A proposed approach for approximating lower truncated normal cumulative distribution: application to reliability of used devices

Figures & data

Figure 1. A comparison between lower truncated and none-truncated normal distribution.

Figure 2. Deviation in CDF over the domain [0: 4].

Figure 3. Deviation in CDF over the domain [−4: 0].

Table 1. Reliability Results Using Different Models

	Actual	Current model	Based on Logistic Approximation.	Based on Polya’s Approximation	Based on Hart’s Approximation	Alodat’s Approximation
Reliability, R(x)	0.15887	0.159068	0.155139	0.157009	0.157722	0.0.158958

Figure 4. The model error versus z-score for the four different truncation points.

Table 2. Maximum absolute deviation of different CDF of lower truncated normal distribution

	Maximum Absolute deviation
	ZL = 0	ZL = −1	ZL = −2	ZL = −3
Introduced	0.0000212	0.00002	0.00000947	0.00000972
Based on Logistic Approximation.	0.018841	0.011012	0.017002	0.012934
Based on Polya’s Approximation	0.006276	0.003856	0.003357	0.003167
Based on Hart’s Approximation	0.0106	0.005727	0.00449	0.00432
Based on Aludaat and Alodat’s Approximation	0.003944	0.002338	0.002534	0.001987