Question

3.48. At Samantha's Super Store, the customer service area processes customer returns, answers customer questions and provides inform- ation, addresses customer complaints, and sells gift certificates. The manager believes that if customers must wait longer than 8 minutes to see a customer service representative they get very irritated. The cus- tomer service process has been designed to achieve a customer wait time of between 6 and 12 minutes. The store manager has conducted 10 samples of five observations each of customer waiting time over a two-week period as follows: SAMPLE WAIT TIME (MIN) 8.3 9.6 10.2 7.4 3.1 2.8 5.9 6.7 8.3 9.2 11.3 7.4 16.2 20.1 9.5 10.7 7.5 9.8 11.3 4.5 4.3 12.410.6 6.7 11.3 5.3 9.7 10.811.3 7.4 9.5 14.2 18.2 12.1 3.6 8.9 8.1 10.3 7.2 5.6 9.3 12.413.7 7.3 5.2 6.7 12.3 10 8.0 10.1 8.5 Construct an T-chart in conjunction with an R-chart to monitor cus- tomer service wait time, and comment on the capability of the service area to meet its designated goal.

Answer 1

Xbar and R-charts are constructed as below:

Compute X and R for each sample Plot control charts using Xbar, R and control limits X is computed as average of the observations for each sample R is computed by subtracting the minimum value from the maximum value of each sample CL LCL UCL CLR LCLR UCLR R-chart X-chart Sample 1 #1 | 8.30 | 9.60 | 10.20| 7.40 | 3.10 | 7.72 | 7.1 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #2 | 2.80 | 5.90 | 6.70 | 8.30 | 9.20 | 6.58 | 6.4 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #3 | 11.30 | 7.40 | 16.20 | 20.10 | 9.50 | 12.90| 12.7 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #4 | 10.70| 7.50 | 9.80 | 11.30 | 4.50 | 8.76 | 6.8 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #5 | 4.30 | 12.40 | 10.60 | 16.70 | 11.30 | 11.06 | 12.4 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #6 | 5.30 | 9.70 | 10.80 | 11.30 | 7.40 | 8.90 | 6 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #7 | 18.2012.10 | 3.60 | 9.50 | 14.20| 11.52| 14.6 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #8 | 8.10 | 10.30| 8.90 | 7.20 | 5.60 | 8.02 | 4.7 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #9 | 9.30 | 12.40 | 13.70| 7.30 | 5.20 | 9.58 | 8.5 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE #10 | 6.70 | 8.50 | 8.00 | 10.10 | 12.30 | 9.12 | 5.6 9.42 4.52 14.31 8.48 0.00 17.93 TRUE TRUE Average 9.416 8.480 R-Chart Determine X and R 20 18 16 14 - 8.480 10 Control chart constants corresponding to sample size N Sample size, N D3 -2.114 D4 1 2345 6 789 10 0.577 A2 Control limits for R-chart X-Chart Control limits for X-chart 16.00 14.00 UCLr =D,F=17.93 12.00 LCLx X-AR 4.52 LCLr D R 0.00 10.00 8.00 Comment about process control 6.00 0 X-value lie outside of control limits. 4.00 Therefore based on X-chart, the process is In Control 0 R-value lie outside of control limits. 1 2345 6 789 10 Therefore based on R-chart, the process is In Control

Determine Standard Deviation of the process For subgroup size, n-5, d22.326 Standard Deviation of the process 3.646 d2

Calculate Process capability index (Cpk) and ratio (Cp) as below:

Lower specification Limit, LSL6 Upper specification Limit, USL 12 = 9.416 Process mean, X μ Process Standard Deviation, ơ- 3.646 Process capability index, Cpk Lower, Cpl- (μ-LSL)/3σ 0.312 = Upper, Cpu_ (USL-μ)/3σ 0.236 Process, Cpk-min ( Cpu , Cpl ) 0.236 Process capability ratio, Cp Cp= (USL-LSL)/60 = 0.274

Both Cpk and Cp values are less than 1.33. Therefore, the process is not capable of the service area to meet its designated goal.