distributed with mean estimated by and standard deviation estimated by**Capability Indices**• A process capability index is an aggregate measure of a process’s ability to meet specification limits • The larger the value, the more capable a process is of meeting requirements**Cp Index**• A measure of potential process performance is the Cp index • Cp> 1 implies a process has the potential of having more than 99.73% of outcomes within specifications**CPL and CPU**• To measure capability in terms of actual process performance: • CPL (CPU)> 1 implies that the process mean is more than 3 standard deviation away from the lower (upper) specification limit**CPL and CPU**(continued) • Used for one-sided specification limits • Use CPU when a characteristic only has a USL • Use CPL when a characteristic only has an LSL**Cpk Index**• The most commonly used capability index is the Cpk index • Measures actual process performance for characteristics with two-sided specification limits Cpk = min(CPL, CPU) • Cpk = 1 indicates that the process average is 3 standard deviation away from the closest specification limit • Larger Cpk indicates greater capability of meeting the requirements**Both Cp and Cpk are identical because process mean is at the**center of the specification spread As the process mean starts to drift away from the center of the specification spread, value of Cpk starts getting smaller (although Cp does not change)**Process CapabilityExample**You are the manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within ten minutes or less. For seven days, you collect data on five deliveries per day. Compute an appropriate capability index for the delivery process.**Process Capability:Hotel Example Solution**Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviation above the mean.