May 2012

stock out pictureThis month's newsletter takes a look at how control charts can be used in purchasing. Purchasing is not an easy job in most companies, particularly in distribution companies. Purchasing is responsible for ensuring that product is available when the customer orders it from the distributor. What do customers want? They want the product they want, when they want it and at what they perceive is a reasonable price.

Sounds simple, right? If you are in sales, you want purchasing to carry every product you might sell. After all, if the customer wants a product and you are out of it, the customer might go elsewhere. And you lose the sale and the commission. On the other hand, management wants purchasing to control costs. They can't carry every possible product - the cost would be huge. Purchasing, with input from sales, must decide what products to carry in stock.

So, there is an on-going battle between sales and purchasing on what should be carried in stock. And purchasing must decide how much to carry in stock and when to re-order. You don't want those stock outs. And purchasing doesn't want to deal with all the dead stock issues - that stuff they put in inventory because salespeople were sure they would sell it - but never did.

Many times, purchasing metrics are part of a company's Key Process Indicators (KPI) or scorecards. Unfortunately, the metrics are usually end-of-the-line measurements like most KPI and scorecard metrics are. Once the metric tells you have a problem, it is often too late. Even with those color coded scorecards. Most scorecards don't take into variation - common and special causes. Those "yellow" warning signs are usually green the next month without doing anything! The challenge is to move upstream in the process for metrics that will give you early warning of potential problems - before the problem gets to the end-of-the line.

Control charts do take into account variation and give you much more insight into the behavior of the metric and the process. So, how can statistical process control and control charts help in purchasing? This newsletter examines this topic.  In this issue:

As always, please feel free to leave a comment at the end of the newsletter.

Our Scenario

Suppose you are the new purchasing manager in a distribution company. The company has been struggling with customer complaints about stock outs - products that are should be in stock but aren't available when the customer orders them. This, of course, hurts customer satisfaction. And it doesn't help the salespeople's morale. They are losing sales. So, you have been tasked with decreasing stock outs and improving service level to the customer. How can control charts help you?

Purchasing Metrics

The distribution company calls the individual products it carries "stocking lines." For example, work gloves might be one stocking line; one type of screw driver another stocking line. A stock out occurs when the quantity on-hand goes to zero. One weekly metric the company tracks is % stock outs, defined as:

% Stock Outs = 100(Stock Outs/Stocking Lines)

There are two other metrics that the company tracks on a weekly basis: % service level and % fill rate. These are defined below.

% Service Level = 100(Lines Filled Complete/Lines Ordered)

% Fill Rate = 100(Quantity Shipped/Quantity Ordered)

A line is filled complete if there is sufficient quantity to fill the order completely. For example, if a customer orders 100 work gloves and you ship 100, the line is filled completely. However, if you only have 99 gloves and ship all those, the line is not filled completely. Each week, the total number of lines filled complete is determined. This is divided by the total number of lines ordered to determine the % service level.

The fill rate is quantity shipped (like 99 work gloves) divided by the quantity ordered (like 100 work gloves). Each week, the total number of items shipped is determined and divided by the total number of items ordered to determine the % fill rate.

The company has goals for each of these three metrics:

  • % Stock Outs: 2% maximum
  • % Service Level: 95% minimum
  • % Fill Rate: 90% minimum

Each week, the metric is determined and placed on a scorecard with all those cute colors to determine if you are doing well (green), might have a problem (yellow), or have a problem (red).

Question for you to consider: what is the problem with these three metrics?

The Purchasing Data

The data for the past half-year are shown in the table below. What can you see from the table?

Table 1: Purchasing Data 

Week Number Stock Outs  Stocking Lines  % Stock Outs 

Lines Filled Complete 

Lines Ordered  Service Level Quantity Shipped  Quantity Ordered  Fill Rate
1 84 1895 4.4% 216 227 95.2% 2615 2724 96.0%
2 87 1895 4.6% 156 171 91.2% 846 855 98.9%
3 66 1895 3.5% 156 171 91.2% 804 855 94.0%
4 68 1899 3.6% 207 228 90.8% 1929 2052 94.0%
5 75 1899 3.9% 154 171 90.1% 1908 2052 93.0%
6 74 1905 3.9% 215 229 93.9% 2556 2748 93.0%
7 72 1905 3.8% 243 267 91.0% 2590 2670 97.0%
8 87 1907 4.6% 181 191 94.8% 1633 1719 95.0%
9 54 1903 2.8% 207 228 90.8% 1245 1368 91.0%
10 145 1922 7.5% 199 250 79.6% 1750 2000 87.5%
11 65 1932 3.4% 238 251 94.8% 2801 3012 93.0%
12 78 1922 4.1% 177 192 92.2% 1882 1920 98.0%
13 76 1925 3.9% 246 270 91.1% 2074 2160 96.0%
14 78 1932 4.0% 141 155 91.0% 1104 1240 89.0%
15 81 1944 4.2% 221 233 94.8% 1314 1398 94.0%
16 59 1954 3.0% 162 176 92.0% 1410 1584 89.0%
17 58 1960 3.0% 164 176 93.2% 1820 1936 94.0%
18 89 1960 4.5% 252 274 92.0% 3222 3288 98.0%
19 40 1958 2.0% 143 157 91.1% 1168 1256 93.0%
20 38 1960 1.9% 186 196 94.9% 1803 1960 92.0%
21 89 1960 4.5% 157 176 89.2% 1170 1232 95.0%
22 78 1960 4.0% 216 235 91.9% 1354 1410 96.0%
23 67 1962 3.4% 138 157 87.9% 1606 1727 93.0%
24 45 1960 2.3% 240 255 94.1% 1469 1530 96.0%
25 56 1968 2.8% 166 177 93.8% 876 885 99.0%
26 89 1968 4.5% 181 197 91.9% 946 985 96.0%

It is often hard to see what is happening by looking at a table of numbers - particularly tables with lots of numbers. It is much easier to see what is happening by looking at the data over time - in a time series format. Why do so many people not see this?

