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4.5 Case Study
4.5.2 Performance Metrics
Three key metrics are identified, in view of available data resources, to monitor performance within the facility: delivery time, shortages, and standard packaging.
4.5.2.1 Delivery Time
Delivery time is the metric for monitoring time required to move SKUs from the stock room to the dif-ferent dz. The target lead time for this operation is 4 h. The shop monitors the number of orders
exceed-ing the 4 h requirement on a per-shift basis. Delivery time is transformed to attribute form at the facility.
Attribute data implies that there are two possible events: success or failure. Failure in this case means that the lapsed time between the first scan (need for a SKU to be restocked) and the second scan (SKU restocked) exceeds 4 h. A p-chart with variable sample size is the preferred SPC method for tracking this attribute data. In the case of delivery time performance, the p-chart is used to monitor the percentage of deliveries made within 4 h. These data are collected automatically from the company’s database. The formulas used to calculate a p-chart with variable sample size are given in Table 4.4. Figure 4.4 shows the performance of shop 1 for a particular month, and Figure 4.5 shows the performance of the first shift of shop 1 for the same month.
The centerline (CL) in Figure 4.4 is calculated as follows: the total number of nonconforming deliveries (173) is divided by the total number of samples (396), or 0.437. The data being plotted represents the fraction p of nonconforming deliveries. For the first sample the fraction nonconforming is equal to the total nonconforming deliveries for the sample (7) divided by the total number of deliveries for that sample (25). The 3-sigma control limits are calculated by placing control limits at three standard deviations beyond the average fraction nonconforming. For example, the control limits for sample one are:
LCL1 0 437 3 0 437 1 0 437
25 0 437 0 297
= . − ∗ . ∗( − . ) = . − . =00 139.
If the LCL for any given sample is smaller than zero, then the value of the LCL is truncated to zero.
UCL1 0 437 3 0 437 1 0 437
25 0 437 0 297
= . + ∗ . ∗( − . ) = . + . =00 734.
The resulting control limits and raw data are plotted in Figure 4.4.
The data are also used to monitor the performance of the shop on a per-shift basis. The calculation of the 3-sigma control limits is done in the same way as those for the shop performance. For example, for sample 15 on the first shift, the fraction nonconforming p is 3/15 = 0.2. The fraction nonconforming, as well as the 3-sigma control limits, for each sample of the data on a per-shift basis are presented in Figure 4.5.
As can be seen in Figures 4.4 and 4.5, the points exceeding the UCL indicate a lack of stability in the process. The source of the nonrandom pattern should be determined and eliminated. The points plot-ting outside control limits require investigation, with the cause assigned and eliminated. Once the cause is eliminated, the associated points are no longer considered in the calculations, revised limits are
Performance Shop 1 (October)
0 0.5 1 1.5 2
Sample Number Sample Fraction Non-conforming
UCL
% CL LCL
1 3 5 7 9 11 13 15 17 19 21
FIGuRE 4�4 p-chart for attributes (shop 1).
calculated and the new plot is inspected for points plotting outside limits. Only extended in-control performance can be used to judge the capability of the process.
4.5.2.2 Shortages
The number of shortages is used to monitor the number of open transactions. The number of short-ages is a performance metric that indicates the quality of the supply side of logistics systems and is readily available from data sources. The performance should be evaluated on planner, shop and facility levels. The later performance metric provides an aggregate view of all the combined shops, implying both the necessary horizontal as well as vertical dimensions of a balance PM system as suggested in Harp et al. [26].
The number of shortages, like the delivery time, is transformed to the attribute form for the facility. An open order must be closed within five days. Failure in this case is the failure to close an open order within the five-day time frame. A p-chart is recommended to track the percentage of open transactions. Since each SKU is assigned to different planners, a p-chart is allocated to each planner. Planner performance is based upon the percentage of open transactions to the total number of SKUs assigned to the planner.
Figure 4.6 shows a p-chart used to monitor the number of shortages of planner 5. Figure 4.7 shows the p-chart used to monitor open transactions at the aggregate level.
Since each shop has a specific number of SKUs, a p-chart is also used to track the percentage of open transactions within a shop (ratio of open transactions to the total number of SKUs in a shop). In Figure 4.8, the p-chart is used to monitor the number of open transactions for shop 2. Furthermore, open transactions per shop should be monitored on an aggregate view as shown in Figure 4.9.
The points plotting outside the UCL indicate lack of stability in the process. Those points must be investigated and assigned to a cause that should be eliminated. After the points associated with this FIGuRE 4�5 p-chart for attributes (shop 1, first shift).
Performance Shop 1 First Shift
0 0.5 1 1.5 2
Sample Number Sample Fraction Non-conforming
UCL
% CL LCL
1 3 5 7 9 11 13 15 17 19 21
Performance Planner 5
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014
Weeks
% Non-conforming
UCL CL Data LCL
1 2 3 4 5 6 7
FIGuRE 4�6 p-chart for attributes (planner 5).
Aggregate view
0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008
Weeks
% Non-conforming
UCL CL Data LCL
1 2 3 4 5 6 7
FIGuRE 4�7 p-chart for attributes (aggregate).
Performance Shop 2
0 0.001 0.002 0.003 0.004 0.005
Weeks
% Non-conforming
UCL CL Data LCL
1 2 3 4 5 6 7
FIGuRE 4�8 p-chart for attributes (shop 2).
cause are eliminated from the calculation, new revised limits are calculated and plotted. The new plot is inspected for stability.
4.5.2.3 Exceptions to Standard Packaging
Exceptions to standard packaging are also monitored for the process. This data presents the proportion of exceptions to standard packaging by shop.
Since management is interested only in the number of incorrect packaging incidents in relation to the total number of packages, a Pareto chart is recommended to monitor standard packaging. The Pareto chart for nonconforming packaging across all seven shops is shown in Figure 4.10. The data are categorized and ranked showing the cumulative percentage of incorrect packaging incidents by shop.
The percentages are obtained by dividing the number of incorrect packaging incidents per shop by the total number of incidents. As a histogram showing the frequency of root causes, the Pareto chart is helpful in prioritizing corrective action efforts. The Pareto chart is used to identify major causes of phenomena like failures, defects, delays, etc. If a Pareto diagram is used to present a ranking of defects over time, the information is useful for assessing the trend of individual defects, frequency of occurrence, and the effect of corrective actions.
Intuitively, the shops with more SKUs will have a greater percentage of incorrect packaging incidents.
However, as can be seen in Figure 4.10, shop 5 has the second greatest percentage of wrong packages even though it has the second smallest number of SKUs. The combination of Pareto charts and trend charts will provide the benefit of a better analysis tool, because the trend chart provides a tool for moni-toring the process in view of its natural variation.