For example, the littleys for the customer satisfaction score (Y1) in a res- taurant chain might be:
Customer satisfaction¼Function of (service quality, culinary satisfaction, restaurant availability, price,. . .)
These business level little ys will become the operations level big Ys. Op- erations level bigYs are useful for Six Sigma project selection criteria, since they are the operational parameters that are perfectly aligned with the busi- ness level metrics.
The operational level littleys for service quality of the restaurant chain may be written as:
Service quality¼Function of (wait time, friendliness of staff, cleanliness of facility, order accuracy,. . .)
Each of the operational level littleys may be further broken down into their components in the process level matrix. For example:
Wait time¼Function of (cycle time for cooking, number of staffed registers, time of day,. . .)
This resulting function can then be used to:
Establish conditions necessary for process optimization and/or variation reduction
Provide process-level Six Sigma project metrics
Define critical metrics for ongoing process control
These flow-down functions, which relate the bigYs to their corresponding little ys, are determined through regression and correlation analysis. Data is collected through designed experiments, data mining, surveys, focus groups, and critical incident techniques. The functions allow process-level metrics to be linked to both customer requirements and business strategy.
random sampling of 400 clients of a customer call center indicated that the service level was satisfactory or better, then the yield of the process can be calculated as 380/400¼95%.
A problem with the yield metric is that it does not provide enough detail of the nature of the errors. As an example, consider the following three processes, each with a 95% yield:
Process A: Of 4000 units started and 3800 completed, 200 defective units each had single defect.
Process B: Of 4000 units started and 3800 completed, 200 defective units had total of 600 defects.
Process C: Of 4000 units started and 3500 completed with no defects, 300 units reworked for 420 defects, 200 units scrapped for 580 defects.
These processes have different outcomes, yet the yield metric fails to dis- criminate between them. In this production process, some units initially with errors can bereworkedand sold as new. For example, units with unacceptable paint finish might be repaired and repainted. Likewise in a service process, a customer initially dissatisfied with the service may be directed to a manager for repair of the situation, resulting in an ultimately satisfied customer.
In terms of the metric, if the reworked units are treated the same as non- reworked units, information is lost. This simplistic yield metric obscures the
‘‘hidden factory’’ responsible for rework and process variation, resulting in increased process cycle times and costs.
A solution to this limitation is offered in the throughput yield metric.
Throughput yield measures the ability of the process to produce error-free units (or error-free service): the average percentage of units (or instances of service) with no errors. Throughput yield (Yt) is calculated by subtracting the defects per unit (DPU) percentage from 100%.
For example, process A (described above) has a DPU of 200/4000¼0.05, so its throughput yield is 95%, same as the yield calculated earlier. Process B has a DPU of 600/4000¼0.15 (a throughput yield of 85%). In this case, the throughput yield reflects the cost of the multiple errors in some of the sample units. Finally, process C has a DPU of 1000/4000¼0.25 (a throughput yield of 75%). In each case, the throughput yield is considerably less than the calculated first-pass yield.
Rolled throughput yield (Yrt) is calculated as the expected quality level after multiple steps in a process. If the throughput yield fornprocess steps isYt1, Yt2,Yt3,. . .Ytn, then:
Yrt¼Yt1*Yt2* Yt3*. . .*Ytn
For example, suppose there are six possible critical to quality steps required to process a customer order, with their throughput yields calculated as .997, .995, .95, .89, .923, .94. The rolled throughput yield is then calculated as:
Yrt¼.997 * .995 * .95 * .89 * .923 * .94¼.728
Thus, only 73% of the orders will be processed error free. It’s interesting to see how much worse the rolled throughput yield is compared to the indi- vidual throughput yields. As processes become more complex (i.e., more CTQ steps), the combined error rates can climb rather quickly. This should serve as a warning to simplify processes, as suggested earlier in Chapter 4.