Control Chart for Stock Outs

purchasing percent figureThe metrics above are fairly common for monitoring purchasing performance in a distribution company. The problem with most scorecard approaches is that the underlying process is not being examined - only this week's results compared to a goal - that may or may not be reasonable. Control charts allow you to look at the process behavior over time - is it improving, staying the same, or getting worse? Are there any special causes of variation present or is all the variation due to common causes of variation? If you are new to control charts or need a refresher, please see our March 2011 newsletter on the purpose of control charts.

The proper control chart to analyze these data is the individuals (X-mR) control chart. We will use this chart to analyze the data here. For more information on the individuals control charts, please see our October 2006 newsletter.

The control chart for % stock outs is shown in Figure 1.

Figure 1: % Stock Outs

stock outs control chart

The average % stock outs for this time frame is 3.8% - definitely above the 2% goal. There is one point that is out of control during this 26 week period - the point above the upper control limits in week 10. This value (7.5%) is not part of the normal variation in the process. Something happened that caused the stock outs to be so high. The reason for this should be found and eliminated. Note that if you were just now charting these data, that special cause of variation would have happened 16 weeks ago - making it very hard to find the reason for the out of control point. This is why it is so important to plot the data in as close to real-time as possible. It makes it much easier to find the reason for special cause.

The normal variation is defined by the lower control limit and the upper control limit. However, the presence of the special cause of variation makes these values inaccurate. Figure 2 shows the % stock out chart with the special cause of variation removed from the calculations, but still plotted.

Figure 2: % Stock Outs without Special Cause of Variation

stock outs control chart without special cause of variation


The lower control limit is 1.6%; the upper control limit is 5.7%. This defines the normal range of variation in the process. Some weeks, the stock outs may be as low as 1.6% and other weeks as high as 5.7%. And this range will continue in the future until the process is fundamentally changed. The key word here is fundamentally. The process will meet the goal of 2% sometimes, but it is just chance that it occurs. Most of the time, it will not meet the goal.

Control Chart for Service Level

The control chart for service level is shown in Figure 3.

Figure 3: % Service Level


service level control chart


The % service level control chart has one special cause of variation - the same week as the stock outs chart. Removing the special cause of variation from the calculations gives an LCL = 85.5% and an UCL = 98.9%. The goal is 95%. So, some weeks it will be met; other weeks it will not. To improve this, again the process must be fundamentally changed.

Control Chart for Fill Rate

The control chart for fill rate is shown in Figure 4.

Figure 4: % Fill Rate

fill rate control chart

This chart does not have any special causes of variation. The process is in control. It is consistent and predictable. As long as the process stays the same, the % fill rate will vary from 85.4% to 103.1% and this is just the normal variation in the process. Is it possible to ship a larger quantity than the quantity ordered for a week? Yes, if you are making up past shipments that were not complete.

Problems with These Three Metrics?

Are there any problems with these three metrics? The biggest problem with these types of metrics is that they are end of the line measurements. You are measuring the process at the output. If there is a problem, it is has already occurred. The challenge to people using control charts is how to move upstream in the process to find out what impacts those output metrics.

For example, what impacts stock outs? That could be supplier delivery. It could lack of expediting open orders. The list goes and on. The challenge is begin to track upstream metrics to allow you to prevent the problems before they occur. If you are expediting, track the % of order expedited on-time. Track on-time supplier performance as well as their service level. All these move you upstream in the process. What other ideas do you have for things upstream that impact stock outs?

What about the number of stocking lines? Did you notice anything interesting in the number of stocking lines in Table 1? It has increased over these 26 weeks as Figure 5 below shows. What does increasing the number of stocking lines do for the potential for stock outs? The potential for sales? This is definitely a balancing act for companies!

Figure 5: Stocking Lines

stocking lines chart



This month's newsletter examined how control charts can be used to monitor metrics in purchasing. Three metrics were examined: % stock outs, % service level, and % fill rate. An individuals control chart can be used to monitor these three metrics. The problem is that these represent end of the line measurements. The challenge is to move upstream in the process to find out what variables impact those end-of-the-line metrics and to control those variables.

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Thanks so much for reading our publication. We hope you find it informative and useful. Happy charting and may the data always support your position.


Dr. Bill McNeese
BPI Consulting, LLC

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Comments (2)

  • anon

    Interesting post, thank you.I'm interested to know why you would use an X-mR chart here and not a p chart?Thank you

    Oct 07, 2015
  • anon

    Thanks for the comment.  The p control chart has to satisfy four conditions to be used.  These are given in the publication at this link.  For example, one is that the probability of being a stock out, for example, has to be the same for all products    That is not the case - faster moving items probably have a higher probability of being stocked out - or a very slow moving item also.  So, if the conditions are not met, you can't use the p control chart.

    Oct 08, 2015

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