XBAR AND S CHART

Yet another powerful tool for the variable data is the Xbar and standard deviation chart. This chart is the most underused in practice because of the computational difficulties. Its power and sensitivity for variation are recognized here; I suggest that if modern organizations really are interested in understanding as well as controlling variation, they should displace the Xbar and R chart with this one. The advent of calculators and computers has nullified the computational difficulties. Specifically, this chart should be used in one of the following instances when

• More sensitive control of the process spread is needed.

• A large sample size ( n > 8) is collected.

• A statistical calculator or computer is used to compute and/or plot the control chart.

Steps for constructing and interpreting an Xbar and s chart are similar to those for the Xbar and R chart. The Xbar and s chart differs from the Xbar because the sample standard deviation is used to describe the spread of the manufacturing process. This statistic replaces the range and is calculated with the following formula:

A statistical calculator is helpful in computing this statistic.

Control limits are based on the center line of the s chart (sbars are based on the sample size ( n ).

The constants are listed in Table 8.3. When the sample size ( n ) is fewer than six, there is no lower control limit for the s chart. A sample Xbar and s chart is shown in Figure 8.17.

Table 8.3: Table of Constants and Formulas: Xbar and s Charts

Chart for (Xbar)		Chart for s chart
Subgroup Size	Factors for Control Limits	Divisors Estimate of Standard Deviation	Factors for Control Limits
n	A 3	C 4	B 3	B 4
2	2.659	0.7979	”	3.267
3	1.954	0.8862	”	2.568
4	1.628	0.9213	”	2.266
5	1.427	0.9400	”	2.089
6	1.287	0.9515	0.030	1.970
7	1.182	0.9594	0.118	1.882
8	1.099	0.9650	0.185	1.815
9	1.032	0.9693	0.239	1.761
10	0.975	0.9727	0.284	1.716
11	0.927	0.9754	0.321	1.679
12	0.886	0.9776	0.354	1.646
13	0.850	0.9794	0.382	1.618
14	0.817	0.9810	0.406	1.594
15	0.789	0.9823	0.428	1.572
16	0.763	0.9835	0.448	1.552
17	0.739	0.9845	0.466	1.534
18	0.718	0.9854	0.482	1.518
19	0.698	0.9862	0.497	1.503
20	0.680	0.9869	0.510	1.490
21	0.663	0.9876	0.523	1.477
22	0.647	0.9882	0.534	1.466
23	0.633	0.9887	0.545	1.455
24	0.619	0.9892	0.555	1.445
25	0.606	0.9896	0.565	1.435

Figure 8.17: A sample Xbar and s chart.