Conversely, the normalized yield may be used as a baseline for process steps when a required rolled throughput yield is defined for the process series. The normalized yieldis calculated as thenth root of the rolled throughput yield. For example, if the desired rolled throughput yield is 73% for a process with six steps, then the normalized yield for each step of the process is (0.73)1/6¼0.95, since 0.95 raised to the sixth power is approximately equal to 0.73. The nor- malized yield provides the minimum throughput yield for each step of the process to achieve a given rolled throughput yield. Of course, if some process steps cannot meet this normalized yield level, then the rolled throughput yield could be less.
From a quality perspective, these throughput yields are an improvement from the simple first-pass yield, but they still lack a fundamental quality: they cannot provide immediate information to prevent errors. Each of these metrics relies upon attribute (i.e., count) data, where the numerical value is incremented based on the property of each sample relative to a quality specification. For example, the metric may be the count of errors in a given sample from the process: the count is incremented only when an error is observed. Attribute data has less resolution than measurement (variables) data, since a count is registered only if an error occurs. In a healthcare process, for example, the number of patients with a fever (attributes data) could be counted, or the measured temperature of the patient (variables data) recorded.
There is clearly more informational content in the variables measurement, since it indicateshow goodorhow bad, rather than just good or bad. This lack of resolution in attributes data will prevent detection of trends toward an undesirable state.
In addition to the lack of resolution, the data is tainted by the criteria from which it was derived. The count of errors is based on comparison of the process measurement relative to a specification. The customer specification may be unilateral (one sided, with either a minimum or maximum) or bilateral (two sided, with both a minimum and maximum). All values within the
CHAPTER 5 Measure Stage 89
specifications are deemed of equal (maximum) value to the customer (i.e., they pass), and all values outside the specifications are deemed of zero value to the customer (i.e., they fail), as shown previously in Figure 3.1.
In most industries, the specifications provide reasonable guidelines, but they are hardly black and white indicators of usability or acceptability of a product or service. As you approach the specifications, the usability becomes gray, and is subject to other mitigating concerns such as delivery dates and costs of replacement. This practicality is not surprising, considering the rather subjective manner in which specifications are often developed. Even in the best of worlds, when frequency distributions are applied to derive probabilistic estimates of requirements, there is uncertainty in the final result. In service industries, specifications are often similar to desirability levels: We may say we want to be seen by the doctor within 45 minutes of arrival, but we’re not likely to walk out at that moment if we think service is pending in just a few more minutes. Rather, we’ll start complaining after 30 minutes, which will build to irritability then disgust (at least for some of us).
Taguchi (1986) expressed this notion in terms of a loss function, where the loss to society (the inverse of the customer satisfaction) is maximized at some value within the customer requirements, then minimized outside the range of acceptable values. For example, with a bilateral specification, the maximum value of the product or service may be at the midpoint between the specifi- cations. As you move in the direction of either specification limit, the value is reduced in some fashion, typically exponentially as shown in Table 5.1. For example, a five-day delivery is undesirable, but a two-day delivery is preferred over the four-day delivery.
Although the specifications provide reasonable guidelines on acceptability to the customer, they are not absolute. Tainting the data by removing the objectivity of a measured value (or choosing a somewhat subjective attribute data over a more objective measured value) represents a loss in informational content that is not warranted or desired.
Rather, the statistical value of the data improves as the resolution increases, at least until a resolution is reached that can reliably estimate the variation in the data. For a proper statistical analysis, the standard deviation must be estimated, which requires enough information (i.e., resolution) to the right of the decimal point to measure the variation. For example, using the data in the Measure A column of Table 5.1, the standard deviation is calculated as 0.548.
The data in this column has been rounded up or down, due to poor resolution of the measurement system. How accurate is this estimate of variation? The data in the Measure B and Measure C columns of the table represent two possible sets of data that, when rounded, would result in the Measure A data. In one case, the variation is overestimated by Measure A; in the other,
variation is underestimated. Note that there are many other possible data sets that would result in the same rounded data shown by Measure A, but in all cases the rounding produces an inaccurate result. These inaccuracies would increase the probabilities of rejecting when the hypothesis is true, false alarm, or accepting when the hypothesis is false, failure to detect, errors. Practically, the value of the improved estimates must be balanced with the cost of the increased data resolution.