Journal of Quality and Reliability Engineering

Research Article

A Nonparametric Shewhart-Type Quality Control Chart for Monitoring Broad Changes in a Process Distribution

Table 1

Charting statistic 𝜓 𝑡 for simulated date: reference X: N(0,1), test samples Y1, and Y2: N(0,1), Y3: N(2,1), and Y4: N(3,4).
 X: 𝑆 0 Y1: #Y1 ≤ X 𝑆 1 ( 𝑥 ) 𝑆 0 ( 𝑥 ) − 𝑆 1 ( 𝑥 ) Y2: #Y2 ≤ X 𝑆 2 ( 𝑥 ) | 𝑆 0 ( 𝑥 ) − 𝑆 2 ( 𝑥 ) | Y3: #Y3 ≤ X 𝑆 3 ( 𝑥 ) | 𝑆 0 ( 𝑥 ) − 𝑆 3 ( 𝑥 ) | Y4: #Y4 ≤ X 𝑆 4 ( 𝑥 ) | 𝑆 0 ( 𝑥 ) − 𝑆 4 ( 𝑥 ) |
N(0,1)N(0,1)N(0,1)N(2,1)N(3,2)
1 −1.551 0.05 −1.657 1 0.1 0.05 −2.04 1 0.1 0.05 −0.952 0 0 0.05 −1.401 0 0 0.05
2 −1.074 0.1 −1.223 2 0.2 0.1 −1.41 2 0.2 0.1 −0.562 0 0 0.1 0.963 1 0.1 0
3 −0.738 0.15 −1.067 4 0.4 0.25 −0.5 2 0.2 0.05 0.49 1 0.1 0.05 1.701 1 0.1 0.05
4 −0.722 0.2 −0.891 4 0.4 0.2 −0.4 2 0.2 0 0.5125 1 0.1 0.1 1.896 1 0.1 0.1
5 −0.683 0.25 −0.427 4 0.4 0.15 −0.23 2 0.2 0.05 0.8878 1 0.1 0.15 2.502 1 0.1 0.15
6 −0.198 0.3 −0.04 5 0.5 0.2 0.088 5 0.5 0.2 1.0848 2 0.2 0.1 2.665 1 0.1 0.2
7 −0.085 0.35 0.224 5 0.5 0.15 0.93 5 0.5 0.15 1.2253 2 0.2 0.15 2.681 1 0.1 0.25
8 −0.069 0.4 0.283 5 0.5 0.1 0.174 5 0.5 0.1 1.4254 2 0.2 0.2 4.544 1 0.1 0.3
9 −0.065 0.45 0.906 5 0.5 0.05 0.686 5 0.5 0.05 1.565 2 0.2 0.25 4.623 1 0.1 0.35
10 −0.05 0.5 1.3 5 0.5 0 1.865 5 0.5 0 2.5184 2 0.2 0.3 5.213 1 0.1 0.4
11 0.101 0.55   6 0.6 0.05  7 0.7 0.15   2 0.2 0.35  1 0.1 0.45
12 0.111 0.6   6 0.6 0  7 0.7 0.1   2 0.2 0.4  1 0.1 0.5
13 0.3953 0.65   8 0.8 0.15  8 0.8 0.15   2 0.2 0.45  1 0.1 0.55
14 0.434 0.7   8 0.8 0.1  8 0.8 0.1   2 0.2 0.5  1 0.1 0.6
15 0.5174 0.75   8 0.8 0.05  8 0.8 0.05   4 0.4 0.35  1 0.1 0.65
16 0.5454 0.8   8 0.8 0  8 0.8 0   4 0.4 0.4  1 0.1 0.7
17 1.0735 0.85   9 0.9 0.05  9 0.9 0.05   5 0.5 0.35  2 0.2 0.65
18 1.3542 0.9    1 0.1  9 0.9 0   7 0.7 0.2  2 0.2 0.7
19 1.9396 0.95    1 0.05  10 1 0.05   9 0.9 0.05  4 0.4 0.55
20 2.1318 1    1 0  10 1 0   9 0.9 0.1  4 0.4 0.6
      𝜓 1 = 𝟎 . 𝟐 𝟓    𝜓 2 = 𝟎 . 𝟐    𝜓 3 = 𝟎 . 𝟓    𝜓 4 = 𝟎 . 𝟕